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Basic Arithmetic Skills Workshop Accompanied by a Study Packet

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About the Accuplacer Exam What is the Accuplacer? Passing Requirements for both ATB and Non-ATB What happens when you fail? How much time do you have? Testing center RULES

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Basic Skills Workshop What this workshop covers What this workshop covers What this workshop does not cover What this workshop does not cover Expected Learning Outcomes Expected Learning Outcomes Can this workshop guarantee a passing grade? Can this workshop guarantee a passing grade? What next steps you should take when you leave here today? What next steps you should take when you leave here today? LET’S GET STARTED, SHALL WE?!?!?

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What is a fraction?? What is a fraction?? What are the parts of a fraction? What are the parts of a fraction?

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FRACTION EXAMPLES!! What would a fraction look like to represent the triangles with smiley faces below? What would a fraction look like to represent the triangles with smiley faces below? If you said 2/7 you’d be correct!

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MORE FRACTIONS Now what’s the fraction of smiley faced triangles?? Now what’s the fraction of smiley faced triangles?? What changed? What changed? If you said 3/7 you’d be correct!!

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ADDING AND SUBTRACTING WITH FRACTIONS Adding with Like Denominators Adding with Like Denominators Adding with Unlike Denominators Adding with Unlike Denominators –Finding the Least Common Multiple Subtracting with Like Denominators Subtracting with Like Denominators Subtracting with Unlike Denominators Subtracting with Unlike Denominators –More with the Least Common Multiple

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REVIEW Add 2/3 + 1/5 Add 2/3 + 1/5 Add 3/4 + 1/2 Add 3/4 + 1/2 Subtract 1/4 - 1/3 Subtract 1/4 - 1/3 Subtract 5/8 – 1/2 Subtract 5/8 – 1/2

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Multiply and Divide Fractions The Rule for Multplying Fractions The Rule for Multplying Fractions The Rule for Dividing Fractions The Rule for Dividing Fractions

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Multiply and Divide the Following Fractions Multiply 3/5 * 2/3 Multiply 3/5 * 2/3 Divide 11/12 ÷ 1/2 Divide 11/12 ÷ 1/2 Multiply 4/6 * 7/8 Multiply 4/6 * 7/8 Divide 4/5 ÷ 1/3 Divide 4/5 ÷ 1/3 GOOD LUCK!

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What does “Lowest Terms” mean? What does “Lowest Terms” mean? How do I know when a fraction is in “Lowest Terms”? How do I know when a fraction is in “Lowest Terms”? What is the GREATEST COMMON FACTOR? What is the GREATEST COMMON FACTOR? What does Relatively Prime mean? What does Relatively Prime mean?

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What does Equivalency Mean? What does Equivalency Mean? How can I tell when 2 fractions are equivalent? How can I tell when 2 fractions are equivalent? What’s the USE?? What’s the USE??

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REVIEW! Create fractions from the shaded parts of each figure, and then reduce that fraction to lowest terms

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What is an Improper Fraction? What is an Improper Fraction? What is a Mixed Number? What is a Mixed Number?

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REVIEW Convert into a mixed number 23/7 Convert into a mixed number 23/7 Convert into an improper fraction 2 4/5 Convert into an improper fraction 2 4/5

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What is a Ratio? What is a Ratio? What is the Difference between a Ratio and a Fraction? What is the Difference between a Ratio and a Fraction?

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Review If the ratio of chocolate candies to strawberry candies is 3:1, and you have 36 chocolate candies, how many strawberry candies do you have? How did you solve that?

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DECIMALS What is a Decimal? What is a Decimal? How do you turn a Fraction into a Decimal? How do you turn a Fraction into a Decimal?

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Decimal Place Value The number of digits after the decimal point will determine the number of decimal places in the number. The last digit in the number will determine the label used to write decimal numbers in words

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Computing with Decimals Adding and Subtracting Adding and Subtracting Multiplying and Dividing Multiplying and Dividing Turning Decimals Back into Fractions Turning Decimals Back into Fractions Turning Decimals into Percents Turning Decimals into Percents

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%%%PERCENTS%%% What does Percentage mean? What does Percentage mean? Calculating Percents Calculating Percents Calculating with Percents Calculating with Percents

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Knowing that a percent is the same as both a decimal and fraction is very useful when trying to solve for an amount based on the percentage value

