WEST-B Test Preparation Study Guide

WEST-B Test Preparation Study Guide
Math Developed by Amy D. Hitchcock, M.A. In cooperation with the Washington State Center of Excellence for Careers in Education, located at Green River College, and the Placement and Testing Center at Highline College Summer 2017

Start Here Click any button to start. Help getting started
NUMBERS & OPERATIONS Understand and apply concepts and principles of numbers and operations. GEOMETRY Understand concepts and principles of geometry and solve related problems. ABOUT MATH Scoring What’s on the test Take a Pre-test MEASUREMENT Understand and apply concepts and procedures of measurement. PROBABILITY & STATISTICS Understand concepts and principles of probability and statistics and solve related problems. ALGEBRA Understand concepts and principles of algebra and solve related problems. Apply MATHEMATICAL REASONING, PROBLEM-SOLVING & COMMUNICATION SKILLS. Help getting started

About WEST-B Math Learn about the math section of the WEST-B and strategies for answering test questions Take a math pretest and make your math study plan

About WEST-B Math WEST-B 60 multiple choice questions.
No penalty for wrong answers. It’s better to guess than skip a question. Your guess could be correct. Passing score is 240 or higher. Scores range from 100 – 300. You need to answer about ⅔ of the questions correctly to pass. No calculators, but scrap paper and a math reference sheet will be provided. Click the button below to learn more about WEST-B Scoring WEST-B Scoring

What’s on the test? WEST-B Test Objectives The WEST-B Math subtest has multiple choice questions aligned with these objectives: Understand and apply concepts and principles of numbers and operations. Adding (+), subtracting (-), multiplying (x), dividing (÷), fractions (½), decimals (0.5), percentages (50%), ratios, proportions, exponents (22), Order of Operations and more Understand concepts and principles of algebra and solve related problems. Sequences, reading and making tables, graphs, and charts, simplify expressions, solve equations and inequalities, and more Understand and apply concepts and procedures of measurement. Units of measurement (12 in= 1 ft), metric system (100cm = 1m), scale (eg. on a map), perimeter, area, and volume Understand concepts and principles of probability and statistics and solve related problems. Probability, collecting, organizing, and displaying data, tables, charts, mean, median, mode, and more Understand concepts and principles of geometry and solve related problems. Shapes, geometry equations (C=𝜋D), symmetry and congruence, xy-coordinates, flips, rotations, and more Apply mathematical reasoning, problem-solving, and communication skills. Write math sentences , fix problems with math sentences, make predictions, draw conclusions, and more

Types of Math Questions
Math questions are multiple choice. You will choose the best answer out of four options. More than one answer may seem correct, but there is only one answer that is the best. Sometimes you have to solve math problems and get one correct answer. For example, = ? 2 6 8 16

Math questions are multiple choice. You will choose the best answer out of four options. More than one answer may seem correct, but there is only one answer that is the best. Sometimes you have to solve math problems and get one correct answer. For example, = ? 2 6 8 16 The answer is B = 6. This seems easy, but you’re doing a lot in this simple problem. First, you have to recognize that the symbol + indicates addition. Then you have to add the numbers correctly. You also have to look at answers that might be correct because each answer shows different relationships between the numbers 2 and 4. Look: A. 2 could be the answer to 4 – 2 = ? OR 4 ÷ 2 = ? C. 8 is the answer to 4 x 2 = ? D. 16 is the answer to 42 = ?

Sometimes the questions will ask you which one is NOT correct. That means that you are looking for the one answer that is wrong or different. For example, Which of the following is NOT true? 2 + 2 = 4 2 x 2 = 4 2 ÷ 2 = 4 22 = 4 The answer is C, because 2 divided by 2 does NOT equal 4.

The WEST-B also includes word problems. For example: Abdi is painting a fence. Each section of the fence requires 1/16 of a gallon of paint. Abdi has 7/8 of a gallon remaining. How many sections of fence can he paint? 7 8 14 16 Think… What information are you given? What information do you need? How would you solve this problem?

The WEST-B also includes word problems. To solve word problems, you have to understand what the question is asking and translate it into math symbols or sentences to figure out the missing information. The answer is (C) 14. Abdi has 7/8 or 14/16 gallons of paint left. Each section requires 1/16. He can paint 14 more sections. For example: Abdi is painting a fence. Each section of the fence requires 1/16 of a gallon of paint. Abdi has 7/8 of a gallon remaining. How many sections of fence can he paint? 7 8 14 16

Tips for Math Tests TIP…
Read problems carefully. Use scrap paper. Figure out exactly what the question is asking for and what you need to know to find the answer. Circle or write down key words in the problem, such as sum, product, etc. Draw pictures of word problems. Write word problems as math sentences. Use estimating to help you eliminate answer choices right away. Work through each step of calculations carefully. Do calculations only when you need to. Some questions can be answered by reading a graph or chart. TIP… If you can eliminate one or two wrong answers right away, you have a better chance of answering correctly, even when you guess. Make a guess and mark questions you aren’t sure about. You can come back to them later.

Pre-test Click the handouts to download them. Handout: Pre-test
WEST-B Sample Test Questions at west.nesinc.com WEST-B Math Reference Sheet Now that you’ve seen the types of questions you’ll see on the test, check what you already know by taking a pre-test. This will help you figure out what you want to study. The test has Reading, Math, and Writing all in one. You can do them all at once or take each section separately. You will be able to download this same pre-test in all of the sections (Math, Reading, and Writing) of this Study Guide. Also download the Math Reference Sheet you’ll have on-screen during the real test. Click the handouts to download them. Handout: Pre-test Handout: Math 01 Reference Sheet

What math do you want to study?
WEST-B Math Sample Questions The table below lists the objectives and skills tested for each question on the math pre-test. Which questions did you get wrong? Which topics do you want to review? Math Pre-test Objectives and Skills Question 1. Objective: Understand and apply concepts and principles of numbers and operations. Skills: Ratios, proportions, arithmetic operations, simplifying expressions, word problems Question 6. Objective: Understand concepts and principles of probability and statistics and solve related problems. Skills: Calculating probability, arithmetic operations, simplifying fractions Q2. Objective: Understand and apply concepts and principles of numbers and operations. Skills: Arithmetic operations, Order of Operations, simplifying expressions Q7. Objective: Understand concepts and principles of algebra and solve related problems. Skills: Variables, substitution, algebraic notation, reading tables Q3. Objective: Understand and apply concepts and procedures of measurement. Map scale, estimating, perimeter Q8. Objective: Understand concepts and principles of algebra and solve related problems. Skills: Solving inequalities/equations, algebraic symbols, arithmetic operations Q4. Objective: Understand concepts and principles of geometry and solve related problems. Skills: Figure analysis, proportions, geometry vocabulary (“similar”) Q9. Objective: Apply mathematical reasoning, problem-solving, and communication skills. Skills: Identify extraneous information, identify relevant information, interpret word problems. Q5. Objective: Understand concepts and principles of geometry and solve related problems. Skills: Reading a graph, identifying the location of a point on a coordinate plane, ordered pairs, x-axis, y-axis Q10. Objective: Apply mathematical reasoning, problem-solving, and communication skills. Skills: Drawing conclusions based on given information, arithmetic operations, vocabulary (“product”), properties of numbers

What math do you want to study?
WEST-B Math Sample Questions The table below lists the objectives and skills tested for each question on the math pre-test. Which questions did you get wrong? Which topics do you want to review? Math Pre-test Objectives and Skills Question 1. Objective: Understand and apply concepts and principles of numbers and operations. Skills: Ratios, proportions, arithmetic operations, simplifying expressions, word problems Question 6. Objective: Understand concepts and principles of probability and statistics and solve related problems. Skills: Calculating probability, arithmetic operations, simplifying fractions Q2. Objective: Understand and apply concepts and principles of numbers and operations. Skills: Arithmetic operations, Order of Operations, simplifying expressions Q7. Objective: Understand concepts and principles of algebra and solve related problems. Skills: Variables, substitution, algebraic notation, reading tables Q3. Objective: Understand and apply concepts and procedures of measurement. Map scale, estimating, perimeter Q8. Objective: Understand concepts and principles of algebra and solve related problems. Skills: Solving inequalities/equations, algebraic symbols, arithmetic operations Q4. Objective: Understand concepts and principles of geometry and solve related problems. Skills: Figure analysis, proportions, geometry vocabulary (“similar”) Q9. Objective: Apply mathematical reasoning, problem-solving, and communication skills. Skills: Identify extraneous information, identify relevant information, interpret word problems. Q5. Objective: Understand concepts and principles of geometry and solve related problems. Skills: Reading a graph, identifying the location of a point on a coordinate plane, ordered pairs, x-axis, y-axis Q10. Objective: Apply mathematical reasoning, problem-solving, and communication skills. Skills: Drawing conclusions based on given information, arithmetic operations, vocabulary (“product”), properties of numbers TIP: Skip ahead in the study guide to the parts you really need to work on. You don’t need to waste time on the stuff you already know. Just make sure you take practice tests and use the computer tutorial to get used to answering all types of questions.

Study Plan Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide and Preparing for the WEST-B: Feeling Confident, Finishing Strong! Now that you’ve taken a pretest and identified what you need to study, fill in the “Studying by Section – Math” portion of your study plan. NOTE… You may have this already. The Make a Plan Section of the Study Guide has activities and information to help you complete the first part of your study plan. Click the worksheet to download it. Handout: Make a Plan 05 Study Plan

Numbers and Operations
WEST-B Objective: Understand and apply concepts and principles of numbers and operations. In this section… Numbers Math symbols Equivalences Fractions, Decimals, and Percentages Math terms Exponents Ratios / Proportions Order of Operations (PEMDAS) Arithmetic

Number Sense Definition from icoachmath.com Number sense is the ability to recognize numbers, identify their values in relation to each other, and understand how to use them in a variety of ways, such as counting, measuring, or estimating. Think: Do you think small children have number sense? Why or why not? How do you think people develop number sense?

Types of Numbers Click on the video for a song about types of numbers.
Video from Mr. Colin Dodds on YouTube Natural Numbers or Counting Numbers 1, 2, 3, 4, 5, … Whole Numbers Natural numbers + 0 0, 1, 2, 3, 4, … Integers Whole numbers + negatives …, - 3, -2, -1, 0, 1, 2, 3, … Rational Numbers Integers + fractions -147, ½, 3.71, 22 Click on the video for a song about types of numbers.

Prime and Composite Numbers
Definitions Multiple: The multiple of an integer is the product of an integer and another integer. For example, 6 is a multiple of 3 because 6 is the product of 3 and 2. In other words, 6 = 3 x is a multiple of 3 and 2. Factor: A factor is a number that divides an integer without a remainder. 3 is a factor of 6 because 6 divided by 3 equals 2, with nothing left over. In other words, 6 ÷3 = 2. 3 and 2 are factors of 6. Prime: A prime number is an integer larger than one with only two factors, one and the number itself. For example, 17 is a prime number. 17 can only be divided by 1 and can’t be divided by any other numbers because there will always be a remainder that must be written as a fraction or decimal. For example. 17 ÷ 2 = is a prime number. Composite: A composite number is a number that has factors in addition to one and the number itself. For example, 16 is a composite number because it can be divided by 1, 2, 4, 8, and 16 with nothing left over. 16 has five factors so it is a composite number. STUDY TIP: Make flashcards for each of the definitions to the left. Write the word on one side of a card and the definition or some examples on the other.

Prime and Composite Numbers Practice
Video from Khan Academy on YouTube PRIME NUMBERS PRACTICE AT KHAN ACADEMY COMPOSITE NUMBERS PRACTICE AT KHAN ACADEMY Click to watch a video about prime and composite numbers, then practice.

Fractions, Decimals, and Percentages
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Fractions are numbers that represent parts of a whole. ⅘ is a fraction. If a whole unit were divided into 5 parts, ⅘ would represent 4 of the 5 parts. For example, if a student has 5 math problems for homework and has finished 4 of the problems, she has completed ⅘ of her homework. The fraction ⅘ is pronounced “four fifths.” 4 is called the numerator and 5 is called the denominator. It can also be written 4 5 ⅘ of the circle is purple. ⅕ of the circle is green. ⅘ of the line is green. ⅕ of the line is purple.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Decimals are numbers that can be written as fractions with a denominator of 10, 100, 1000, and so on. Examples: is read as “4 and 6 tenths” and is written as 4.6 in decimal form. 0.63 is read as “63 one hundredths” and is written in fraction form as 2.005 is read as “2 and 5 one thousandths” and is written in fraction form as

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Percentages can be written as numbers with a percent sign (%), as a decimal, or as a fraction with a denominator of 10, 100, 1000, and so on. A percentage is a fraction or decimal times 100. Examples: 50% can be written in decimal form as 0.5 or as a fraction or ½ 25% can be writing as 0.25 or as the fraction ¼ 100% can be written in decimal form as 1.0 or as the fraction 63% can also be written in decimal form as 0.63 and or as the fraction (0.63 x 100 = 63%; x 100 = 63%)

Converting Fractions, Decimals, and Percentages
Video from Duane Habecker on YouTube On the previous page, we saw an example: 0.63 = = 63% A percentage is a fraction or decimal times 100. Can you think of another way to visualize converting a decimal to a percent?

Converting Fractions, Decimals, and Percentages
Video from Duane Habecker on YouTube On the previous page, we saw an example: 0.63 = = 63% A percentage is a fraction or decimal times = 63% To quickly convert a decimal to a percent, move the decimal point two places to the right.

Practice converting fractions, decimals, and percentages
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Look at the table below. Before you click “Next,” practice saying or writing numbers as decimals, fractions, and words. Decimal Fraction Percent Words 0.8 8 10 80% 0.45 45 100 3.11 3 and 11 one hundredths One and 6 tenths 4 one hundredths

Practice converting fractions, decimals, and percentages
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Look at the table below. Before you click “Next,” practice saying or writing numbers as decimals, fractions, and words. Decimal Fraction Percent Words 0.8 8 10 80% 8 tenths 0.45 45 100 45% 45 one hundredths 3.11 311% 3 and 11 one hundredths 1.6 1 6 10 160% One and 6 tenths 0.04 4 100 4% 4 one hundredths

Working with Fractions, Decimals, and Percentages
ATTENTION: Fractions, decimals, and percentages are really important. Take time to complete the lessons if you need to review these concepts. Rather than reproduce GCF Learn Free’s excellent and comprehensive lessons here, you can read and practice everything you need at GCFLearnFree.org FRACTION LESSONS at GFCLearnFree.org DECIMAL LESSONS at GCFLearnFree.org PERCENTAGES LESSONS at GCFLearnFree.org

Math Symbols ꓿ ≠ < > ≤ ≥ Symbol and Meaning Example
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Symbol and Meaning Example How to Read It ꓿ …is equal to… 2 + 5 = 5 + 2 Two plus five is equal to five plus two. ≠ …is not equal to… 2 - 5 ≠ 5 - 2 Two minus five is not equal to five minus two. < …is less than… 5 - 2 < 5 + 2 Five minus two is less than five plus two. > …is greater than… 5 + 2 > 5 - 2 Five plus two is greater than five minus two. ≤ …is less than or equal to… 5 + x ≤ 0 Five plus x is less than or equal to zero. ≥ …is greater than or equal to… 0 ≥ 5 + x Zero is greater than or equal to five plus x.

Comparing and Ordering Numbers
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Understanding numbers so that you can compare them and put them in order is important for estimating whether a test answer is likely to be correct. For example… 3 x 2 = ? 0.6 6.0 5.0 0.5 Think… Can we eliminate any answers right away? Why or why not?

Comparing and Ordering Numbers
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Understanding numbers so that you can compare them and put them in order is important for estimating whether a test answer is likely to be correct. For example… 3 x 2 = ? 0.6 6.0 5.0 0.5 We can eliminate (A) and (D) right away because they are both less than 1. It’s impossible for a number less than 1 to be the answer to a question about multiplying two whole numbers. Knowing the relationships between numbers can help us narrow down our options on the test. Now we only have two choices left.

Place Value Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definition from Merriam-Webster Learner’s Dictionary Place value is one way of ordering numbers. Every digit in a number is in a particular place. DEFINTION… Place (n.) mathematics: the position of a digit in a number For example… In the number 316, the digit 1 is in the tens place. Move the decimal point two places to the right. a number with three decimal places [=a number with three digits that follow the decimal point; a number like or .678] In the number 2.468, the 4 is in the first decimal place. Think… How do you say 2, out loud?

Place Value PLACE VALUE LESSONS At Khan Academy
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from Khan Academy on YouTube Place value is one way of ordering numbers. Every digit in a number is in a particular place. Watch the video below then click the button for more lessons. PLACE VALUE LESSONS At Khan Academy TIP: Use the menu on the left at Khan Academy to complete videos and practice lessons.

Ordering Numbers with Place Value
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide One way to order numbers is to compare the place value of each digit. For example, Which is greater? 43.8 or 48.3? 48.3 > In other words, 48.3 is greater than Even though both numbers have a four in the tens place, the digits in the ones place (8 and 3) tell us which number is larger. Is greater than or less than 5.79? < In other words, is less than Even though both numbers are between 5 and 6, the digits in the tenths place (1 and 7) tell us which number is greater. Directions: Write the numbers in the first column in order from smallest to largest. NUMBERS ORDERED NUMBERS 6, 80, 22 100, 10, 1000 5.089, 589, 5.89, 50.89 756, 765, 657, 576 -8, 7, -2

Ordering Numbers with Place Value
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide One way to order numbers is to compare the place value of each digit. For example, Which is greater? 43.8 or 48.3? 48.3 > In other words, 48.3 is greater than Even though both numbers have a four in the tens place, the digits in the ones place (8 and 3) tell us which number is larger. Is greater than or less than 5.79? < In other words, is less than Even though both numbers are between 5 and 6, the digits in the tenths place (1 and 7) tell us which number is greater. Directions: Write the numbers in the first column in order from smallest to largest. NUMBERS ORDERED NUMBERS 6, 80, 22 6, 22, 80 100, 10, 1000 10, 100, 1000 5.089, 589, 5.89, 50.89 5.089, 5.89, 50.89, 589 756, 765, 657, 576 576, 657, 756, 765 -8, 7, -2 -8, -2, 7

NUMBER LINE VIDEO PRACTICE
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Number Line from TutorVista.com A number line is a visual way of ordering numbers. It can be very helpful for seeing how numbers relate to each other. NUMBER LINE VIDEO PRACTICE At SchoolYourself.org TIP: This video is interactive. Use your keyboard and mouse to enter your responses to move on to the next part.

Number Line Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Number Line from TutorVista.com A number line extends in both directions. As your eyes move to the right, the value of the numbers increases. As your eyes move to the left, the value of the numbers decreases. Think… Which is greater, 2 or -8? Is 0 greater than or less than 9? Is 0 greater than or less than -9? Is -6 greater than or less than -5? GREATER LESSER

Number Line Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Number Line from TutorVista.com A number line extends in both directions. As your eyes move to the right, the value of the numbers increases. As your eyes move to the left, the value of the numbers decreases. Think… Which is greater, 2 or -8? 2 is greater than -8. It’s to the right on the number line. In math symbols, we can write: 2 > -8 or -8 < 2 Is 0 greater than or less than 9? 0 is less than 9. It’s to the left on the number line. 0 < 9 or 9 > 0 Is 0 greater than or less than -9? 0 is greater than -9. It’s to the right on the number line. 0 > -9 or -9 < 0 Is -6 greater than or less than -5? -6 is less than -5. It’s to the left on the number line. -6 < -5 or -5 > -6 GREATER LESSER

Number Line Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Number Line from TutorVista.com A number line extends in both directions. As your eyes move to the right, the value of the numbers increases. As your eyes move to the left, the value of the numbers decreases. Think… Which is greater, 2 or -8? 2 is greater than -8. It’s to the right on the number line. In math symbols, we can write: 2 > -8 or -8 < 2 Is 0 greater than or less than 9? 0 is less than 9. It’s to the left on the number line. 0 < 9 or 9 > 0 Is 0 greater than or less than -9? 0 is greater than -9. It’s to the right on the number line. 0 > -9 or -9 < 0 Is -6 greater than or less than -5? -6 is less than -5. It’s to the left on the number line. -6 < -5 or -5 > -6 SYMBOLS > Greater than. 2 is greater than > -8 < Less than. -8 is less than < 2 TIP: Picture the symbol as an open mouth. It wants to eat the bigger number. GREATER LESSER

Ordering Numbers Practice
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click a button below for more practice with place value and number lines. WHOLE NUMBERS ON A NUMBER LINE At KhanAcademy.org FRACTIONS ON A NUMBER LINE At KhanAcademy.org DECIMALS ON A NUMBER LINE At KhanAcademy.org WRITING NUMBERS IN THEIR EXPANDED FORMS At KhanAcademy.org ORDERING NEGATIVE NUMBERS At KhanAcademy.org TIP: Use the menu on the left at KhanAcademy.org to see videos and practice with related math concepts.

Arithmetic Review and Vocabulary
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide PRACTICE ADDING AND SUBTRACTING At GCFLearnFree.org DEFINITIONS: ARITHMETIC: Calculating by adding, subtracting, multiplying, or dividing (+ - x ÷) SUM: the result of adding numbers together. 5 is the sum of 2 and 3. DIFFERENCE: the result of subtracting numbers. 5 – 3 = 2. Two is the difference. PRODUCT: the result of multiplying numbers. 6 is the product of 3 and 2. QUOTIENT: the result of dividing numbers. 6 ÷ 3 = 2. Two is the quotient. PRACTICE MULTIPLYING AND DIVIDING At GCFLearnFree.org

Arithmetic Practice Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click the worksheet to download basic arithmetic practice with an answer key. Handout: Math 02 Arithmetic Operations

Working with Fractions, Decimals, and Percentages (Again)
If you haven’t practiced with fractions and decimals yet, now is a good time to pause and look at the lessons at GCFLearnFree.org FRACTION LESSONS at GFCLearnFree.org DECIMAL LESSONS at GCFLearnFree.org PERCENTAGES LESSONS at GCFLearnFree.org

More Practice with Fractions
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click the worksheet to download a fraction handout and practice with an answer key. Handout: Math 03 Fractions

Ratios and Proportions
Definitions from Merriam-Webster Learner’s Dictionary DEFINITION: Ratio (n.) the relationship that exists between the size, number, or amount of two things, also called a proportion A ratio is sometimes called a proportion. The ratio of students to teachers at the college is 12 to 1. OR The proportion of students to teachers at the college is 12 to 1. Ratios or proportions can be written these ways: 12 to 1 12 : 1 12 1

Ratios and Proportions Example
Definitions from Merriam-Webster Learner’s Dictionary For example… College A is a small college. There are students and 300 teachers. College B is a large college. There are 24,000 students and 2000 teachers. At both colleges, the ratio of students to teachers is 12 to 1. That means that for every 12 students there is 1 teacher. College A and College B are proportional because the ratio is the same, even though the numbers of students and teachers at each school is different. Relationships between different things can be proportional or in proportion. students teachers = = = 24,

Definitions from Merriam-Webster Learner’s Dictionary For example… College A is a small college. There are students and 300 teachers. College B is a large college. There are 24,000 students and 2000 teachers. At both colleges, the ratio of students to teachers is 12 to 1. That means that for every 12 students there is 1 teacher. College A and College B are proportional because the ratio is the same, even though the numbers of students and teachers at each school is different. Relationships between different things can be proportional or in proportion. Think… What do you notice about the relationship between the numerator and the denominator of the fractions representing ratios of students to teachers? What do you notice about the relationships between the fractions? students teachers = = = 24,

Definitions from Merriam-Webster Learner’s Dictionary For example… College A is a small college. There are students and 300 teachers. College B is a large college. There are 24,000 students and 2000 teachers. At both colleges, the ratio of students to teachers is 12 to 1. That means that for every 12 students there is 1 teacher. College A and College B are proportional because the ratio is the same, even though the numbers of students and teachers at each school is different. Relationships between different things can be proportional or in proportion. Think… What do you notice about the relationship between the numerator and the denominator of the fractions representing ratios of students to teachers? What do you notice about the relationships between the fractions? students teachers = = = 24, Hint: Try dividing 3600 by 300. Try multiplying 12 times 300 and 3600 times 1.

Definitions from Merriam-Webster Learner’s Dictionary There a couple of ways to check if College A is proportional to College B. College A College B students teachers = = = 24, First, we can divide the numerators by the denominators to reduce both fractions to That is, 3600 ÷ 300 = 12 ✓ and 24,000 ÷ 2000 = 12 ✓

Definitions from Merriam-Webster Learner’s Dictionary There a couple of ways to check if College A is proportional to College B. College A College B students teachers = = = 24, Or we can cross multiply. For example, 12 1 = · 300 = 1 · = 3600 ✓

Definitions from Merriam-Webster Learner’s Dictionary There a couple of ways to check if College A is proportional to College B. College A College B students teachers = = = 24, Or we can cross multiply. AND… = 24, · 2000 = 300 · 24,000 7,200,000 = 7,200,000 ✓

Definitions from Merriam-Webster Learner’s Dictionary There a couple of ways to check if College A is proportional to College B. College A College B students teachers = = = 24, Or we can cross multiply. AND… = 24, · 2000 = 300 · 24,000 7,200,000 = 7,200,000 ✓ Cross multiplying is very useful for solving proportions problems when we don’t know one of the elements, but we do know the proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring?

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? Think… Did you say 20 cookies? What did you do to figure it out? How did you come up with that answer?

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? You may have been able to do this problem in your head because it’s a common problem we calculate all the time. In fact, every time you have to decide how much food is enough for everyone, you are working with proportions. Think… Did you say 20 cookies? What did you do to figure it out? How did you come up with that answer?

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? Let’s work out the problem formally using proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. First, what do we know and what do we want to know? You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? Let’s work out the problem formally using proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. We know the number of cookies per person and the number of people at the party. We don’t know the number of cookies to bring. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? Let’s work out the problem formally using proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. Next, we’ll set up the problem as a proportion with something standing for the total number of cookies. Let’s use the letter c for cookies. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 = 1 2 = 10 𝑐 Let’s work out the problem formally using proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. Why ? Because for every 1 person, we want to bring 2 cookies. The ratio of people to cookies is 1 : 2. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 = 1 2 = 10 𝑐 Let’s work out the problem formally using proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 = 1 2 = 10 𝑐 1 2 = 10 𝑐 1 · c = 2 · 10 Now we cross multiply. Let’s work out the problem formally using proportions.

Definitions from Merriam-Webster Learner’s Dictionary Directions: Read the example and try to answer the question any way you can—in your head, on paper, with a calculator, whatever. You’re going to a party and you want to bring cookies. You want to make sure there are enough cookies for everyone to have 2. There will be 10 people at the party. How many cookies do you need to bring? 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 = 1 2 = 10 𝑐 1 2 = 10 𝑐 1 · c = 2 · 10 c = 20 1 times c is c. Therefore, c = 20. You need to bring 20 cookies to the party. Let’s work out the problem formally using proportions.

Ratios and Proportions Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet Think… Can you visualize this problem? Draw a picture of the problem on scrap paper. What do we know and what do we need to know?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft h ft We know the height of the student, the length of her shadow, and the length of the tree’s shadow. We need to know the height of the tree. Let’s call it h for height.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft h ft Now we can set up the problem as a proportion because there is a proportional relationship between the height of a thing and its shadow.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet Set up the problem, height over length 4 ft 5 ft 65 ft h ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft h ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65 5ℎ= 260 Cross multiply

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft h ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65 5ℎ= 260 Divide each side by 5

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft 52 ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65 5ℎ= 260 5 5 h = 52 Cancel the 5s to get h

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Think… Does our answer, B, make sense? Which answer options could we have eliminated right away? Why? A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft 52 ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65 5ℎ= 260 5 5 h = 52

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. We could have eliminated C and D right away before we did any calculations. We know that the student is shorter than her shadow. The tree must also be shorter than its shadow. 81 feet and 260 feet are both longer than the 65-foot shadow. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft 52 ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65 5ℎ= 260 5 5 h = 52

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. There is no penalty for wrong answers, so if you don’t remember how to work out a problem, try to eliminate answers that don’t make sense based on what we know. With only a couple of answers left, you’d have a chance of guessing correctly. There’s a pretty good chance you’d guess right. A student who is 4 feet tall casts a shadow that is 5 feet long. If a tree casts a shadow that is 65 feet long, how tall is the tree? 16 feet 52 feet 81 feet 260 feet 4 ft 5 ft 65 ft 52 ft ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡𝑟𝑒𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 4 5 = ℎ 65 5ℎ= 260 5 5 h = 52

Ratios and Proportions Practice
at Khan Academy Click a button to practice solving problems with ratios and proportions. PROPORTIONS WORD PROBLEMS at Khan Academy

Equivalences Definition from Merriam-Webster Learner’s Dictionary Understanding the relationships between numbers and operations is really helpful for your own understanding of math concepts and for your work as a teacher. The equivalences we’ll look at in this Study Guide are: Multiplication / Addition Commutative Property Associative Property Identity Property Multiplication / Exponents Definition: Equivalence (n): the quality or state of having the same value, function, meaning, etc.

2 x 4 is the same as 4 groups of two.
Equivalences Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Multiplication can be rewritten as addition. 4 x 2 is the same as 2 groups of four. 4 x 2 = They are equivalent. 2 x 4 is the same as 4 groups of two. 2 x 4 = They are equivalent. 2 4

Equivalences Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Similarly, 4 x 2 is equivalent to 2 x 4. It doesn’t matter which number comes first. The product is 8 either way. 4 x 2 = 2 x 4 2 4

Other Equivalences Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 2 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Think… Why is 2 + 4 + 3 equivalent to 3 + 4 + 2?
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Think… Why is equivalent to ? How does it work? The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide How it works… First, add the first two numbers. 2 + 4 = = 7 Then add the sum of the first two numbers to the last number. 6 + 3 = = 9 Therefore, is equivalent to because both equal 9. The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Think… Why is 2 x 4 x 3 equivalent to 3 x 4 x 2?
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Think… Why is 2 x 4 x 3 equivalent to 3 x 4 x 2? How does it work? The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Think…
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Think… Why is 2 + (4 + 3) equivalent to (2 + 4) + 3? How does it work? Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. How it works… First, add the two numbers in parentheses. (4 + 3) = 7 (2 + 4) = 6 Then add the sum of those numbers to the last number. 7 + 2 = = 9 Therefore, 2 + (4 + 3) is equivalent to (2 + 4) + 3 because both equal 9. Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Think… Why is 2 x (4 x 3) equivalent to
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Think… Why is 2 x (4 x 3) equivalent to (2 x 4) x 3? How does it work? Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890

Other Equivalences Think… Why is 2 + 0 equivalent to 2?
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following are other equivalences you should be familiar with for the ParaPro. You don’t need to know the names of the properties, but you do need to recognize when two math sentences are equivalent. Name What it means Examples Commutative property of addition and multiplication Changing the order of the numbers does not change the sum or product. = 9 = 2 x 4 x 3 = 24 = 3 x 4 x 2 Associative property of addition and multiplication Changing the grouping of the numbers does not change the sum or product. 2 + (4 + 3) = 9 = (2 + 4) + 3 2 x (4 x 3) = 24 = (2 x 4) x 3 Identity property of addition Any number plus 0 is equivalent to that number. 2 + 0 = 1 1,234,567, = 1,234,567,890 Identity property of multiplication Any number times 1 is equivalent to that number. 2 x 1 = 2 1,234,567,890 x 1 = 1,234,567,890 Think… Why is equivalent to 2? Why is 2 x 1 equivalent to 1?

Exponents Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from Khan Academy on YouTube Click to watch a video introduction to exponents. Exponents are a short way of writing repeated multiplication. An exponent stands for how many times a number is multiplied by itself. EXPONENT 24 = 2 x 2 x 2 x 2 BASE 2 multiplied 4 times

It’s trickier when the exponents are bigger.
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide To calculate the value of exponents, you can do the multiplication. For example: 24 = 2 x 2 x 2 x 2 That is, 2 multiplied 4 times. It’s trickier when the exponents are bigger. 2375 Multiplying 375 2s by hand would take a really long time. That’s why we have the short version: the exponent form. 2 x 2 = 4 (that’s two 2s) 4 x 2 = 8 (three 2s) 8 x 2 = 16 (four 2s) Therefore, = 16. The WEST-B will not ask you to calculate the value of large exponents, but practice simplifying exponents using the resources on the next page.

Exponents EXPONENTS PRACTICE At KhanAcademy.org
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from Khan Academy on YouTube Click the video below for more exponent explanation for visual and auditory learners. EXPONENTS PRACTICE At KhanAcademy.org TIP: Use the menu on the left at Khan Academy to review related videos and practice lessons.

Order of Operations Some questions on the WEST-B are related to solving complex math sentences. For example: · 8 + 9 Think… How would you solve this problem? What steps do you do first? What is the solution you came up with? Is it possible to solve this more than one way?

Order of Operations Some questions on the WEST-B are related to solving complex math sentences. For example: · 8 + 9 There are a few of ways to solve this, but only one is correct. The first way we could solve this to go left to right and do the addition, multiplication, and addition calculations. For example: 5 + 3 · = 8 · = = = 73 Solution 1. 73

Order of Operations Some questions on the WEST-B are related to solving complex math sentences. For example: · 8 + 9 There are a few of ways to solve this, but only one is correct. TIP: There are a few ways to represent multiplication in a math sentence. For example a x b a · b (a)(b) a(b) ab The first way we could solve this to go left to right and do the addition, multiplication, and addition calculations. For example: 5 + 3 · = 8 · = = = 73 Solution 1. 73

Order of Operations Some questions on the WEST-B are related to solving complex math sentences. For example: · 8 + 9 There are a few of ways to solve this, but only one is correct. The second way we could solve this to do all the addition first then multiply. For example: 5 + 3 · = 8 · = = 136 Solution 1. 73 Solution

Order of Operations Some questions on the WEST-B are related to solving complex math sentences. For example: · 8 + 9 There are a few of ways to solve this, but only one is correct. The third way we could solve this to do the multiplication first then add. For example: 5 + 3 · = = = 38 Solution 1. 73 Solution Solution 3. 38

Order of Operations Some questions on the WEST-B are related to solving complex math sentences. For example: · 8 + 9 There are a few of ways to solve this, but only one is correct. The third way we could solve this to do the multiplication first then add. For example: 5 + 3 · = = = 38 Solution 1. 73 Solution Solution 3. 38 But that’s three DIFFERENT solutions, which is not great, especially on a multiple choice test.

Order of Operations So which is correct? And how do we do it? We use the ORDER OF OPERATIONS, so that everyone does the calculations the same way and we all get the same result. Order of Operations: Parentheses Exponents Multiplication and Division Addition and Subtraction Also known as PEMDAS.

Order of Operations So which is correct? And how do we do it? We use the ORDER OF OPERATIONS, so that everyone does the calculations the same way and we all get the same result. Order of Operations: Parentheses Exponents Multiplication and Division Addition and Subtraction Also known as PEMDAS. PEMDAS means that when you see a complex math sentence with several types of operations, calculate and simplify the sentence by first doing the stuff inside the (Parentheses), then doing the Exponents, then Multiplying x&÷ Dividing, and finally, Adding +&- Subtracting.

Order of Operations So which is correct? And how do we do it? We use the ORDER OF OPERATIONS, so that everyone does the calculations the same way and we all get the same result. Order of Operations: Parentheses Exponents Multiplication and Division Addition and Subtraction Also known as PEMDAS. PEMDAS means that when you see a complex math sentence with several types of operations, calculate and simplify the sentence by first doing the stuff inside the (Parentheses), then doing the Exponents, then Multiplying x&÷ Dividing, and finally, Adding +&- Subtracting. TIP: On test day, write PEMDAS at the top of your scrap paper to remind you of the Order of Operations as you’re taking the test.