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FORMULA (IMPORTANT!!) Percent Part Percent Part 100 = Whole 100 = Whole Percent = percentage value Percent = percentage value Part = fractional part (numerator) Part = fractional part (numerator) Whole = the entire group (denominator) Whole = the entire group (denominator) 100 = remains always, since a percentage is always a fraction over 100. 100 = remains always, since a percentage is always a fraction over 100. Percent Part 100 = Whole

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REVIEW If 400 people are in at a wedding, and 17% of them ordered the beef entry, how many beef entries must the chef prepare? If 400 people are in at a wedding, and 17% of them ordered the beef entry, how many beef entries must the chef prepare? If at that same wedding, you count 257 female guests, what percentage of the guests are female? If at that same wedding, you count 257 female guests, what percentage of the guests are female? If 92% of the guests the bride and groom invited attended the wedding, how many people did they invite? If 92% of the guests the bride and groom invited attended the wedding, how many people did they invite?

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More Review A survey was conducted using a sample of NYC residents that found that 72% of people use mass transit. If the total sample size they used was 600 people, how many people responded that they use mass transit? A survey was conducted using a sample of NYC residents that found that 72% of people use mass transit. If the total sample size they used was 600 people, how many people responded that they use mass transit? If you ate 8 chocolates out of a box of 20 chocolates, how percentage of the chocolates did you eat? If you ate 8 chocolates out of a box of 20 chocolates, how percentage of the chocolates did you eat? If 560 of students vote to extend summer break at a local school, representing 80% of their schools total enrollment, how many students attend the school? If 560 of students vote to extend summer break at a local school, representing 80% of their schools total enrollment, how many students attend the school?

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Of the most dreaded tasks to tackle in mathematics, the word problem beats them all by a mile. Often believed to be confusing and filled with needless information meant to throw a student off track (and often they are), a word problem is not always difficult in the problem it is asking you to solve, but first determining what it is asking you. Here are some key words for examining a word problem. Of the most dreaded tasks to tackle in mathematics, the word problem beats them all by a mile. Often believed to be confusing and filled with needless information meant to throw a student off track (and often they are), a word problem is not always difficult in the problem it is asking you to solve, but first determining what it is asking you. Here are some key words for examining a word problem. Difference: means subtraction Difference: means subtraction Sum: means to add Sum: means to add Quotient: is the answer to a division problem Quotient: is the answer to a division problem Product: is the answer to multiplication Product: is the answer to multiplication

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4 Steps to Problem Solving 1. UNDERSTANDING THE PROBLEM –Can you state the problem in your own words? –What are you trying to find or do? –What are the unknowns? –What information do you obtain from the problem? –What information, if any, is missing or not needed? Adapted from "Science World," November 5, 1993 (http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm ) Adapted from "Science World," November 5, 1993 (http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm )http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm

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2. Devise a Plan Look for a pattern. Look for a pattern. Examine related problems, and determine if the same technique can be applied. Examine related problems, and determine if the same technique can be applied. Examine a simpler or special case of the problem to gain insight into the solution of the original problem. Examine a simpler or special case of the problem to gain insight into the solution of the original problem. Make a table. Make a table. Make a diagram. Make a diagram. Write an equation. Write an equation. Use guess and check. Use guess and check. Work backward. Work backward. Identify a subgoal Identify a subgoal

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3. CARRYING OUT THE PLAN Implement the strategy or strategies in step 2, and perform any necessary actions or computations. Implement the strategy or strategies in step 2, and perform any necessary actions or computations. Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step. Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step. Keep an accurate record of your work. Keep an accurate record of your work.

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4. LOOKING BACK Check the results in the original problem. (In some cases this will require a proof.) Check the results in the original problem. (In some cases this will require a proof.) Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable? Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable? Determine whether there is another method of finding the solution. Determine whether there is another method of finding the solution. If possible, determine other related or more general problems for which the techniques will work. If possible, determine other related or more general problems for which the techniques will work.

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TIME TO TAKE THE EXAM Tips to pass the entrance exam

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1. Take the exam when you are ready 1. Take the exam when you are ready 2. Be rested and fit on testing day 2. Be rested and fit on testing day 3. Don’t be rushed 3. Don’t be rushed 4. Stay confident. 4. Stay confident.

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On behalf of the Staff of the Learning Enhancement Center We would like to wish you…

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4 Steps to Problem Solving.. UNDERSTANDING THE PROBLEM Can you state the problem in your own words? What are you trying to find or do? What are the unknowns?

4 Steps to Problem Solving.. UNDERSTANDING THE PROBLEM Can you state the problem in your own words? What are you trying to find or do? What are the unknowns?

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