PEMDAS Order of Operations
Returning to our original example, which had three possible solutions before we looked at the order of operations, we can see that only one solution is correct. 5 + 3 · = First, we look left to right for any parentheses. We have no parentheses in this problem, so we can cross that off. We can look for and cross off exponents too. PEMDAS

Returning to our original example, which had three possible solutions before we looked at the order of operations, we can see that only one solution is correct. 5 + 3 · = = Next, we look left to right for multiplication and division. Multiply 3 and 8 for a product of 24. PEMDAS

Returning to our original example, which had three possible solutions before we looked at the order of operations, we can see that only one solution is correct. 5 + 3 · = = = = 38 Finally, we look for Addition and Subtraction. Add or subtract from left to right for one correct answer: 38. PEMDAS

Please excuse my dear Aunt Sally.
Order of Operations Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from Khan Academy on YouTube Click to watch a video explaining the order of operations with more examples There is a common pneumonic device that students sometimes use to help them remember the Order of Operations. It’s a sentence in which the first letter of each word starts with PEMDAS. Please excuse my dear Aunt Sally. TIP: Memorize this sentence or make up a new sentence that you will remember.

More Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide 15 – 32 = First, simplify the exponent. 15 – 9 = Second, subtract. = 6 3 (7 + 3) = First, simplify inside the parentheses. 3 (10) = Second, multiply. = 30 PEMDAS

More Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide 15 – 32 = First, simplify the exponent. 15 – 9 = Second, subtract. = 6 3 (7 + 3) = First, simplify inside the parentheses. 3 (10) = Second, multiply. = 30 PEMDAS NOTE: When a number appears right next to parentheses with no symbol in between, it means MULTIPLY. You can understand it to be 3 x (10).

Order of Operations Practice
Click a button for practice with the Order of Operations. PEMDAS PRACTICE At KhanAcademy.org PEMDAS PRACTICE At GCFLearnFree.org

PEMDAS More Practice 5 (9 – 2) + 3 = 3 + 2 (7 – 4)3 =
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Simplify the following, using the correct order of operations. Also try writing the steps in sentences. For example, “First, simplify inside the parentheses., Next….” 5 (9 – 2) + 3 = 3 + 2 (7 – 4)3 = 70 ÷ x 3 = PEMDAS

More Practice Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Simplify the following, using the correct order of operations. Also try writing the steps in sentences. For example, “First, simplify inside the parentheses., Next….” 5 (9 – 2) + 3 = First, simplify inside the parentheses. 5 (7) + 3 = Second, multiply = Finally, add. = 38 3 + 2 (7 – 4)3 = First, simplify inside the parentheses (3)3 = Second, simplify the exponent (27) = Third, multiply = Finally, add. = 57 70 ÷ x 3 = First, divide and multiply, left to right = Finally, add. = 19 PEMDAS

Order of Operations Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Simplify the expression 44 – 4 · ÷ 4. 84 32 16 8 Think… What is the first step to simplifying this math sentence, or expression? How might you explain this problem in the classroom?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. PEMDAS Simplify the expression 44 – 4 · ÷ 4. 84 32 16 8 The first step is to simplify the exponent because this expression does not have parentheses.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. PEMDAS Simplify the expression 44 – 4 · ÷ 4. 84 32 16 8 44 – 4 · ÷ 4 Simplify the exponent 44 – 4 · ÷ 4 Multiply and divide, left to right 44 – Add and subtract, left to right 16

Measurement WEST-B Objective: Understand and apply concepts and procedures of measurement. In this section… Units of measurement Converting measurements Scale Carrying and Borrowing Units Basics of Perimeter, Area, and Volume Rate

Units of Measurement Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide We use numbers and math all the time in our everyday lives. For example, when you have to be at work at 9am, what time do you need to leave home to arrive on time? In real life, math is rarely just plain numbers. We most often use numbers to figure out distance, money, and so on. Think… What are some ways you use numbers and math in your life? Make a list of three or four examples.

Units of Measurement Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Although it may seem pretty simple for us to decide when we need to leave home to be at work on time, it is actually a complex process. Understanding the mathematical process behind the everyday calculations we do will be helpful for passing WEST-B Math and for teaching in the classroom. In order to be on time, we have to think about the distance from home to work, how we’re going to get there, and how long it will take. We may be thinking about distance in terms of miles and we may be thinking of how long it will take in terms of hours or minutes. Those are units of measurement.

Units of Measurement Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Although it may seem pretty simple for us to decide when we need to leave home to be at work on time, it is actually a complex process. Understanding the mathematical process behind the everyday calculations we do will be helpful for passing WEST-B Math and for teaching in the classroom. In order to be on time, we have to think about the distance from home to work, how we’re going to get there, and how long it will take. We may be thinking about distance in terms of miles and we may be thinking of how long it will take in terms of hours or minutes. Those are units of measurement. Before we get into the complex problems you’ll probably see on the WEST-B, we’re going to review the foundational skills of carrying, borrowing, and converting between different units of measurement. You may have to use those skills as part of solving problems when you take the test. There will be links to further review and practice before we go on to sample problems involving scale, perimeter, area, and volume.

WEST-B Math Reference Sheet
Now is a good time to download the Math Reference Sheet if you haven’t already. The Reference Sheet lists units of measurement and their conversions and it will be available on-screen during the real test. Click the handout to download it. Handout: Math 01 Reference Sheet

Units of Measurement Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The first thing to remember is that you can’t combine different units of measurement, just as you can’t combine different terms when you’re solving equations. You can think about them the same way. Look at the chart below for examples. Variables Units 2x + 3y Not like terms. Can’t add. 2 feet + 3 inches Not the same units. Can’t add. 4w + 7w Like terms. Add to get 11w. 4 yards + 7 yards Same units. Add to get 11 yards. 3x + 3x2 3 ft + 5 ft2 (4x)2 Distribute to get 42x2 = 16x2 (4cm)2 Distribute to get 42cm2 = 16cm2 In order to combine different units of measurement, we have to convert them to the same unit.

Carrying and borrowing units
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide In real life, we express time, length, distance, and so on in mixed units. For example, we may talk about a movie that’s 2 hours, 10 minutes long or a person who is 5 feet, 8 inches tall. When we’re adding and subtracting mixed units, we may have to carry units or borrow units for our answers to make sense. For example: Add 3 ft, 8 in and 6 ft, 9 in.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide In real life, we express time, length, distance, and so on in mixed units. For example, we may talk about a movie that’s 2 hours, 10 minutes long or a person who is 5 feet, 8 inches tall. When we’re adding and subtracting mixed units, we may have to carry units or borrow units for our answers to make sense. For example: Add 3 ft, 8 in and 6 ft, 9 in. 3 ft 8 in + 6 ft 9 in 9ft 17in First, combine like units.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide In real life, we express time, length, distance, and so on in mixed units. For example, we may talk about a movie that’s 2 hours, 10 minutes long or a person who is 5 feet, 8 inches tall. When we’re adding and subtracting mixed units, we may have to carry units or borrow units for our answers to make sense. For example: Add 3 ft, 8 in and 6 ft, 9 in. 3 ft 8 in + 6 ft 9 in 9ft 17in 9ft + (1ft, 5in) = 10ft, 5in But 17 inches is more than a foot. It’s 1 foot and five inches, so we can “carry” the 1 foot and add it to the 9 feet we already calculated.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Now let’s look at borrowing… For example: Subtract 8 ft, 2 in – 6 ft, 9 in

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Now let’s look at borrowing… For example: Subtract 8 ft, 2 in – 6 ft, 9 in 8 ft, 2 in  7 ft, 14 in - 6 ft, 9 in - 6 ft, 9 in First, we want to subtract like units. But we can’t subtract 9 inches from 2 inches, so we need to “borrow” some inches from the 8 feet we also have. Take 12 inches out of the 8ft and add them to the 2 inches, making 7 ft, 14 in.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Now let’s look at borrowing… For example: Subtract 8 ft, 2 in – 6 ft, 9 in 8 ft, 2 in  7 ft, 14in - 6 ft, 9 in - 6 ft, 9 in 1 ft, 5 in Then, subtract.

Units of Length Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Most countries use the metric system. All of the units in the metric system are related to the number 10. Metric Units of Length Millimeters (mm) Centimeters (cm) Meters (m) Kilometers (km) 10 1 100 1000 In other words… 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km

Units of Length Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide In the U.S., we use the “Imperial” or “English” measurement system. You may see metric or English units of measurement on the WEST-B. English Units of Length Inch / Inches (in) Foot / Feet (ft) Yard / Yards (yd) Mile / Miles (mi) 12 1 3 5280 In other words… 12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi

Units of Length Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide In the U.S., we use the “Imperial” or “English” measurement system. You may see metric or English units of measurement on the WEST-B. Think… How many inches are in 3 feet? How do you know? English Units of Length Inch / Inches (in) Foot / Feet (ft) Yard / Yards (yd) Mile / Miles (mi) 12 1 3 5280 In other words, 12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi

Converting Units of Length
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide First, what do we know and what do we need to know? How many inches are in 3 feet? We know that 12 inches = 1 foot. We need to know ?? inches = 3 feet

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide How many inches are in 3 feet? We know that 12 inches = 1 foot. We need to know ?? inches = 3 feet 𝑖𝑛𝑐ℎ𝑒𝑠 𝑓𝑒𝑒𝑡 = = 𝑛 3 Next, set up the problem as a proportion with something in place of the ??. Let’s use n for inches.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide How many inches are in 3 feet? We know that 12 inches = 1 foot. We need to know ?? inches = 3 feet 𝑖𝑛𝑐ℎ𝑒𝑠 𝑓𝑒𝑒𝑡 = = 𝑛 3 1 · n = 12 · 3 n = 36 Now, cross multiply.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide How many inches are in 3 feet? We know that 12 inches = 1 foot. We need to know ?? inches = 3 feet 𝑖𝑛𝑐ℎ𝑒𝑠 𝑓𝑒𝑒𝑡 = = 𝑛 3 1 · n = 12 · 3 n = 36 There are 36 inches in 3 feet. Think… Which is bigger, feet or inches?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide How many inches are in 3 feet? We know that 12 inches = 1 foot. We need to know ?? inches = 3 feet 𝑖𝑛𝑐ℎ𝑒𝑠 𝑓𝑒𝑒𝑡 = = 𝑛 3 1 · n = 12 · 3 n = 36 There are 36 inches in 3 feet. Think… Which is bigger, feet or inches? Feet are bigger. Every 1 foot has 12 inches in it. In this problem we were converting from smaller (in.) to bigger (ft.) and we multiplied inches and feet. 12 in x 3ft = inches in 3ft

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. First, what do we know and what do we need to know? How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑒𝑡𝑒𝑟𝑠 = = 500 𝑚 Next, set up the problem as a proportion with something in place of the ??. Let’s use m for meters.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑒𝑡𝑒𝑟𝑠 = = 500 𝑚 100m = 500 Now, cross multiply.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑒𝑡𝑒𝑟𝑠 = = 500 𝑚 100m = 500 Then, divide both sides by 100.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑒𝑡𝑒𝑟𝑠 = = 500 𝑚 100m = 500 m = 5 Cancel the 100s to get m by itself and reduce the fraction.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑒𝑡𝑒𝑟𝑠 = = 500 𝑚 100m = 500 m = 5 There are 5 meters in 500 cm. Think… Which is bigger, meters or centimeters?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the following question. How many meters in 500 centimeters? We know that cm = 1 m We need to know 500 cm = ?? m 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑒𝑡𝑒𝑟𝑠 = = 500 𝑚 100m = 500 m = 5 There are 5 meters in 500 cm. Think… Which is bigger, meters or centimeters? Meters are bigger. Every 1 meter has 100 cm in it. In this problem we were converting from bigger (m) to smaller (cm) and first we cross multipled, then we divided centimeters by centimeters. 500 cm ÷ 100 cm = 5 m in 500 cm

More units of measurement
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary You will have the Math Reference Sheet available to you on-screen during the WEST-B. Here are some additional units of measurement you may see on the exam. All conversions can be done using proportions. Measurements of Weight Measurements of Volume 1 ton = 2000 pounds (lb) 1 gallon (gal) = 4 quarts (qt) 1 pound (lb) = 16 ounces (oz) 1 quart (qt) = 2 pints (pt) 1 kilogram (kg) = 1000 grams (g) 1 pint (pt) = 2 cups (c) 1 gram = 1000 milligrams (mg) 1 cup (c) = 8 fluid ounces (fl oz) Weight (n): a measurement that indicates how heavy a person or thing is Volume (n): a measurement that indicates the amount of space that is filled by something

More Help There are tons of resources online for practicing using proportions and other methods for conversion. Many teachers help kids with shortcut methods that save time. You might find that one of those methods works better for you. Instead of linking to one particular lesson or practice set, we’ve included links to search results at Google and YouTube. Explore and see what method makes the most sense to you and practice using that one to solve problems. CONVERSION VIDEO LESSONS search results on YouTube CONVERSION PRACTICE search results at Google TIP: Another method or explanation may or may not make more sense to you. The proportions method we practiced here will always work and you’ll be using proportions for many problems on this test and in real life, so stick with that one if you’re getting it!

Perimeter, Area, and Volume Basics
Perimeter, area, and volume are covered in detail in the Geometry section of this study guide. However, it is important to know the basics of these concepts in order to solve measurement problems on the WEST-B. DEFINITIONS: Perimeter (n.) the total length of the lines that form a shape; the distance around a shape. Calculate by adding the lengths of all the sides of the shape. (P = a + b + c) Area (n.) the amount of space inside a shape, surface, region, room, etc. Calculate the area of a rectangle by multiplying the length of one side of the rectangles by the width. (A = lw) More formulas for the area of other shapes are in the Geometry section. Volume (n.) the amount of space inside a 3D shape, such as a box. Calculate by multiplying the length of the box times the width times the height. (V = lwh) More formulas for the volume of other shapes are in the Geometry section.

Scale Video from MathAntics on YouTube Scale is all about the relationship between a real thing and a drawing or diagram of the thing. For example, a map is a scaled drawing of a place. The map is much smaller of course, but it’s (usually) proportional to the real place—or it’s not a very helpful map. For example, a road that is 5 miles long might be 5 inches long on a map. There is a relationship between miles and inches. Every inch on the map represents 1 mile in real life. Watch the whole video for a review of proportions or fast forward it to 6:48 to see just the section on scale.

Scale To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home?

Scale To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home? What do we know? What do we want to know?

Scale We know the number of centimeters per mile on the map and we know the total number of centimeters between home and the store on the map. We want to know how many miles between home and the store. We can set up a proportion with centimeters on the top (or bottom—it doesn’t matter which) and miles on the bottom. We’ll use x to stand in for what we don’t know. To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home? 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑖𝑙𝑒𝑠 = 10 𝑐𝑚 1 𝑚𝑖 = 20 𝑐𝑚 𝑥 𝑚𝑖

Scale To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home? 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑖𝑙𝑒𝑠 = 10 𝑐𝑚 1 𝑚𝑖 = 20 𝑐𝑚 𝑥 𝑚𝑖 10x = 20 Cross multiply.

Divide both sides by 10 and cancel.
Scale To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home? 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑖𝑙𝑒𝑠 = 10 𝑐𝑚 1 𝑚𝑖 = 20 𝑐𝑚 𝑥 𝑚𝑖 10x = Divide both sides by 10 and cancel.

Scale To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home? 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑖𝑙𝑒𝑠 = 10 𝑐𝑚 1 𝑚𝑖 = 20 𝑐𝑚 𝑥 𝑚𝑖 10x = x = 2

20 cm on the map is 2 miles in real life.
Scale To calculate scale, we use proportions, because scale is a proportional relationship between a real life object and a representation of that object, such as a map, drawing, diagram, etc. Maps and diagrams may have something printed on them to let you know the scale of the drawing. For example, 1 in. = 1 mi. For example: A map has a scale of 10cm = 1 mile. The distance between your home and the grocery store on the map is 20cm. How many miles is it to the grocery store from your home? 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑚𝑖𝑙𝑒𝑠 = 10 𝑐𝑚 1 𝑚𝑖 = 20 𝑐𝑚 𝑥 𝑚𝑖 10x = x = 2 It’s 2 miles from your home to the grocery store. 20 cm on the map is 2 miles in real life.

Scale Question Think… What do we know? What do we need to know?
Space Needle from Vecteezy.com The following is a sample of the kind of question you might see on the WEST-B. Try to solve it before you click Next. If the actual height of the Space Needle is 605 feet, then what is the scale of this diagram? 1 cm = 60 ft 1 cm = 60.5 ft 1 cm = 120 ft 1 cm = 121 ft Think… What do we know? What do we need to know?

Scale Question Space Needle from Vecteezy.com The following is a sample of the kind of question you might see on the WEST-B. Try to solve it before you click Next. If the actual height of the Space Needle is 605 feet, then what is the scale of this diagram? 1 cm = 60 ft 1 cm = 60.5 ft 1 cm = 120 ft 1 cm = 121 ft We know the height of the real Space Needle, 605 ft, and the height of the Space Needle in the diagram, 5 cm. We need to know the scale—that is, how many feet does one centimeter represent in the diagram?

Scale Question We can set up a proportion to figure it out. Let’s put feet over centimeters because we want to know the number of feet per centimeter, or ft/cm, and we know that there are 605 ft per 5 cm. Space Needle from Vecteezy.com The following is a sample of the kind of question you might see on the WEST-B. Try to solve it before you click Next. If the actual height of the Space Needle is 605 feet, then what is the scale of this diagram? 𝑓𝑒𝑒𝑡 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑓𝑡 5 𝑐𝑚 = ?? 𝑓𝑡 1 𝑐𝑚 1 cm = 60 ft 1 cm = 60.5 ft 1 cm = 120 ft 1 cm = 121 ft

Scale Question Space Needle from Vecteezy.com The following is a sample of the kind of question you might see on the WEST-B. Try to solve it before you click Next. If the actual height of the Space Needle is 605 feet, then what is the scale of this diagram? 𝑓𝑒𝑒𝑡 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑓𝑡 5 𝑐𝑚 = ?? 𝑓𝑡 1 𝑐𝑚 605 ft ÷ 5 cm = ?? ft/cm 1 cm = 60 ft 1 cm = 60.5 ft 1 cm = 120 ft 1 cm = 121 ft Anything divided by one is itself so we don’t need to bother with cross multiplying. We can just divide 605 ft by 5 cm to solve for ?? ft/cm.

In other words, the scale of this diagram is
Scale Question Space Needle from Vecteezy.com The following is a sample of the kind of question you might see on the WEST-B. Try to solve it before you click Next. If the actual height of the Space Needle is 605 feet, then what is the scale of this diagram? 𝑓𝑒𝑒𝑡 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑒𝑟𝑠 𝑓𝑡 5 𝑐𝑚 = ?? 𝑓𝑡 1 𝑐𝑚 605 ft ÷ 5 cm = ?? ft/cm = 121 ft/cm 1 cm = 60 ft 1 cm = 60.5 ft 1 cm = 120 ft 1 cm = 121 ft In other words, the scale of this diagram is 1 cm = 121 ft because each centimeter on the ruler represents 121 ft of the Space Needle.

Scale and Perimeter Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If a pilot flew a plan from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly? 2000 miles 1700 miles 1400 miles 1100 miles Think… You won’t have a ruler when you take the WEST-B and all the scale of this map shows us is the length of the line that is equivalent to 200 miles. It doesn’t specify a unit of measurement, so it could be in inches, centimeters, or even feet (if it’s a really big map!). Does it matter that we don’t know the unit? Why or why not? What might you suggest to a student without a ruler?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If a pilot flew a plan from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly? 2000 miles 1700 miles 1400 miles 1100 miles STRATEGY… You can measure the scale using the edge of a piece of scrap paper, which you will have available during the test. Transfer the scale to the paper and hold it up against each of the three legs of the pilot’s route to get the measurement of each side of the triangle.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If a pilot flew a plan from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly? 2000 miles 1700 miles 1400 miles 1100 miles Think… Why is this a perimeter problem? Once you have the approximate length of the three sides of the triangle, what will you do with them to solve this problem?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If a pilot flew a plan from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly? 2000 miles 1700 miles 1400 miles 1100 miles Steps: Transfer the scale to the edge of your scrap paper. Measure Santa Fe to Tulsa, Tulsa to Houston, and Houston to Santa Fe. Count how many times you can put the scale along the line. Santa Fe to Tulsa: More than 2 times, but less than 3 Tulsa to Houston: 2 – 3 times Houston to Santa Fe: 3 – 4 times Multiply each estimate by 200 miles, the length of the scale. Santa Fe to Tulsa: 400 – 600 miles Tulsa to Houston: 400 – 600 miles Houston to Santa Fe: 600 – 800 miles Add them all up to get a range of approximate mileage for the route. In other words, find the perimeter of the triangle. 400 – 600 + 600 – 800 1400 – 2000 miles

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If a pilot flew a plan from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly? 2000 miles 1700 miles 1400 miles 1100 miles Steps: Transfer the scale to the edge of your scrap paper. Measure Santa Fe to Tulsa, Tulsa to Houston, and Houston to Santa Fe. Count how many times you can put the scale along the line. Santa Fe to Tulsa: More than 2 times, but less than 3 Tulsa to Houston: 2 – 3 times Houston to Santa Fe: 3 – 4 times Multiply each estimate by 200 miles, the length of the scale. Santa Fe to Tulsa: 400 – 600 miles Tulsa to Houston: 400 – 600 miles Houston to Santa Fe: 600 – 800 miles Add them all up to get a range of approximate mileage for the route. In other words, find the perimeter of the triangle. 400 – 600 + 600 – 800 1400 – 2000 miles We can eliminate D because 1100 miles doesn’t fit in our estimated range. Of the three remaining answers, which is best?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If a pilot flew a plan from Santa Fe to Tulsa to Houston and then back to Santa Fe along the route indicated below, approximately how many miles did the pilot fly? 2000 miles 1700 miles 1400 miles 1100 miles Steps: Transfer the scale to the edge of your scrap paper. Measure Santa Fe to Tulsa, Tulsa to Houston, and Houston to Santa Fe. Count how many times you can put the scale along the line. Santa Fe to Tulsa: More than 2 times, but less than 3 Tulsa to Houston: 2 – 3 times Houston to Santa Fe: 3 – 4 times Multiply each estimate by 200 miles, the length of the scale. Santa Fe to Tulsa: 400 – 600 miles Tulsa to Houston: 400 – 600 miles Houston to Santa Fe: 600 – 800 miles Add them all up to get a range of approximate mileage for the route. In other words, find the perimeter of the triangle. 400 – 600 + 600 – 800 1400 – 2000 miles We know that the total distance is greater than—not equal to—1400 and less than—not equal to—2000 miles. B is best because it fits in the range.

MORE CHALLENGING SCALE PRACTICE
Click a button for more practice with scale. We encourage you to try the challenge scale problems at Khan Academy because the two or three step problems there are similar to what you may see on the WEST-B. SCALE PRACTICE at ixl.com MORE CHALLENGING SCALE PRACTICE at Khan Academy

Rate Rate is similar to scale in that we use proportions to express them. Instead of expressing relative size, though, rate expresses things like speed, efficiency, or relative cost. Some examples of rate are: miles per hour miles per gallon price per pound Think… What other examples of rates can you think of? Think about getting paid at work or eating healthy by paying attention to calories. How would you define “rate”?

Rate RATE PRACTICE MORE CHALLENGING RATE PRACTICE
Examples: If a painter paints 20 houses in 5 months, about how many houses can she paint in a month? 20 ℎ𝑜𝑢𝑠𝑒𝑠 5 𝑚𝑜𝑛𝑡ℎ𝑠 = 𝑥 ℎ𝑜𝑢𝑠𝑒𝑠 1 𝑚𝑜𝑛𝑡ℎ x = 20 ÷ 5 = 4 houses/month She can paint about 4 houses a month. How many houses can she paint in a year? 4 ℎ𝑜𝑢𝑠𝑒𝑠 1 𝑚𝑜𝑛𝑡ℎ = 𝑥 ℎ𝑜𝑢𝑠𝑒𝑠 12 𝑚𝑜𝑛𝑡ℎ𝑠 (1 𝑦𝑒𝑎𝑟) x = 4 · 12 = 48 houses/year She can paint about 48 houses/year. RATE PRACTICE at Khan Academy MORE CHALLENGING RATE PRACTICE at Khan Academy

Algebra WEST-B Objective: Understand concepts and principles of algebra and solve related problems. In this section… Sequences Linear equations and inequalities Word problems

Number Sequences Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definition from Merriam-Webster Learner’s Dictionary The WEST-B might ask you to predict the next number in a sequence of numbers. DEFINITION Sequence (n.) the order in which things happen or should happen a group of things that come one after the other, a series For example, 1, 2, 3, 4, 5, ... A sequence of counting numbers. a, b, c, d, e, … A sequence of letters in alphabetical order. M, A, R, I, A The sequence of letters in the name Maria. 0, 1, 0, 1, 0, …. A sequence of two repeating numbers.

Number Sequence Practice
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, … 10, 8, 6, 4, 2, 0, … 3 2 , 2, 5 2 , 3, 7 2 , 4, … 2, 6, 18, 54, 162, … 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, …. 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , …

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, … 3 2 , 2, 5 2 , 3, 7 2 , 4, … 2, 6, 18, 54, 162, … 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, …. 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , … Think…. Explain why 19 is the next number in the sequence. What do you notice about the relationships between 1 and 4, 4 and 7, 7 and 10, and so on?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, … 3 2 , 2, 5 2 , 3, 7 2 , 4, … 2, 6, 18, 54, 162, … 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, …. 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , … To get the next number in the sequence, add 3 to the previous number. 1 + 3 = 4 4 + 3 = 7 7 + 3 = 10 … = 19

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, … 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, …. 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , …

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, … 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, …. 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , … What is another explanation for the answer of 9/2? Can you see another pattern in this sequence?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, … 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − , , − , , … Think…. Explain why 486 is the next number in the sequence. What do you notice about the relationships between 2 and 6, 6 and 18, 18 and 54, and so on?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , … 3, -6, 12, -24, 48, -96, … 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − , , − , , … To calculate the next number in the sequence, multiply the previous number by 3. 2 x 3 = 6 6 x 3 = 18 18 x 3 = 54 … 162 x 3 = 486

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , 1 8 (Divide each number by 2.) 3, -6, 12, -24, 48, -96, 192 (Multiply each number by -2: 3 x -2 = -6 -6 x -2 = 12 … -96 x -2 = 192) 1 2 , , , , … 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , …

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , 1 8 (Divide each number by 2.) 3, -6, 12, -24, 48, -96, 192 (Multiply each number by -2: 3 x -2 = -6 -6 x -2 = 12 … -96 x -2 = 192) 1 2 , , , , 1 32 ÷2 ÷2 ÷ ÷2 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , … Think…. Explain why 1/32 is the next number in the sequence. What do you notice about the relationships between 1/2 and 1/4, 1/4 and 1/8, and so on?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , 1 8 (Divide each number by 2.) 3, -6, 12, -24, 48, -96, 192 (Multiply each number by -2: 3 x -2 = -6 -6 x -2 = 12 … -96 x -2 = 192) 1 2 , , , , 1 32 ÷2 ÷2 ÷ ÷2 0, 2, 0, 2, 0, 2, … 9. − 1 4 , , − , , … To get the next number in the sequence, divide the previous number by 2. Remember that dividing a fraction by 2 is the same as multiplying by ½, the reciprocal of 2. For example, 1 2 ÷2= 1 2 × 1 2 = 1 4

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , 1 8 (Divide each number by 2.) 3, -6, 12, -24, 48, -96, 192 (Multiply each number by -2: 3 x -2 = -6 -6 x -2 = 12 … -96 x -2 = 192) 1 2 , , , , 1 32 ÷2 ÷2 ÷ ÷2 0, 2, 0, 2, 0, 2, 0 9. − 1 4 , , − , , − 5 36

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , 1 8 (Divide each number by 2.) 3, -6, 12, -24, 48, -96, 192 (Multiply each number by -2: 3 x -2 = -6 -6 x -2 = 12 … -96 x -2 = 192) 1 2 , , , , 1 32 ÷2 ÷2 ÷ ÷2 0, 2, 0, 2, 0, 2, 0 9. − 1 4 , , − , , − 5 36 This one is challenging. The fractions are related in a complex way—not simply addition, subtraction, multiplication or division. Can you explain why the answer is -5/36?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Identify the next term in each of the following sequences. Write your answers on scrap paper and discuss with a study partner if you have one. To get the next number, we have to look at the numerators and denominators separately and think about why some of the fractions are negative and others are positive. Add one to each numerator to get the next one… 1, 2, 3, 4, 5. The denominators are a different story. What if we wrote the denominator differently? For example, − , , − , , … Writing the denominator as the square of a number makes it much easier to see the pattern. The next denominator must be 62, or 36. Finally, we can see that the fractions alternate between positive and negative. The fractions with odd numerators (1 and 3) are negative. The fractions with even numerators (2 and 4) are positive. Since our fraction has a numerator of 5 we can predict that it will be negative, -5/36. 1, 4, 7, 10, 13, 16, 19 10, 8, 6, 4, 2, 0, -2 (Subtract 2 from each number.) 3 2 , 2, 5 2 , 3, 7 2 , 4, 9 2 (Alternate fraction and whole numbers. Add 2 to the numerator of each fraction.) 2, 6, 18, 54, 162, 486 x3 x3 x3 x3 16, 8, 4, 2, 1, 1 2 , 1 4 , 1 8 (Divide each number by 2.) 3, -6, 12, -24, 48, -96, 192 (Multiply each number by -2: 3 x -2 = -6 -6 x -2 = 12 … -96 x -2 = 192) 1 2 , , , , 1 32 ÷2 ÷2 ÷ ÷2 0, 2, 0, 2, 0, 2, 0 9. − 1 4 , , − , , − 5 36

Solving and Simplifying
You may have noticed that we have sometimes used the word simplify rather than solve, multiply, divide, etc. For example: 5 (6 ÷ 2) First, simplify inside the parentheses. 5 (3) Next, multiply 5 and 3... Think… Why might you tell your students to simplify rather than solve or perform some other operation? Is it possible to solve a math sentence such as 3x + 5? What about 3x + 5 = 20? Why or why not?

Linear Equations Definitions from Mathwords.com and LearnersDictionary.com It’s not possible to solve the following math sentence, but it is possible to simplify it to make it easier to understand. 3x + 5 – 2x Simplify. x + 5 On the other hand, it is possible to solve the following math sentence, which is called a linear equation. 3x + 5 = 20 Solve for x. x = 5 DEFINITIONS: Simplify (v): To use the rules of arithmetic and algebra to rewrite an expression—or math sentence—as simply as possible. Equation (n): a statement that two expressions are equivalent (such as = 11 or 2x – 3 = 7)

Linear Equations: Solving for x (or y, or z)
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definition from Merriam-Webster Learner’ s Dictionary DEFINITION Variable (n): A quantity that can have any one of a set of values or a symbol that represents such a quantity In other words, a variable in a linear equation is a symbol (such as x, y, or z) that stands for an unknown number. It doesn’t matter what the symbol is, but it’s usually a letter. A variable can change value, which can change the solution to the problem. For example: x x + 3 1 1 + 3 = 4 2 2 + 3 = 5 3 3 + 3 = 6 4 4 + 3 = 7

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Problems on the WEST-B may ask you to “solve for x.” To solve for x, we have to isolate the variable on one side of the equal sign. That means you’ll end up with a variable on one side and a constant on the other. For example, x = 8 A constant. 8 always equals 8. A variable. x might be any quantity. In this equation, x stands for 8.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide To isolate the variable, we simplify and move things around using arithmetic operations. Whatever you do to one side, you have to do to the other to keep the sides equal. To move something to the other side, perform the opposite operation. Operation Opposite Ways to write the operation Addition Subtraction 2 + 4 2 – 4 Multiplication Division 2 x 4, 2 · 4, (2)(4), 2(4), 2x, 2y 2 ÷ 4, 2/4, ,

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide To isolate the variable, we simplify and move things around using arithmetic operations. Whatever you do to one side, you have to do to the other to keep the sides equal. To move something to the other side, perform the opposite operation. Operation Opposite Ways to write the operation Addition Subtraction 2 + 4 2 – 4 Multiplication Division 2 x 4, 2 · 4, (2)(4), 2(4), 2x, 2y 2 ÷ 4, 2/4, , You may see multiplication and division written few different ways on the WEST-B. All the ways we’ve shown you here are equivalent. They mean the same thing. For example, 2 x 4 = 2 · 4

Isolating the variable
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide ADDITION x + 2 = 7 Do the opposite—subtraction Subtract 2 from each side to keep x + 0 = 5 them equal. x = 5 SUBTRACTION x – 12 = 5 Do the opposite—addition Add 12 to both sides to keep x + 0 = 17 them equal. x = 17 MULTIPLICATION 6x = 138 Do the opposite—division. 6x = 138 Divide both sides by 6 to keep 6 6 them equal. 16x = Cancel the sixes (because 6 ÷ 6 = 1) and divide. x = 23 DIVISION x = 6 Do the opposite—multiplication. 4 4 · x = 6 · 4 Multiply both sides by 4 to keep 4 them equal. 14x = 6 · 4 Cancel the fours (because 4 4 = 1) and 14 multiply. x = 24

Multiple step Equations
Videos from KhanAcademy on YouTube The examples on the previous page ask you to do one step (add, subtract, multiply, or divide) in order to isolate the variable. You will probably see problems on the WEST-B that involve more than one step. Take your time and do one step at a time. Solving 2-step Equations Solving Equations with Variables on Both Sides

Multiple step Equations
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from KhanAcademy on YouTube PRACTICE WITH TWO-STEP EQUATIONS At Khan Academy PRACTICE WITH VARIABLES ON BOTH SIDES At Khan Academy PRACTICE WITH EQUATIONS WITH PARENTHESES At Khan Academy Solving Equations with Parentheses

Multi-step Equation Practice
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 1. 3x + 2 = x/2 + 3 = 7 3. 13 – (3 – x) = 5 4. 3(x - 4) + 2(x + 6) = 5

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 3x + 2 = Subtract 2 from both sides. 3x = 6 3x = 6 Divide both sides by 3 and cancel x = 2 x/2 + 3 = Subtract 3 from both sides. x/2 = 4 2 · x/2 = 4 · 2 Multiply both sides by 2 and cancel x = 8 3. 13 – (3 – x) = – 1(3 – x) = 5 Distribute (multiply) -1 to each (-1 · 3) + (-1x) = 5 term inside the parentheses (-3) + (-1x) = 5 Simplify – 3 – 1x = 5 Keep simplifying 10 – 1x = 5 Subtract 10 from each side to isolate the variable -1x = -5 Divide each side by -1 and cancel x = 5 4. 3(x - 4) + 2(x + 6) = 5 SOLUTION ON NEXT PAGE…

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. Any number times 1 is the same as that number, so (3 – x) is the same as 1(3 - x). 3x + 2 = Subtract 2 from both sides. 3x = 6 3x = 6 Divide both sides by 3 and cancel x = 2 x/2 + 3 = Subtract 3 from both sides. x/2 = 4 2 · x/2 = 4 · 2 Multiply both sides by 2 and cancel x = 8 3. 13 – (3 – x) = – 1(3 – x) = 5 Distribute (multiply) -1 to each (-1 · 3) + (-1x) = 5 term inside the parentheses (-3) + (-1x) = 5 Simplify – 3 – 1x = 5 Keep simplifying 10 – 1x = 5 Subtract 10 from each side to isolate the variable -1x = -5 Divide each side by -1 and cancel x = 5 4. 3(x - 4) + 2(x + 6) = 5 SOLUTION ON NEXT PAGE…

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 3(x - 4) + 2(x + 6) = 5 3(x - 4) + 2(x + 6) = 5 Distribute (multiply) each set of parentheses by the number outside the parentheses to get rid of parentheses (i.e. 3 · x, 3 · -4, 2 · x, 2 · 6). 3x – x + 12 = x + 2x = 5 Rewrite if you want to, to put the variables together and the constants together. 5x = 5 Add and subtract to simplify. 5x = 5 Divide both sides by 5 and cancel x = 1

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 3(x - 4) + 2(x + 6) = 5 3(x - 4) + 2(x + 6) = 5 Distribute (multiply) each set of parentheses by the number outside the parentheses to get rid of parentheses (i.e. 3 · x, 3 · -4, 2 · x, 2 · 6). 3x – x + 12 = x + 2x = 5 Rewrite if you want to, to put the variables together and the constants together. 5x = 5 Add and subtract to simplify. 5x = 5 Divide both sides by 5 and cancel x = 1 Another way to say simplify is combine like terms. “Like terms” are the same type of number. In this example, 3x and 2x are like terms because they both have a variable, x. We can add 3x and 2x to get 5x. -12 and 12 are like terms because they are both constants. We can combine -12 and 12 to get 0.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 3(x - 4) + 2(x + 6) = 5 3x – x + 12 = 5 Distribute (multiply) each set of parentheses by the number outside the 3x + 2x = 5 parentheses to get rid of parentheses (i.e. 3 · x, 3 · -4, 2 · x, 2 · 6). Rewrite. 5x = 5 Add and subtract to simplify. 5x = 5 Divide both sides by 5 and cancel x = 1 Think… How do we know we’re right? How would you help students check their own work?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 3(x - 4) + 2(x + 6) = 5 3x – x + 12 = 5 Distribute (multiply) each set of parentheses by the number outside the 3x + 2x = 5 parentheses to get rid of parentheses (i.e. 3 · x, 3 · -4, 2 · x, 2 · 6). Rewrite. 5x = 5 Add and subtract to simplify. 5x = 5 Divide both sides by 5 and cancel x = 1 We can check that x = 1 by substituting 1 for each x in our original equation then using PEMDAS (the Order of Operations) to solve. 3(x – 4) + 2(x + 6) = 5, x = 1 Substitute 1 for each x: 3(1 – 4) + 2(1 + 6) = 5 Do the operations inside the parentheses: 3(-3) + 2(7) = 5 Multiply: = 5 Add or subtract: = 5 We were right! x = 1 ✔ 5 = 5

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Evaluate (solve) the following problems on scrap paper. Share your responses with a study partner if you can. 3(x - 4) + 2(x + 6) = 5 3x – x + 12 = 5 Distribute (multiply) each set of parentheses by the number outside the 3x + 2x = 5 parentheses to get rid of parentheses (i.e. 3 · x, 3 · -4, 2 · x, 2 · 6). Rewrite. 5x = 5 Add and subtract to simplify. 5x = 5 Divide both sides by 5 and cancel x = 1 We can check that x = 1 by substituting 1 for each x in our original equation then using PEMDAS (the Order of Operations) to solve. 3(x – 4) + 2(x + 6) = 5, x = 1 Substitute 1 for each x: 3(1 – 4) + 2(1 + 6) = 5 Do the operations inside the parentheses: 3(-3) + 2(7) = 5 Multiply: = 5 Add or subtract: = 5 We were right! x = 1 5 = 5 Click here to go back to the page with VIDEOS AND PRACTICE. Or click Next to go on.

More Equation Practice
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click the button to practice evaluating single-step and multi- step equations at Khan Academy. EQUATION PRACTICE At KhanAcademy.org TIP: Click the Start button on the Khan Academy page to practice solving all types of equations or scroll down for a menu of exercises for more targeted practice.

More Practice with Algebra and Sequences
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click the worksheet to download an algebra quiz with an answer key. Handout: Math 04 Algebra

Algebra / Sequences Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which equation describes the relationship between the x and y values in the table below? y = 3x y = x + 2 y = 3x – 1 y = 2x + 1 x y 1 3 2 5 7 4 9 Think… What do you notice about the x and y values as you read the table from top to bottom. Can you pick out a pattern? Is that pattern reflected in the answer choices?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. As you read from top to bottom, you may have seen a pattern of first adding 2, then 3, then 4 to x to get the y value. Unfortunately, that pattern is not reflected in our answer options, so we need another strategy for solving this problem. What would you suggest a student do to figure this out? Which equation describes the relationship between the x and y values in the table below? y = 3x y = x + 2 y = 3x – 1 y = 2x + 1 x y 1 3 2 5 7 4 9

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which equation describes the relationship between the x and y values in the table below? y = 3x y = x + 2 y = 3x – 1 y = 2x + 1 x y 1 3 2 5 7 4 9 You can figure this out by substituting the x values into the equations to see which equation works for all of the x and y values in the table above. For example, substituting 1 for x works in both (A) and (B)—3 · 1 = 3 and = 3—but it doesn’t work in (C)—(3 · 1) – 1 ≠ 3. We can eliminate C as an option, then try substituting 2 for x to see which equations give us 5 and which don’t. Keep going until you’ve found the one equation that works for all the values.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which equation describes the relationship between the x and y values in the table below? y = 3x y = x + 2 y = 3x – 1 y = 2x + 1 x y 1 3 2 5 7 4 9 Through substitution, we can eliminate all the equations but D. For every x value in the table, 2x + 1 = the corresponding y value.

Linear Inequalities The good news about linear inequalities is that they are mostly exactly like solving linear equations. For example, 2(x - 8) > 4 Rather than telling us that the left side is equivalent the right side, it’s telling us that the left side is greater than the right side. That is, x can be any number that will make the left side greater than the right side, 4. DEFINITION: Inequality (n). A math sentence that sets the two sides of the sentence apart with a greater than, less than, greater than or equal to, or less than or equal to sign (>, <, ≥, or ≤) rather than an equal sign.

Linear Inequalities For example, 2(x - 8) > 4
2(x - 8) > 4 2x – 16 > 4 Distribute the Add 16 to both sides 2x > 20 Divide both sides by x > 10 Let’s try it. For example, 2(x - 8) > 4 Rather than telling us that the left side is equivalent the right side, it’s telling us that the left side is greater than the right side. That is, x can be any number that will make the left side greater than the right side, 4.

2(x - 8) > 4 2x – 16 > 4 Distribute the Add 16 to both sides 2x > 20 Divide both sides by x > 10 For example, 2(x - 8) > 4 Rather than telling us that the left side is equivalent the right side, it’s telling us that the left side is greater than the right side. That is, x can be any number that will make the left side greater than the right side, 4. This means that can be any number greater than 10 to make the left side greater than 4.

Now let’s test it out with a number greater than 10.
Linear Inequalities Now let’s test it out with a number greater than 10. x > 10 Let x = 11 2(11 – 8) > 4 2(3) > 4 6 > 4 ✔ For example, 2(x - 8) > 4 Rather than telling us that the left side is equivalent the right side, it’s telling us that the left side is greater than the right side. That is, x can be any number that will make the left side greater than the right side, 4.

And with a number less than 10.
Linear Inequalities x > 10 Let x = 11 2(11 – 8) > 4 2(3) > 4 6 > 4 ✔ Let x = 9 2(9 – 8) > 4 2(1) > 4 2 > 4 For example, 2(x - 8) > 4 Rather than telling us that the left side is equivalent the right side, it’s telling us that the left side is greater than the right side. That is, x can be any number that will make the left side greater than the right side, 4. And with a number less than 10.

x > 10 Let x = 11 2(11 – 8) > 4 2(3) > 4 6 > 4 ✔ Let x = 9 2(9 – 8) > 4 2(1) > 4 2 > 4 For example, 2(x - 8) > 4 Rather than telling us that the left side is equivalent the right side, it’s telling us that the left side is greater than the right side. That is, x can be any number that will make the left side greater than the right side, 4. We were right. x must be greater than 10 to make the math sentence true.

Linear Inequalities Video from mathbff on YouTube We said that solving linear inequalities is mostly exactly like solving linear equations. There’s only one additional rule to learn. Click to watch a video about solving inequalities. When you multiply or divide both sides by a negative number, you have to flip the inequality sign. For example, -2x > 4 x < -2

Linear Inequalities Practice
LINEAR INEQUALITIES LESSONS AND PRACTICE at KhanAcademy.org Click the button for practice problems. TIP: Scroll down on the Khan Academy web page for videos and exercises for targeted practice with inequalities.

Algebra Word Problems On the WEST-B, you may be asked to solve or simplify plain equations and inequalities, but you’ll also definitely see word problems. For many people, word problems are intimidating and cause worry. In this section, you’ll practice some strategies for solving word problems using your math and English language skills. TIPS FOR WORD PROBLEMS: Figure out what the question is asking for. Look for key words that tell you what operations (adding, subtracting, multiplying, dividing) you should use. If you practice on paper, circle or underline important information in the problem. On test day, write key information on your scrap paper. Draw pictures of the problem. Write the problem as a number sentence, then solve it using your math knowledge.

Translating English to Math Sentences
Here are some words you might see in WEST-B problems that will help you translate a word problem into a number sentence you can solve. Addition Subtraction Multiplication Division Equivalences sum difference product quotient is plus minus times divided by same as increased by decreased by multiplied by divided into equal to more than less than twice, double, triple per equals added to of equivalent

Translating English to Math Sentences
Video from Fort Bend Tutoring on YouTube Click to watch examples of translating word problems to math sentences. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible.

STEPS TO TRANSLATING WORD PROBLEMS:
Examples DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible.

Examples Four less than the product of a number and 7.
DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. Step 1: What do we need to know? What should we call it?

DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. Step 1: What do we need to know? What should we call it? We need to know “a number.” Let’s call it n for “number.” Our variable is n.

DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. We need to know “a number.” Let’s call it n for “number.” Our variable is n. Step 2: Let’s look for numbers and key words in the word problem.

Examples - Four less than the product of a number and 7.
DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. Less than means subtraction so we’ll write a minus sign. We need to know “a number.” Let’s call it n for “number.” Our variable is n. -

Examples DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. The number we’re subtracting is 4 because we’re looking for 4 less than some number. We need to know “a number.” Let’s call it n for “number.” Our variable is n. - 4

Examples DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. We need to know “a number.” Let’s call it n for “number.” Our variable is n. · Product means multiplication. Let’s use the dot symbol instead of an x because we have a variable, n, in our equation so it might be confusing.

Examples 7 · n - 4 Four less than the product of a number and 7.
DIRECTIONS: Write the following statement as a math sentence. Four less than the product of a number and 7. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. We need to know “a number.” Let’s call it n for “number.” Our variable is n. 7 · n - 4 We can also write this sentence 7n – 4. We always put the number before the variable. What are we multiplying? A number (our variable, n) and 7.

Examples DIRECTIONS: Write the following statement as a math sentence. Three times a number plus four is the same as the number itself decreased by three. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible.

Examples DIRECTIONS: Write the following statement as a math sentence. Three times a number plus four is the same as the number itself decreased by three. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. Step 1: What don’t we know? Let’s call it n. A number, n.

Examples DIRECTIONS: Write the following statement as a math sentence. Three times a number plus four is the same as the number itself decreased by three. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. A number, n. Step 2: Look for key words and numbers. What are the operations you see in the problem?

Examples DIRECTIONS: Write the following statement as a math sentence. Three times a number plus four is the same as the number itself decreased by three. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. A number, n. Multiplication (times) Addition (plus) Equivalence (is the same as, equals) Subtraction (decreased by, minus) Step 2: Look for key words and numbers. What are the operations you see in the problem?

Examples DIRECTIONS: Write the following statement as a math sentence. Three times a number plus four is the same as the number itself decreased by three. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. A number, n. Multiplication (times) Addition (plus) Equivalence (is the same as, equals) Subtraction (decreased by, minus) Now let’s look at the numbers and write our math sentence.

Examples DIRECTIONS: Write the following statement as a math sentence. Three times a number plus four is the same as the number itself decreased by three. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. A number, n. Multiplication (times) Addition (plus) Equivalence (is the same as, equals) Subtraction (decreased by, minus) 3 · n + 4 = n - 3 3 times n plus 4 equals n minus 3

Examples DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible.

Examples The sum of three consecutive integers is 21.
DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. What do we need to know? How can we write it using just one variable? We need to know 3 consecutive integers. Consecutive means one after the other. In other words, if our first integer is x, the next integer in order would be x + 1. The one after that would be x + 2. For example, if the first integer is 1, the next is (or 2), and the third is (or 3).

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. plus equals Now let’s look at the rest and write our math sentence. Our variables are: x x + 1 x + 2

Examples x + (x + 1) + (x + 2) = 21
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. plus equals Now let’s look at the rest and write our math sentence. Our variables are: x x + 1 x + 2 x + (x + 1) + (x + 2) = 21

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. x + (x + 1) + (x + 2) = 21 TIP: Solve and check your equation to make sure you identified your variables correctly and wrote an accurate math sentence.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. x + (x + 1) + (x + 2) = 21 Ignore the parentheses. Think… Why can we ignore the parentheses in this problem? TIP: Solve and check your equation to make sure you identified your variables correctly and wrote an accurate math sentence.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. x + (x + 1) + (x + 2) = 21 Ignore the parentheses. 3x + 3 = 21 Combine like terms. TIP: Solve and check your equation to make sure you identified your variables correctly and wrote an accurate math sentence.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. x + (x + 1) + (x + 2) = 21 Ignore the parentheses. 3x + 3 = 21 Combine like terms. Subtract 3 from both sides 3x = 18 TIP: Solve and check your equation to make sure you identified your variables correctly and wrote an accurate math sentence.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. x + (x + 1) + (x + 2) = 21 Ignore the parentheses. 3x + 3 = 21 Combine like terms. Subtract 3 from both sides 3x = 18 Divide both sides by 3 3 3 x = 6 TIP: Solve and check your equation to make sure you identified your variables correctly and wrote an accurate math sentence.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The sum of three consecutive integers is 21. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. x + (x + 1) + (x + 2) = 21 Ignore the parentheses. 3x + 3 = 21 Combine like terms. Subtract 3 from both sides 3x = 18 Divide both sides by 3 3 3 x = 6 Now let’s check our work…. 6 + (6 + 1)+ (6 + 2) = 21 = 21 21 = 21 ✔ TIP: Solve and check your equation to make sure you identified your variables correctly and wrote an accurate math sentence. Our three consecutive integers are 6, 7, and 8.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The cost, C, of manufacturing wooden trains is equal to $250 plus $1.75 for each train built. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The cost, C, of manufacturing wooden trains is equal to $250 plus $1.75 for each train built. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. Step 1: What do we need to know? What should we call it?

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The cost, C, of manufacturing wooden trains is equal to $250 plus $1.75 for each train built. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. Step 1: What do we need to know? What should we call it? We need to know the cost, C, but in order to know that, we also need to know how many trains are built. Let’s call our variable t for trains. C = cost of making trains t = number of trains

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The cost, C, of manufacturing wooden trains is equal to $250 plus $1.75 for each train built. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. C = cost of making trains t = number of trains Step 2: Look at the numbers and key words.

Examples Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide DIRECTIONS: Write the following statement as a math sentence. The cost, C, of manufacturing wooden trains is equal to $250 plus $1.75 for each train built. STEPS TO TRANSLATING WORD PROBLEMS: Define the variable or variables. That is, figure out what you don’t know that you need to know. Translate the words into numbers and symbols, using just one variable if possible. C = cost of making trains t = number of trains C = t 1.75 times t gives us the cost for all the trains, plus the starting cost of $250. For example, if the company wanted to make 100 trains, it would cost $250 + $1.75(100), or $250 + $175, for a total of $425.

Practice Click a button to practice with word problems.
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click a button to practice with word problems. ONE-STEP EQUATION WORD PROBLEMS PRACTICE at Khan Academy LINEAR INEQUALITIES WORD PROBLEMS PRACTICE at Khan Academy TWO-STEP EQUATION WORD PROBLEMS PRACTICE at Khan Academy LINEAR EQUATION WORD PROBLEMS PRACTICE at Khan Academy

More Practice Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click the worksheet to download multiple choice word problems (with solutions) like the ones you’ll see on the ParaPro. Handout: Math 05 Algebra Word Problems

Geometry WEST-B Objective: Understand concepts and principles of geometry and solve related problems. In this section… Geometric shapes Volume Congruence and Similarity Perimeter and Circumference Surface Area Coordinate planes Area Properties of Shapes and Angles

Geometric Shapes DEFINITIONS: Think…
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary DEFINITIONS: Geometry (n). a branch of mathematics that deals with points, lines, angles, surfaces, and solids Shape (n). the form or outline of an object Think… How many geometric shapes can you name? What makes those shapes special? For example, what makes a rectangle a rectangle? What makes a square a square?

Geometric Shapes Definitions from Merriam-Webster Learner’s Dictionary WEST-B Math Reference Sheet On the next pages, you’ll see pictures and definitions of the shapes you’ll need to know for the WEST-B. Those are: Triangles: Equilateral, Isosceles, Right Rectangles and Squares Circles 3D shapes: Rectangular Solid and Cube Click the handout to download the WEST-B Math Reference sheet if you haven’t done so already. It will be available on-screen during the test and has diagrams and key formulas for the shapes you need to know. Take notes on it as you go through this section. Handout: Math 01 Reference Sheet

Triangles Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary Image credits: Triangle: WolframAlpha, Equilateral Triangle: OpenClipArt, Isosceles Triangle: Wikipedia, Right Triangle: Wikimedia Commons Triangle (n). a shape with three sides and three angles. The measure of the three angles add up to 180°. Isosceles triangle (n). a triangle in which two sides have the same length and angles opposite those sides have the same measure Equilateral triangle (n). a triangle in which all three sides are the same length and all three angles have the same measure Right triangle (n). a triangle that has a right angle, which measures 90°. The hypotenuse of right triangle is the side across from the right angle.

Rectangles Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary Image credits: Rectangle Wikipedia, Square Wikimedia Commons Rectangle (n). a four-sided shape that is made up of two pairs of parallel lines and that has four right angles Square (n). a four-sided shape that is made up of four straight sides that are the same length and that has four right angles

Rectangles Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary Image credits: Rectangle Wikipedia, Square Wikimedia Commons Rectangle (n). a four-sided shape that is made up of two pairs of parallel lines and that has four right angles Square (n). a four-sided shape that is made up of four straight sides that are the same length and that has four right angles These matching marks across two sides of the rectangle mean that the sides are congruent—that is, equal in length. A square in a corner of a shape shows that the angle of the corner is a right angle, which measures 90°. All four angles of a rectangle and a square are congruent—that is, equal in measure.

Circle Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary Image credit FlyLib DEFINITIONS Circle (n). a perfectly round shape; a line that is curved so that its ends meet and every point on the line is the same distance from the center Center (n). a point in the middle of the circle Radius (n). a straight line from the center of a circle to any point on the outer edge Diameter (n). a straight line from one point on a circle to another point that passes through the center point Circumference (n). the length of a line that makes the complete circle Arc (n). a portion of the circle between two points on the circle. arc

3D Shapes Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary Image credits: Solid CNX.org, Cube Wikimedia Commons Solid (n). an object that has length, width, and height; a three-dimensional object Cube (n). A rectangular solid that has six square sides—all sides are the same size and all edges are the same length

Perimeter and Circumference
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The perimeter of a shape is the distance around a two-dimensional figure. You can always add the lengths of all the sides together to calculate the perimeter of a polygon, but some shapes also have certain formulas you can use. Those formulas are listed in the table below. Shape Perimeter Formula Triangle P = a + b + c Rectangle P = 2l + 2w Square P = 4s Circle P = C = 2πr = πD For the formulas above, l = length, w = width, s = side, C = circumference, r = radius, D = diameter

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The perimeter of a shape is the distance around a two-dimensional figure. You can always add the lengths of all the sides together to calculate the perimeter of a polygon, but some shapes also have certain formulas you can use. Those formulas are listed in the table below. Think… Why is the formula for the perimeter of a rectangle 2 times its length plus 2 times its width? Why is the formula for a perimeter of a square 4 times the length of one of its sides? What is special about those shapes? Shape Perimeter Formula Triangle P = a + b + c Rectangle P = 2l + 2w Square P = 4s Circle P = C = 2πr = πD For the formulas above, l = length, w = width, s = side, C = circumference, r = radius, D = diameter

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The perimeter of a shape is the distance around a two-dimensional figure. You can always add the lengths of all the sides together to calculate the perimeter of a polygon, but some shapes also have certain formulas you can use. Those formulas are listed in the table below. NOTE: The perimeter of a circle is special. It’s called the circumference and it’s equal to 2 times pi times the radius of the circle. π (pi) is a number roughly equal to (Actually, it’s much longer than that because the decimal never ends and never repeats). Shape Perimeter Formula Triangle P = a + b + c Rectangle P = 2l + 2w Square P = 4s Circle P = C = 2πr = πD For the formulas above, l = length, w = width, s = side, C = circumference, r = radius, D = diameter

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The perimeter of a shape is the distance around a two-dimensional figure. You can always add the lengths of all the sides together to calculate the perimeter of a polygon, but some shapes also have certain formulas you can use. Those formulas are listed in the table below. NOTE: The perimeter of a circle is special. It’s called the circumference and it’s equal to 2 times pi times the radius of the circle. π (pi) is a number roughly equal to (Actually, it’s much longer than that because the decimal never ends and never repeats). Shape Perimeter Formula Triangle P = a + b + c Rectangle P = 2l + 2w Square P = 4s Circle P = C = 2πr = πD Think… Why can the formula for the circumference of a circle be either 2 times π times the radius OR π times the diameter? What is the relationship between radius and diameter? For the formulas above, l = length, w = width, s = side, C = circumference, r = radius, D = diameter

Perimeter and Circumference Examples
Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet. What is the circumference of a circle with a diameter of 10½ inches? Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet. What is the circumference of a circle with a diameter of 10½ inches? Think… What advice would you give a student who struggles with geometric shape word problems? Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet. What is the circumference of a circle with a diameter of 10½ inches? 4 ft It can be helpful to draw the shape before starting any calculations. 7 ft Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula What is the circumference of a circle with a diameter of 10½ inches? 4 ft 7 ft Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w What is the circumference of a circle with a diameter of 10½ inches? 4 ft 7 ft Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w P = Use PEMDAS to solve P = 22 ft What is the circumference of a circle with a diameter of 10½ inches? 4 ft 7 ft Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w P = Use PEMDAS to solve P = 22 ft What is the circumference of a circle with a diameter of 10½ inches? Check your work… Rectangles have two sets of two equal sides, so we can fill in the rest of the drawing using what we know. Then we can add all the sides: 7 ft + 4 ft + 7 ft + 4 ft = 22 ft The distance around the rectangle is 22 feet. 7 ft 4 ft 4 ft 7 ft Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w P = Use PEMDAS to solve P = 22 ft What is the circumference of a circle with a diameter of 10½ inches? 7 ft 4 ft 4 ft 7 ft Remember: l = length w = width s = side r = radius

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w P = Use PEMDAS to solve P = 22 ft What is the circumference of a circle with a diameter of 10½ inches? C = 2πr Write the formula C = 2π(5¼) Substitute for r C = 10½π Simplify 7 ft 4 ft 4 ft 7 ft Remember: l = length w = width s = side r = radius D = 10½ in

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w P = Use PEMDAS to solve P = 22 ft What is the circumference of a circle with a diameter of 10½ inches? C = 2πr Write the formula C = 2π(5¼) Substitute for r C = 10½π Simplify 7 ft 4 ft Think… Is there a simpler way to do this problem? What is it? What did we do that made it more complicated? 4 ft 7 ft Remember: l = length w = width s = side r = radius D = 10½ in

Here are some examples of how to calculate the perimeter and circumference of certain shapes. Try these problems on your own before you click Next. P = a + b + c P = 2l + 2w P = 4s C = 2πr A simpler way to do this problem is to use the formula C = πD since we are given the diameter. To solve C = 2πr, we had to divide the diameter by two to get the radius, then multiply it by two to simplify the equation. That’s not simple at all. We could have done this and ended up with the same answer… C = πD Write the formula C = 10½π Substitute for D Find the perimeter of a rectangle that has a width of 4 feet and a length of 7 feet P = 2l + 2w Write the formula P = 2(4) + 2(7) Substitute for l and w P = Use PEMDAS to solve P = 22 ft What is the circumference of a circle with a diameter of 10½ inches? C = 2πr Write the formula C = 2π(5¼) Substitute for r C = 10½π Simplify 7 ft 4 ft 4 ft 7 ft Remember: l = length w = width s = side r = radius D = 10½ in

Perimeter and Circumference Practice
Click a button below to do practice problems. PERIMETER PRACTICE at KhanAcademy.org (Scroll down for practice sets) PERIMETER WORD PROBLEMS at KhanAcademy.org CIRCUMFERENCE PRACTICE at KhanAcademy.org

Area Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from MathAntics on YouTube Area is the size of the surface of a shape. It is measured in “square units” or “units squared.” For example, The area of this rectangle is 8 cm2. We can cover the area inside the rectangle with 8 squares that are a centimeter wide and centimeter long. Click to watch a video explanation of area. 1 2 cm 4 cm

Formulas for area Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The table below shows the formulas for calculating the area of various shapes. Shape Area Formula Triangle A = ½bh Rectangle A = lw Square A = s2 Circle A= πr2 For the formulas above, b = base, h = height, l = length, w = width, s = side, r = radius

Area example For a rectangle, area equals length times width. Example…
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide For a rectangle, area equals length times width. Example… l = 2 cm, w = 4 cm A = lw Write the formula A = (2 cm)(4 cm) Substitute for l and w Multiply A = 8 cm2 1 2 cm 4 cm

Area Practice A = ½bh A = lw A = s2 A = πr2 Remember: b = base
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the area of the shapes below before you click Next. Then check your work. 1. 10 ft 7.3 ft A = ½bh A = lw A = s2 A = πr2 2. 5¼ in Remember: b = base w = width h = height s = side l = length r = radius

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the area of the shapes below before you click Next. Then check your work. 1. 10 ft 7.3 ft A = ½bh Write the formula A = ½(10 ft)(7.3 ft) Substitute for b and h A = (5)(7.3) ft2 Multiply A = 36.5 ft2 A = ½bh A = lw A = s2 A = πr2 2. 5¼ in Remember: b = base w = width h = height s = side l = length r = radius

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the area of the shapes below before you click Next. Then check your work. 1. 10 ft 7.3 ft A = ½bh Write the formula A = ½(10 ft)(7.3 ft) Substitute for b and h A = (5)(7.3) ft2 Multiply A = 36.5 ft2 A = ½bh A = lw A = s2 A = πr2 A = πr2 Write the formula A = π(5¼ in)2 Substitute for r A = π (5¼)2(in2) Simplify the exponents. A = π (21/4)2(in2) A = π (212/42)in2 Keep simplifying. A = π (441/16)in2 Simplify the fraction. A = π in2 2. 5¼ in Remember: b = base w = width h = height s = side l = length r = radius

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the area of the shapes below before you click Next. Then check your work. 1. To simplify the fraction, divide the numerator by the denominator: 32 121 112 9 10 ft 7.3 ft A = ½bh Write the formula A = ½(10 ft)(7.3 ft) Substitute for b and h A = (5)(7.3) ft2 Multiply A = 36.5 ft2 A = ½bh A = lw A = s2 A = πr2 441 can be divided by times with 9 left over, or A = πr2 Write the formula A = π(5¼ in)2 Substitute for r A = π (5¼)2(in2) Simplify the exponents. A = π (21/4)2(in2) A = π (212/42)in2 Keep simplifying. A = π (441/16)in2 Simplify the fraction. A = π in2 2. 5¼ in Remember: b = base w = width h = height s = side l = length r = radius

Area Practice AREA OF SQUARES & RECTANGLES PRACTICE
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click a button below to do practice problems. AREA OF SQUARES & RECTANGLES PRACTICE at Khan Academy AREA OF TRIANGLES PRACTICE at Khan Academy AREA OF CIRCLES PRACTICE at Khan Academy

Volume Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from MathAntics on YouTube Volume is the amount of space inside a three dimensional (3D) shape. It is measured in “cubic units” or “units cubed.” For example, The volume of this rectangular solid is 8 cm3. We can fill the inside of the box with 8 cubes that are a centimeter wide, a centimeter long, and a centimeter tall. Click to watch a video explanation of volume. 1 2 cm 4 cm 1 cm

Formulas for volume Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The table below shows the formulas for calculating the area of various shapes. Shape Area of Base Shape Volume Formula Rectangular solid A = lw V = lwh Cube A = s2 V = s3 Cylinder A = πr2 V = πr2h For the formulas above, h = height, l = length, w = width, s = side, r = radius

Formulas for volume Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The table below shows the formulas for calculating the area of various shapes. Think… What do you notice about the formulas for the volume of rectangular solids, cubes, and cylinders? Shape Area of Base Shape Volume Formula Rectangular solid A = lw V = lwh Cube A = s2 V = s3 Cylinder A = πr2 V = πr2h For the formulas above, h = height, l = length, w = width, s = side, r = radius

Formulas for volume Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The table below shows the formulas for calculating the area of various shapes. The formulas for the volume of a rectangular solid, a cube, and a cylinder are all the AREA of the base shape (rectangle, square, or circle) times the height of the 3D shape. Shape Area of Base Shape Volume Formula Rectangular solid A = lw V = lwh Cube A = s2 V = s3 Cylinder A = πr2 V = πr2h For the formulas above, h = height, l = length, w = width, s = side, r = radius

Volume Practice V = lwh V = s3 V = πr2h Remember: h = height s = side
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the volume of the shapes below before you click Next. Then check your work. 1. V = lwh V = s3 V = πr2h 2. Remember: h = height s = side l = length r = radius w = width

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the volume of the shapes below before you click Next. Then check your work. 1. V = lwh V = s3 V = πr2h V = πr2h Write the formula V = π(5cm)2(10cm) Substitute for r and h V = π(25cm2)(10cm) Simplify V = 250π cm3 Multiply 2. Remember: h = height s = side l = length r = radius w = width

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the volume of the shapes below before you click Next. Then check your work. 1. V = lwh V = s3 V = πr2h V = πr2h Write the formula V = π(5cm)2(10cm) Substitute for r and h V = π(25cm2)(10cm) Simplify V = 250π cm3 Multiply 2. V = lwh Write the formula V = (3in)(5in)(8in) Substitute for l, w, and h V = 15in2(8in) Multiply left to right V = 120 in3 Remember: h = height s = side l = length r = radius w = width

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Find the volume of the shapes below before you click Next. Then check your work. 1. V = lwh V = s3 V = πr2h V = πr2h Write the formula V = π(5cm)2(10cm) Substitute for r and h V = π(25cm2)(10cm) Simplify V = 250π cm3 Multiply TIP: The WEST-B is multiple choice. Eliminate any obviously incorrect answers first, such as those with the wrong unit of measurement (for example, cm2 instead of cm3). Then look for answers that are as close to yours as possible. If you don’t see an answer with π in it, try multiplying your answer by 3.14. 2. V = lwh Write the formula V = (3in)(5in)(8in) Substitute for l, w, and h V = 15in2(8in) Multiply left to right V = 120 in3 Remember: h = height s = side l = length r = radius w = width

Volume Practice VOLUME OF RECTANGULAR SOLIDS PRACTICE
Click a button below to do practice problems. TIP: Use the menu on the left at KhanAcademy.org for videos and practice with related math concepts. VOLUME OF RECTANGULAR SOLIDS PRACTICE at Khan Academy VOLUME & SURFACE AREA WORD PROBLEMS at Khan Academy

Surface Area Video from jstarks21 on YouTube Surface Area image from CK12.org, License CC BY-NC 3.0 Surface area is the amount of space on the surface of a 3D shape. It’s measured in square units, just like area, because the surface is a 2-dimensional plane around the outside of a 3D object. Click to watch a short video explanation of surface area. 5 in 8 in 3 in We can flatten out the box, calculate the area of each face, then add the 6 resulting areas together to get a total surface area of 158 in2.

Formulas for surface area
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The table below shows the formulas for calculating the surface area of rectangular solids and cubes. Think… What do you notice about the formulas for the surface area of rectangular solids and cubes? Shape Area of Base Shape Surface Area Rectangular solid A = lw SA = 2lw + 2lh +2wh Cube A = s2 SA = 6s2 For the formulas above, h = height, l = length, w = width, s = side

Formulas for surface area
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The table below shows the formulas for calculating the surface area of rectangular solids and cubes. Because rectangular prisms have 2 faces that are the same on the top and bottom, right and left sides, and front and back, we can double the area of each face and add them together to get the surface area. Similarly, we can multiply the area of one face by 6 to get the surface area of a cube. Shape Area of Base Shape Surface Area Rectangular solid A = lw SA = 2lw + 2lh +2wh Cube A = s2 SA = 6s2 For the formulas above, h = height, l = length, w = width, s = side

SURFACE AREA WORD PROBLEMS
Surface Area Practice Click a button below to do practice problems. TIP: Use the menu on the left at KhanAcademy.org for videos and practice with related math concepts. SURFACE AREA PRACTICE at Khan Academy SURFACE AREA WORD PROBLEMS at Khan Academy

Properties of Angles and Shapes
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Certain shapes and angles have properties that will be helpful to know. A line is a series of points that extends indefinitely in both directions. It can be written in problems like this: 𝐴𝐵 . A ray is a line that has one end point and extends indefinitely in one direction. It can be written like this: 𝐴𝐵 A line segment has two endpoints, and is usually written like this: 𝐴𝐵 A B line A B ray A B line segment Parallel lines are always the same distance apart and never cross or meet. Perpendicular lines form a 90° angle, a right angle. parallel lines perpendicular lines

Properties of Angles and Shapes
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Image credits: Straight Line Math is Fun; Right Angle Snapwiz.com Certain shapes and angles have properties that will be helpful to know. Lines, rays, and line segments have an angle of 180°. If a line is divided by one or more additional lines, the resulting angles add up to 180°. For example, in the picture, one angle is 30° and the other is 150°, which add up to 180°. Angles that form a straight line are called supplementary angles. Right angles are angles that measure 90°. If a right angle is divided by one or more lines, the resulting angles add up to 90°. For example, in the picture, one angle is 35° and the other is 55°, which add up to 90°. Angles that form a right angle are called complementary angles. 55° 35° Triangles have three angles that add up to 180°. Rectangles have 4 right angles that add up to 360°. Circles measure 360°. The measure of the angle of the diameter of a circle is 180° (because it’s a straight line).

COMPLEMENTARY AND SUPPLEMENTARY ANGLES PRACTICE
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Click a button below to do practice problems. TIP: Use the menu on the left at KhanAcademy.org for videos and practice with related math concepts. COMPLEMENTARY AND SUPPLEMENTARY ANGLES PRACTICE at Khan Academy MORE ANGLES PRACTICE at Khan Academy

Properties of Shapes Word Problem
Directions: Answer the following problem. Share your response with a study partner if you have one. The measure of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measure of each angle. Think… What do you know about the angles in triangles? What would you suggest as a first step for a student trying to solve this problem?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measure of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measure of each angle. The angles of a triangle add up to 180°. It can be helpful to draw a picture of the word problem.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measure of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measure of each angle. Draw a picture. Let’s call our angles ∠ A, ∠ B, and ∠ C instead of 1, 2, and 3 so we don’t get confused. The symbol ∠ means angle. The angles of a triangle add up to 180°. It can be helpful to draw a picture of the word problem. A C B

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measure of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measure of each angle. Draw a picture. Let’s call our angles ∠ A, ∠ B, and ∠ C instead of 1, 2, and 3 so we don’t get confused. The symbol ∠ means angle. Give the angles values based on the info we’re given in the word problem. The angles of a triangle add up to 180°. It can be helpful to draw a picture of the word problem. A C B

Angles Word Problem Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measure of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measure of each angle. Draw a picture. Let’s call our angles ∠ A, ∠ B, and ∠ C instead of 1, 2, and 3 so we don’t get confused. The symbol ∠ means angle. Give the angles values based on the info we’re given in the word problem. The angles of a triangle add up to 180°. It can be helpful to draw a picture of the word problem. A C B ∠ A = A, the first angle ∠ B = (A - 5°)

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measure of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measure of each angle. Draw a picture. Let’s call our angles ∠ A, ∠ B, and ∠ C instead of 1, 2, and 3 so we don’t get confused. The symbol ∠ means angle. Give the angles values based on the info we’re given in the word problem. The angles of a triangle add up to 180°. It can be helpful to draw a picture of the word problem. A C B ∠ A = A, the first angle ∠ B = (A - 5°) ∠ C = 3B = 3(A - 5°)

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measurement of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measurement of each angle. Now let’s set up the problem and solve for A. All the angles in the triangle add up to 180°. ∠ A + ∠ B + ∠ C = 180° A + (A - 5°) + 3(A - 5°) = 180° Substitute for ∠ A, ∠ B, & ∠ C. A + A - 5° + 3A - 15° = 180° Use PEMDAS to simplify. Distribute the parentheses. 5A - 20° = 180° Add and subtract. +20° +20° Add 20 to both sides to isolate the variable. 5A = 200° Divide both sides by 5 to solve for A. A = 40° A C B ∠ A = A, the first angle ∠ B = (A - 5°) ∠ C = 3B = 3(A - 5°)

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measurement of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measurement of each angle. Now let’s set up the problem and solve for A. All the angles in the triangle add up to 180°. ∠ A + ∠ B + ∠ C = 180° A + (A - 5°) + 3(A - 5°) = 180° Substitute for A, B, & C. A + A - 5° + 3A - 15° = 180° Use PEMDAS to simplify. Distribute the parentheses. 5A - 20° = 180° Add and subtract. +20° +20° Add 20 to both sides to isolate the variable. 5A = 200° Divide both sides by 5 to solve for A. A = 40° A We’re not done yet. We still need to figure out the other angles. Now we know the first angle and we can substitute to find B and C. ∠ A = 40° ∠ B = A - 5° ∠ B = 40° - 5° = 35° ∠ C = 3B ∠ C = 3(35°) = 105° 40° 105° 35° C B ∠ A = A, the first angle ∠ B = (A - 5°) ∠ C = 3B = 3(A - 5°)

Angles Word Problem Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measurement of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measurement of each angle. Now let’s set up the problem and solve for A. All the angles in the triangle add up to 180°. ∠ A + ∠ B + ∠ C = 180° A + (A - 5°) + 3(A - 5°) = 180° Substitute for A, B, & C. A + A - 5° + 3A - 15° = 180° Use PEMDAS to simplify. Distribute the parentheses. 5A - 20° = 180° Add and subtract. +20° +20° Add 20 to both sides to isolate the variable. 5A = 200° Divide both sides by 5 to solve for A. A = 40° A Let’s check if we’re correct. Does equal 180? 40 35 ✓ 40° 105° 35° C B ∠ A = A, the first angle ∠ B = (A - 5°) ∠ C = 3B = 3(A - 5°)

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Answer the following problem. Share your response with a study partner if you have one. The measurement of the second angle of a triangle is 5° less than the measure of the first angle. The third angle is 3 times as large as the second angle. Find the measurement of each angle. Now let’s set up the problem and solve for A. All the angles in the triangle add up to 180°. ∠ A + ∠ B + ∠ C = 180° A + (A - 5°) + 3(A - 5°) = 180° Substitute for A, B, & C. A + A - 5° + 3A - 15° = 180° Use PEMDAS to simplify. Distribute the parentheses. 5A - 20° = 180° Add and subtract. +20° +20° Add 20 to both sides to isolate the variable. 5A = 200° Divide both sides by 5 to solve for A. A = 40° A Let’s check if we’re correct. Does equal 180? 40 35 ✓ 40° Think… Does our drawing look correct for the angles we found? Why or why not? Does it matter? 105° 35° C B ∠ A = A, the first angle ∠ B = (A - 5°) ∠ C = 3B = 3(A - 5°)

Pythagorean Theorem The Pythagorean Theorem is handy for solving all kinds of problems. The formula says that the square of the length of the hypotenuse of a right triangle— the side of a triangle opposite the right angle—is equal to the sum of the squares of each of the other sides. The formula is: a2 + b2 = c2 a c b For example, If a = 3 and b = 4, then c = 5 a2 + b2 = c2 = 52 = 25

PRACTICE WITH THE PYTHAGOREAN THEOREM
Video from Jake Scott on YouTube Click to watch a video of real teachers using music to teach the Pythagorean theorem. PRACTICE WITH THE PYTHAGOREAN THEOREM at Khan Academy TIP: Use the menu at the left at KhanAcademy.org to watch video lessons and practice a variety of word problems. The WEST-B may test you on high level uses of the Pythagorean Theorem so we encourage you to explore and practice the “Application” section of the lessons in addition to the “Intro” section.

Triangles Question Think…
The following is another question you might see on the WEST-B. Try to solve this problem before you click Next. Abdi drives 8 miles straight from his house, then turns right and drives another 6 miles straight to get to work, following the path in the diagram below. How far is Abdi’s home from his work – if he could drive there directly along the line segment 𝐻𝑊 ? 2 miles 10 miles 14 miles 32 miles Think… What is a good first step for this problem? What would you tell a student to do? Work (W) Home (H)

Triangles Question The following is another question you might see on the WEST-B. Try to solve this problem before you click Next. Abdi drives 8 miles straight from his house, then turns right and drives another 6 miles straight to get to work, following the path in the diagram below. How far is Abdi’s home from his work – if he could drive there directly along the line segment 𝐻𝑊 ? 2 miles 10 miles 14 miles 32 miles What do we know and what do we need to know? We know that Abdi drives 8 miles before he turns right and 6 miles after. We need to know the length of the line segment 𝐻𝑊 . Let’s label our diagram, using x for the missing information. Draw it on your scrap paper during the test. Work (W) Home (H) 8 mi 6 mi x mi

Triangles Question The following is another question you might see on the WEST-B. Try to solve this problem before you click Next. Now let’s write the formula for calculating the hypotenuse of a right triangle and substitute what know and need to know. If you don’t remember the formula, check your Math Reference Sheet. Abdi drives 8 miles straight from his house, then turns right and drives another 6 miles straight to get to work, following the path in the diagram below. How far is Abdi’s home from his work – if he could drive there directly along the line segment 𝐻𝑊 ? a2 + b2 = c2 = x2 2 miles 10 miles 14 miles 32 miles Work (W) Home (H) 8 mi 6 mi x mi

Triangles Question The following is another question you might see on the WEST-B. Try to solve this problem before you click Next. Abdi drives 8 miles straight from his house, then turns right and drives another 6 miles straight to get to work, following the path in the diagram below. How far is Abdi’s home from his work – if he could drive there directly along the line segment 𝐻𝑊 ? a2 + b2 = c2 = x2 = x2 Simplify the exponents. 100 = x2 Add. 100 = x2 Take the square root of both sides to isolate the x. 10 = x 2 miles 10 miles 14 miles 32 miles Now we solve for x. Work (W) Home (H) 8 mi 6 mi x mi

Congruence and Similarity
Shapes and angles are congruent if they have the exact same measures. They don’t have to be pointed in the same direction, but if you picked one up, rotated it, and put it on top of the other one, they would match perfectly. Shapes are similar if they have the same angles and the same proportions. The size of the shapes can be different, but they have to be proportional. For example, these rectangles are similar because the ratio of the length and width for both is 2 : 1. 2 4 2 1 congruent angles

Congruence and Similarity
Click a button for more information and practice with congruence and similarity. CONGRUENCE AND SIMILARITY ARTICLE at mathisfun.com CONGRUENCE AND SIMILARITY LESSONS AND PRACTICE at KhanAcademy.org CONGRUENT ANGLES & PARALLEL LINES LESSONS AND PRACTICE at KhanAcademy.org TIP: Scroll to the bottom of the page for links to related topics. TIP: Use the menu at the left at Khan Academy to watch videos and practice with related math concepts.

Congruence and Similarity Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which triangle is similar to the triangle shown above? A. B. C. D. Think… Without doing any calculations, are there any answer choices that you can eliminate right away? Why or why not? 5 4 6 4 5 2.5 2 3 4

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which triangle is similar to the triangle shown above? A. B. C. D. 5 4 In the context of geometry, similar means proportional. Do you recognize the triangle that has the same proportions as the original triangle? 6 4 5 2.5 2 3 4

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. If you don’t immediately recognize the correct answer, that’s ok. We just have to think about it a little bit. The base of our original triangle has a length of 4 and each side has a length of 5. It’s an isosceles triangle with a base to side ratio of 4 to 5. We are looking for another isosceles triangle with the ratio We can eliminate D because it’s an equilateral triangle. Which triangle is similar to the triangle shown above? A. B. C. D. 5 4 6 4 5 2.5 2 3 4

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which triangle is similar to the triangle shown above? A. B. C. D. We can also eliminate C because the base is longer than the sides. The ratio we’re looking for is 4 : 5. The base of our original triangle is shorter than the sides. 5 4 6 4 5 2.5 2 3 4

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which triangle is similar to the triangle shown above? A. B. C. D. Now let’s look at our remaining two answers. In A, the base is 4, but the sides are not 5. Already that’s a problem because it’s no longer in proportion to the original. 4 : 5 ≠ 4 : 6. 5 4 6 4 5 2.5 2 3 4

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which triangle is similar to the triangle shown above? A. B. C. D. The answer must be B. If you’d like to check it, go for it. Does = ? Yep, 4 divided by 2 is 2 and 5 divided by 2 is 2.5. They have the same proportions. The triangle in B is similar to the original triangle. 5 4 6 4 5 2.5 2 3 4

Coordinate Planes DEFINITIONS:
Coordinate plane (n.) A plane formed by intersecting number lines called the x- and y-axes. X-axis (n.) The horizontal number line. Positive numbers go to the right and negative numbers go to the left. Y-axis (n.) The vertical number line. Positive numbers go up and negative numbers go down. Ordered pair (n.) A pair of numbers used to locate a point on a coordinate plane, (x, y); the first number tells how far to move horizontally and the second number tells how far to move vertically. For example… (4, -3) Move right 4, and down 3 (-2, 1) Move left 2 and up 1 Quadrant (n.) ¼ of the coordinate plane. Origin (n.) The intersection of the x- and y-axes, (0, 0) (4, -3) (-2, 1) (0, 0)

Coordinate Planes Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Video from Numberrock on YouTube Click the video below to watch a song about Coordinate Planes, then click a button to practice. COORDINATE PLANE PRACTICE at Khan Academy COORDINATE PLANE WORD PROBLEMS at Khan Academy

Coordinate Planes Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a kind of question you might see on the WEST-B. This question was on your pre-test. What are the coordinates of point D? (3, -2) (-2, 3) (2, -3) (-3, 2) Think… Can you plot all of the ordered pairs in the answer options on this coordinate plane?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a kind of question you might see on the WEST-B. This question was on your pre-test. What are the coordinates of point D? (3, -2) (-2, 3) (2, -3) (-3, 2) Let’s plot A, (3, -2). 3 is positive and its in the x position of the ordered pair. We need to go right is in the y position of the ordered pair. We need to go down 2. A (3, -2)

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a kind of question you might see on the WEST-B. This question was on your pre-test. What are the coordinates of point D? (3, -2) (-2, 3) (2, -3) (-3, 2) Let’s plot A, (3, -2). 3 is positive and its in the x position of the ordered pair. We need to go right is in the y position of the ordered pair. We need to go down 2. We can eliminate A. Point D is in the same quadrant. What are the other two answers we can eliminate right now? Why? A (3, -2)

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following is a kind of question you might see on the WEST-B. This question was on your pre-test. What are the coordinates of point D? (3, -2) (-2, 3) (2, -3) (-3, 2) Let’s plot A, (3, -2). 3 is positive and its in the x position of the ordered pair. We need to go right is in the y position of the ordered pair. We need to go down 2. We can eliminate B and D now as well because the x value in both pairs is negative. That means the points will be to the left of the y axis. We count left from the origin to plot -x values. The answer is C (2, -3)—right 2, and down 3. A (3, -2)

Probability and Statistics
WEST-B Objective: Understand concepts and principles of probability and statistics and solve related problems. In this section… Probability Interpreting tables, charts, and graphs Organizing and displaying data Mean, median, and mode

Probability Probability is often expressed as a fraction like this:
Probability is the likelihood of something occurring. For example, if you flip a coin, you will either get heads or tails. The probability that you will get heads is ½. That means that over a long period of time, you’ll get heads half the time and tails half the time. In one coin flip, you have two options and the probability that you’ll get one of those two options is ½. Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠

Probability is the likelihood of something occurring. For example, if you flip a coin, you will either get heads or tails. The probability that you will get heads is ½. That means that over a long period of time, you’ll get heads half the time and tails half the time. In one coin flip, you have two options and the probability that you’ll get one of those two options is ½. Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠 For example, let’s say you call heads in the coin flip. There is one head on the coin and that’s the thing you want, so 1 is in the numerator of the fraction. There are two sides to the coin—the total number of all the things—so 2 is in the denominator. The likelihood that you’ll get heads is —or 1 out of 2.

Example: There are 20 cupcakes on a plate. 15 are filled with chocolate and 5 are filled with raspberry jam. You want a raspberry cupcake. What is the probability that the cupcake you choose will be raspberry? Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠

What do you want? How many are there?
Probability Example: There are 20 cupcakes on a plate. 15 are filled with chocolate and 5 are filled with raspberry jam. You want a raspberry cupcake. What is the probability that the cupcake you choose will be raspberry? Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠 What do you want? How many are there?

Example: There are 20 cupcakes on a plate. 15 are filled with chocolate and 5 are filled with raspberry jam. You want a raspberry cupcake. What is the probability that the cupcake you choose will be raspberry? 5 raspberry cupcakes Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠 You want a raspberry cupcake and there are 5 of them. Put that in the numerator.

There are 20 cupcakes total. Put that in the denominator.
Probability Example: There are 20 cupcakes on a plate. 15 are filled with chocolate and 5 are filled with raspberry jam. You want a raspberry cupcake. What is the probability that the cupcake you choose will be raspberry? 5 raspberry cupcakes 20 total cupcakes Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠 There are 20 cupcakes total. Put that in the denominator.

Example: There are 20 cupcakes on a plate. 15 are filled with chocolate and 5 are filled with raspberry jam. You want a raspberry cupcake. What is the probability that the cupcake you choose will be raspberry? 5 raspberry cupcakes 20 total cupcakes 1 4 or 25% Probability is often expressed as a fraction like this: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡ℎ𝑖𝑛𝑔𝑠 Reduce the fraction. You can also turn it into a percentage. There is a 25% chance that you’ll get a raspberry cupcake.

Probability Practice PROBABILITY LESSON PROBABILITY PRACTICE
at Math Is Fun Click a button to read more about probability and do practice problems at Math Is Fun, and to practice and watch videos at Khan Academy. PROBABILITY PRACTICE Khan Academy

Probability Question Think…
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A box contains 20 red marbles, 15 blue marbles, 25 yellow marbles, and 2 black marbles. If a person selects a marble at random, what is the probability that the marble will be black? 1 62 1 61 1 31 1 30 Think… What does the person want? How many are there? How many total marbles are there in the box?

Probability Question WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. A box contains 20 red marbles, 15 blue marbles, 25 yellow marbles, and 2 black marbles. If a person selects a marble at random, what is the probability that the marble will be black? 1 62 1 61 𝟏 𝟑𝟏 1 30 The person wants a black marble. There are 2 in the box. There are a total of 62 marbles. Our probability fraction is: 2 62 or 1 31 The answer is C.

Representing and Interpreting Data
Data is information that can be presented in a variety of ways. The WEST-B might ask you to Read and interpret charts and graphs Choose an appropriate chart or graph to represent certain data Calculate the percentage change from a chart or graph Make predictions based on trends Calculate the mean, median, or mode of a data set

Representing Data Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide It’s difficult to read and understand data when it is in plain number form—that’s why newspapers, textbooks, and teachers often present data in picture form as a chart or a graph. It’s much easier to compare information and see patterns and relationships when data is organized visually. There are many ways to represent data. The chart, graph, or table you choose to represent data depends on what you are trying to show. See the next page for various charts and graphs and what they’re good for.

Charts and Graphs The following are common chart and graph types and their purposes. TABLES List numbers or text in labeled columns to see side-by-side values. LINE GRAPHS Look at trends over time. BAR GRAPHS Compare amounts with vertical or horizontal bars. Longer bars = more. PIE CHARTS Compare parts to the whole. The “slices” of the pie represent portions of the total.

Interpreting Graphics
Climate graph from USClimateData.com The graph on the left shows average climate, or weather, information for Seattle over one year. There’s a ton of information in this graph. Think… What are the three important pieces of information this graph is showing us? Would it be helpful to read the information on the graph in a written paragraph? Why or why not?

Climate graph from USClimateData.com The graph shows us these three important pieces of information: The average low temperature in Seattle for each month.

Climate graph from USClimateData.com The graph shows us these three important pieces of information: The average low temperature in Seattle for each month. The average high temperature in Seattle for each month.

Climate graph from USClimateData.com The graph shows us these three important pieces of information: The average low temperature in Seattle for each month. The average high temperature in Seattle for each month. The average precipitation (rain or snow) in Seattle for each month.

Climate graph from USClimateData.com That’s a lot on one graph. Can you imagine a passage that might include all of the same information? For example… In January in Seattle, the average high temperature is about 45°F and the average low temperature is about 35°F. The average precipitation is about 5.25 inches. In February, the average high temperature is about 48°F and the average low temperature is about 38°F. The average precipitation is about 4.25 inches…………..

Climate graph from USClimateData.com That’s a lot on one graph. Can you imagine a passage that might include all of the same information? For example… In January in Seattle, the average high temperature is about 45°F and the average low temperature is about 35°F. The average precipitation is about 5.25 inches. In February, the average high temperature is about 48°F and the average low temperature is about 38°F. The average precipitation is about 4.25 inches………….. ……Yikes, that’s already really long and boring and we only got through February! There are ten more months to go.

Climate graph from USClimateData.com The problem is not only that writing out information in paragraph form can be long and boring. It’s also that it is difficult to tell from a paragraph the trends and patterns in the information. Graphs, along with text, can give us a visual representation, or a picture, of those trends and patterns. Think… In general, is there more precipitation in Seattle in winter or summer? In general, are temperatures higher in winter or summer? How can you tell?

Parts of a Graph Each part of a graph gives us important information.
Climate graph from USClimateData.com Each part of a graph gives us important information.

Climate graph from USClimateData.com Each part of a graph gives us important information. TITLE The title tells us this graph is about the Climate in Seattle.

Climate graph from USClimateData.com Each part of a graph gives us important information. LEGEND or KEY The legend or key tells us what all the lines or symbols on the graph stand for—in other words, what they represent. The blue line means low, the red line means high, and the blue bars stand for precipitation.

Climate graph from USClimateData.com Each part of a graph gives us important information. VERTICAL or Y-AXIS Low what? High what? How do we know what is low or high, or how the precipitation is measured? We look at the vertical axis, which is usually on the left. This graph has 2 different vertical axes, so we have to make inferences based on context and what we know about climate and weather.

Climate graph from USClimateData.com Each part of a graph gives us important information. VERTICAL or Y-AXIS The left Y-axis is labeled with degrees. The right Y-axis is labeled with inches. The axis we read depends on what we’re measuring. We know that temperatures are measured in degrees and precipitation (rain or snow) is measured in inches.

Climate graph from USClimateData.com Each part of a graph gives us important information. VERTICAL or Y-AXIS When we look at the red line for High, we can infer from the context that this means high temperatures, which are measured in degrees. The clue is in the title, Seattle Climate Graph. Therefore, when we look at the red line for information, we will read the left Y-axis. The lowest temperature is at the bottom; the highest temperature is at the top.

Climate graph from USClimateData.com Each part of a graph gives us important information. VERTICAL or Y-AXIS The legend tells us that blue bars represent precipitation. We know that precipitation is measured in inches. Therefore, when we look at the blue bars for information, we will read the Y-axis on the right. The least number of inches is at the bottom. The most number of inches is at the top.

Climate graph from USClimateData.com Each part of a graph gives us important information. HORIZONTAL or X-AXIS The horizontal axis in this graph measures time in months. It’s very common for X-axes to measure time from left to right. The earliest time is usually on the left and the latest time is usually on the right.

Practice Climate graph from USClimateData.com Directions: Look at the graph to answer the following questions. Write your answers on a piece of paper. What is the average low temperature in Seattle in March? What is the average precipitation in December? In general, is there more precipitation in Seattle in winter or summer? In general, are temperatures higher in winter or summer?

Practice Climate graph from USClimateData.com Directions: Look at the graph to answer the following questions. Write your answers on a piece of paper. What is the average low temperature in Seattle in March? The average low temperature in Seattle in March is about 40°F. What is the average precipitation in December? In general, is there more precipitation in Seattle in winter or summer? In general, are temperatures higher in winter or summer? Find March on the X-axis Look up to find where the blue line for Low crosses March. Then, look at the left Y-axis to read the temperature in degrees. Estimate 40°F. 3 2 1

Practice Climate graph from USClimateData.com Directions: Look at the graph to answer the following questions. Write your answers on a piece of paper. What is the average low temperature in Seattle in March? The average low temperature in Seattle in March is about 40°F. What is the average precipitation in December? The average precipitation in December is about 5 ½ inches. In general, is there more precipitation in Seattle in winter or summer? In general, are temperatures higher in winter or summer? Find December on the X-axis Look up to find where the blue bar for precipitation ends. Then, look at the right Y-axis to read the number of inches. Estimate 5 ½ inches. 2 3 1

Practice Climate graph from USClimateData.com Directions: Look at the graph to answer the following questions. Write your answers on a piece of paper. Look at the blue bars. In which months are the bars the longest? In which are they the shortest? Longer bars means more inches of precipitation. What is the average low temperature in Seattle in March? The average low temperature in Seattle in March is about 40°F. What is the average precipitation in December? The average precipitation in December is about 5 ½ inches. In general, is there more precipitation in Seattle in winter or summer? In general, there is more precipitation in Seattle in winter. In general, are temperatures higher in winter or summer?

Practice Climate graph from USClimateData.com Directions: Look at the graph to answer the following questions. Write your answers on a piece of paper. Look at the red and blue lines for temperature. In which months are they the highest? What is the average low temperature in Seattle in March? The average low temperature in Seattle in March is about 40°F. What is the average precipitation in December? The average precipitation in December is about 5 ½ inches. In general, is there more precipitation in Seattle in winter or summer? In general, there is more precipitation in Seattle in winter. In general, are temperatures higher in winter or summer? In general, temperatures are higher in summer.

Practice Climate graph from USClimateData.com Directions: Look at the graph to answer the following questions. Write your answers on a piece of paper. What is the average low temperature in Seattle in March? The average low temperature in Seattle in March is about 40°F. What is the average precipitation in December? The average precipitation in December is about 5 ½ inches. In general, is there more precipitation in Seattle in winter or summer? In general, there is more precipitation in Seattle in winter. In general, are temperatures higher in winter or summer? In general, temperatures are higher in summer.

Interpreting Graphics Question
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following question asks you to interpret information from a graph. What conclusion can be drawn from the data presented in the graph? Japanese American businesses were more successful in California than in other states. The number of Japanese American businesses in Los Angeles and San Francisco increased greatly from 1900 to 1909. In 1909, there were more Japanese American businesses in Los Angeles than there were in San Francisco. In 1909, most Japanese American businesses in Los Angeles and San Francisco were large companies. The question is asking you to make inferences from the graph. Before you look at the answer choices, think… What is the title of this graph? What is this graph comparing? How do you know?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following question asks you to interpret information from a graph. What conclusion can be drawn from the data presented in the graph? Japanese American businesses were more successful in California than in other states. The number of Japanese American businesses in Los Angeles and San Francisco increased greatly from 1900 to 1909. In 1909, there were more Japanese American businesses in Los Angeles than there were in San Francisco. In 1909, most Japanese American businesses in Los Angeles and San Francisco were large companies. Think… Are there any answers we can eliminate right away?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following question asks you to interpret information from a graph. What conclusion can be drawn from the data presented in the graph? Japanese American businesses were more successful in California than in other states. The number of Japanese American businesses in Los Angeles and San Francisco increased greatly from 1900 to 1909. In 1909, there were more Japanese American businesses in Los Angeles than there were in San Francisco. In 1909, most Japanese American businesses in Los Angeles and San Francisco were large companies. We can eliminate (A) and (D) right away. This graph is comparing the number of Japanese American businesses in two cities in the years 1900 and The answer in (A) is about comparing businesses in two or more states, California and others. The answer in (D) is about the size of the businesses, not the total number. Neither of these are represented in the graph.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following question asks you to interpret information from a graph. What conclusion can be drawn from the data presented in the graph? Japanese American businesses were more successful in California than in other states. The number of Japanese American businesses in Los Angeles and San Francisco increased greatly from 1900 to 1909. In 1909, there were more Japanese American businesses in Los Angeles than there were in San Francisco. In 1909, most Japanese American businesses in Los Angeles and San Francisco were large companies. The answers that are left are about the trends or patterns in the graph. Is it true that there were a lot more Japanese American businesses in Los Angeles and San Francisco in 1909 than there were in 1900—that is, did the number of businesses increase greatly? Is it true that in 1909 there were more Japanese American businesses in LA (blue bar) than in San Francisco (orange bar)? NO! So……

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following question asks you to interpret information from a graph. What conclusion can be drawn from the data presented in the graph? Japanese American businesses were more successful in California than in other states. The number of Japanese American businesses in Los Angeles and San Francisco increased greatly from 1900 to 1909. In 1909, there were more Japanese American businesses in Los Angeles than there were in San Francisco. In 1909, most Japanese American businesses in Los Angeles and San Francisco were large companies. …..(B) is correct. In 1900, there were 100 Japanese American businesses in San Francisco and about 75 in Los Angeles. In 1909, there were over 500 in San Francisco and about 475 in LA. That’s a big increase in just 9 years.

Reading and Interpreting Data Practice
Click to practice reading and interpreting data with other types of charts and graphs at Khan Academy. READING AND INTERPRETING DATA at Khan Academy

Mean, Median, and Mode Click to watch a video with examples
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Definitions from Merriam-Webster Learner’s Dictionary Video from MathAntics on Youtube Click to watch a video with examples DEFINITIONS Mean (n.) A number that is calculated by adding quantities together and then dividing the total by the number of quantities; an average Median (n.) The middle value in a series of values arranged from smallest to largest Mode (n.) The value that appears most often in a set of values.

Mean, Median, and Mode Example
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the mean, median, and mode for the following data set. A fly fisherman fishing in Rock Falls River kept track of the number of fish he caught and released per hour. The data are given below:

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the mean, median, and mode for the following data set. A fly fisherman fishing in Rock Falls River kept track of the number of fish he caught and released per hour. The data are given below: First, calculate the mean. Add all the values together: = 28 Divide the sum of all the values by the number of values. We have 10 values = 2.8 Mean (n.) A number that is calculated by adding quantities together and then dividing the total by the number of quantities; an average

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the mean, median, and mode for the following data set. A fly fisherman fishing in Rock Falls River kept track of the number of fish he caught and released per hour. The data are given below: Now the median… Arrange all the values in order from smallest to largest: Find the center. Divide the list into two equal groups Calculate the median by finding the mean of the two middle values: = 5, 5 ÷ 2 = 2.5 Median (n.) The middle value in a series of values arranged from smallest to largest Mean = 2.8

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the mean, median, and mode for the following data set. A fly fisherman fishing in Rock Falls River kept track of the number of fish he caught and released per hour. The data are given below: Finally, the mode… Look at the data sorted from smallest to largest again: Count which value appears most often: There are four 2s. 2 is the mode. Mode (n.) The value that appears most often in a set of values. Mean = 2.8 Median = 2.5

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide Directions: Calculate the mean, median, and mode for the following data set. A fly fisherman fishing in Rock Falls River kept track of the number of fish he caught and released per hour. The data are given below: Finally, the mode… Look at the data sorted from smallest to largest again: Count which value appears most often: There are four 2s. 2 is the mode. Think… The mean, median, and mode in this data set are all pretty close to one another, and we often calculate the average of things. What are some averages you use in your everyday life? Can you think of a situation where it would be helpful to know the median rather than the mean? What about the mode? Mode (n.) The value that appears most often in a set of values. Mean = 2.8 Median = 2.5 Mode = 2

Mean, Median, and Mode Practice
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide MEAN, MEDIAN, AND MODE PRACTICE at Khan Academy Click a button to practice mean, median, and mode. MEAN, MEDIAN, AND MODE PRACTICE at MathGames.com

Reasoning, Problem-solving, and Communication
WEST-B Objective: Apply mathematical reasoning, problem-solving, and communication. In this section… Identifying missing or extraneous information Tips for Math Reasoning, Problem-Solving, and Communication Identifying errors

Reasoning, Problem-Solving, and Communication
Everything you review and practice in this Math Study Guide will help you build mathematical reasoning, problem-solving and communication skills. In particular, practicing word problems and translating them to math sentences is critical. (This is covered in detail in the Algebra section). Think… Why do you think mathematical reasoning, problem-solving, and communication skills are tested on the WEST-B?

Identifying Extraneous Information Question
WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person Think… What is your process for solving this problem? What will you do first? How would you explain it to a student?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person Let’s approach this like any other word problem. What do we know and what do we need to know?

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person We need to know the total cost of the trip, so we’re looking for information in the problem that will help us find that answer.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75. What we really need to know is not the total cost of the trip, but rather, what information we need in order to figure that out. We don’t actually need to figure it out, though.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person Of the info we have, which would help us figure out the total cost of the trip? We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person We’re given two rates: The cost per bus, and the cost of food per person. We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person To calculate the total cost, we need to know the number of people and the number of buses. We have that information, too. We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person There’s only one thing on our list that is unnecessary information—the distance to the competition. The best answer is C. We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75.

WEST-B Math Sample Questions Question Copyright © 2010 Pearson Education, Inc. The following question is a sample of the kind of question you might see on the WEST-B. This question was on your pre-test. Which piece of information is extraneous for the solution of the problem below? A school band is going to a regional competition 85 miles from the school. A total of 80 students and chaperones will be traveling in 2 buses. The transportation cost is $ per bus. The cost of food for each person is $18.75. What is the total cost of the trip? number of people on the trip cost of each bus number of miles each bus will travel cost of food for each person TIP: For a “Missing Information” Question, you’d use the same reasoning process. Identify what you know and what you need to know. Think about the math behind the problem (in this case, rates) and the information you need to work out the problem. Check to see if you have all the info you need. There’s only one thing on our list that is unnecessary information—the distance to the competition. The best answer is C. We know: The competition is 85 miles from the school. 80 people will be going. They’re taking 2 buses. The buses cost $ each. The cost of food per person is $18.75.

Identifying Errors You may see questions on the WEST-B that ask you to identify the errors in reasoning or translation from a word problem to a math sentence. TIP: It helps to work out the problem for yourself, then you can easily compare your work with the problem to identify mistakes.

Identifying Errors Question
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following is a question like one you may see on the WEST-B. A test question stated the following: “Add the sum of 5 and 3, and then multiply by the sum of 6 and 8.” The student wrote the following: 5 + 3(6 + 8). What should have the student written? 5 + 3 x 6 + 8 (5 + 3 x 6) + 8 (5 + 3 x 6 + 8) (5 + 3) x (6 + 8) Before you look at the answer choices, try to write out the word problem for yourself and compare it to what the student wrote.

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following is a question like one you may see on the WEST-B. A test question stated the following: “Add the sum of 5 and 3, and then multiply by the sum of 6 and 8.” The student wrote the following: 5 + 3(6 + 8). What should have the student written? 5 + 3 x 6 + 8 (5 + 3 x 6) + 8 (5 + 3 x 6 + 8) (5 + 3) x (6 + 8) Did you write (5 +3) · (6 + 8)? Why or why not? What skills did you use to solve this problem? How would you explain it to the student?

Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The following is a question like one you may see on the WEST-B. A test question stated the following: “Add the sum of 5 and 3, and then multiply by the sum of 6 and 8.” The student wrote the following: 5 + 3(6 + 8). What should have the student written? 5 + 3 x 6 + 8 (5 + 3 x 6) + 8 (5 + 3 x 6 + 8) (5 + 3) x (6 + 8) We wrote (5 +3) · (6 + 8). That’s the same thing as D, which is the correct answer. We can look at the key words add, sum, and multiply, then use our knowledge of the order of operations to write the math sentence using parentheses so that the addition will be done first.

Identifying Errors Practice
Adapted from the ICCB Paraprofessional Test Preparation Curriculum Guide The ParaPro test—a standardized test for people pursuing certification as a Paraeducator—has many questions about identifying errors and using math reasoning in the classroom context. Click to download sample questions from that exam that will help you build your math reasoning and communication skills for the WEST-B. Handout: Math 05 Reasoning and Application

Tips for Practicing Math Reasoning and Problem-Solving Skills
As you work through the rest of this Math Study Guide, take practice tests, and solve practice problems, keep these questions in mind to build your reasoning and problem- solving skills. Ask yourself: Did I translate the problem into numbers and symbols? Does the math sentence I wrote fit the problem? Did I choose a strategy that fit the problem? Did I work it out step-by-step and show my work? Can I follow my own logic? Did I use the right unit label? (For example, cm2 for area). Was my answer complete and accurate? Does my answer match what the problem was asking? Can I explain what I did to solve the problem?

In this section, did you….?
Learn about the Math section of the WEST-B Learn about the topics on the test See sample test questions Take a pretest Review numbers, math symbols, and math terms Practice arithmetic with integers, fractions, decimals, and percentages Practice using ratios and proportions for a variety of problems Learn about equivalences Practice exponents and PEMDAS Review units of measurement and carrying/borrowing units Convert measurements Practice calculating scale and reading maps and diagrams Practice calculating rate Practice sequences Solve linear equations and inequalities Do algebra word problems and practice translating to math sentences Review geometric shapes Calculate perimeter, circumference, area, volume, and surface area Learn about properties of certain shapes and angles Learn about congruence and similarity Plot points on a coordinate plane Calculate probability Learn about ways to display and interpret data Calculate mean, median, and mode Review concepts of math reasoning, problem-solving, and communication

In this section, did you….?
Learn about the Math section of the WEST-B Learn about the topics on the test See sample test questions Take a pretest Review numbers, math symbols, and math terms Practice arithmetic with integers, fractions, decimals, and percentages Practice using ratios and proportions for a variety of problems Learn about equivalences Practice exponents and PEMDAS Review units of measurement and carrying/borrowing units Convert measurements Practice calculating scale and reading maps and diagrams Practice calculating rate Practice sequences Solve linear equations and inequalities Do algebra word problems and practice translating to math sentences Review geometric shapes Calculate perimeter, circumference, area, volume, and surface area Learn about properties of certain shapes and angles Learn about congruence and similarity Plot points on a coordinate plane Calculate probability Learn about ways to display and interpret data Calculate mean, median, and mode Review concepts of math reasoning, problem-solving, and communication TIPS: Practice and review the topics you’re still unsure about. Review your pretest and take it again. Take other practice tests online or in books. Do the WEST-B tutorial to get an idea of what it will be like to take the computer-based test.

Help Getting Started This study guide can help you:
Make a plan to study for the WEST-B Learn about the reading, writing, and math sections of the test Practice answering test questions Click here to go to the next page. Click here to go to the first page, the home page. Click here to go to the previous page.

How much time will this take?
You can use this study guide for any amount of time, but it’s a good idea to study for at least an hour a day. The first section, “Make a Plan,” will take two hours or more to finish. The other sections will take longer. You can go as fast or as slow as you want. Skip sections you don’t need to study. Don’t spend time on things you already know. In each section, you will be able to: Review the skills and topics you need to do well on the test by watching videos, reading, thinking, and practicing Go to other websites to practice and get information Practice taking test questions and learn about the answers

WEST-B Test Preparation Study Guide

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