CRCT Test-taking Tips & Strategies

UNIT 1 Tips & Strategies Before reading the problem and trying to answer the question: Order data sets given in the problem. Read graphs for understanding

Unit 1 TIP #1 Order data sets given in the problem. Knight TV has asked each grade level to tape a segment on the canned food drive. Would 6th grade be better off reporting their mean, median or mode as their average number of canned food items collected weekly? Explain your answer.

Unit 1 TIP #2 Read graphs for understanding Type of graph Title Why do you think a histogram was chosen to display the data? What title would you suggest for this graph? Explain your answers.

Unit 1 TIP #2 Read graphs for understanding. Key or table Axes’ labels What labels belong on the horizontal and vertical axes?

Read graphs for understanding. Scale Intervals Unit 1 TIP #2 Read graphs for understanding. Scale Intervals Why are the scale and intervals of both axes appropriate?

Unit 1 TIP #2 Read graphs for understanding. How many yards had fewer than six trees? A) 79 C) 21 B) 58 D) 8

UNIT 2 Tips & Strategies Find factors in pairs starting with 1, continue checking divisibility systematically GCF- list & check factors of smallest number LCM- list & check multiples of largest number Only prime numbers are used in prime factorization

Unit 2 TIP #1 Factors of 48: 1, 48, 2, 24, 3, 16, 4, 12, 6, 8 or 1, 2, 3, 4, 6, 8, 12, 16, 24, & 48 48 48 ÷ 1 = 48 48 ÷ 2 = 24 48 ÷ 3 = 16 48 ÷ 4 = 12 48 ÷ 6 = 8 48 ÷ 8 = 6 To find factors of a number, test divisibility by numerical order starting with 1, then 2, then 3 and so on. Record factors in pairs. STOP when the factors ‘turn around’

GCF of 48 and 72 Factors of 48: 48 ÷ 1 = 48 1, 48 48 ÷ 2 = 24 2, 24 72 ÷ 48 = 1 R 24 NO, 48 is divi-sible by 48, but 72 is not divisible by 48 72 ÷ 24 = 3, YES, 72 and 48 are both divisible by 24 so . . . 24 is the GCF of 48 and 72 GCF Venn Diagram Unit 2 TIP #2 GCF- Starting with the greatest factor of the smallest number, see if the larger number is also divisible by the smallest number’s factors.

Unit 2 TIP #3 LCM of 48 and 72 Multiples of 72: 72, 144, 72 ÷ 48 = 1 R 24 NO, 72 is a multiple of itself but is not a multiple of 48 144 ÷ 48 = 3, YES, 144 is a multiple of both 72 and 48 so . . . 144 is the LCM of 48 and 72 LCM Venn Diagram LCM- Starting with the least multiple of the greatest number, see if the greatest number’s multiples are also multiples of the smaller number.

Memorize the first ten prime numbers: Prime factorization No matter which factor pair you start with, only prime factors are in the prime factorization of a number Exponents tell how many times a prime factor is used in the prime factorization Example: Breaking Apart Prime Factors Unit 2 TIP #4 Memorize the first ten prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

UNIT 3 Tips & Strategies Equivalent fractions may be written in simplest form or higher terms (useful for + or – with common denominators) Comparing fractions – 3 cases Estimate with benchmarks before you add or subtract fractions Know the algorithms and patterns when multiplying or dividing fractions Rational numbers have equivalent fraction, decimal and percent representations

Equivalent Fractions 𝟖 𝟑𝟎 = 𝟐×𝟐×𝟐 𝟐×𝟑×𝟓 = 𝟒 𝟏𝟓 Unit 3 TIP #1 Simplest Form/Lowest Terms 𝟖 𝟑𝟎 = 𝟐×𝟐×𝟐 𝟐×𝟑×𝟓 = 𝟒 𝟏𝟓 GCF of 𝒏𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓 𝒅𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓 is 1 Higher Terms (used in + & -) Numerator & denominator are multiplied by a fraction form of one* Funbrain Equivalent Fractions Choose medium to hard difficulty! Unit 3 TIP #1 Fractions can be written in lowest terms or higher terms by multiplying or dividing by a fraction form of 1* ∗1= 1 1 = 2 2 = 3 3 =. . . = 𝑛 𝑛

Comparing Fractions Unit 3 TIP #2 Same N Same D Different N & D 1st 2nd MathPlayground Compare applet Unit 3 TIP #2 3 cases for Comparing fractions: -Numerator is the same- smaller denominator is the larger fraction -Denominator is the same- larger numerator is the larger fraction -Different numerator & denominator- compare cross products

Estimate b4u Operate Unit 3 TIP #3 Study Stack Estimating Flashcards Estimate Before You Add or Subtract Fractions Round fractions to the nearest benchmark: 0 ½ 1 and so on before adding or subtracting to see if your answer is reasonable.

Multiplication & Division Fraction Multiplication & Division multiplication algorithm Interesting to note, multiplying a whole number by a fraction smaller than one makes a product smaller than the whole number Example: 2 x ¼ = ½ Multiply Fractions - just enter the problem in the form and click multiply! division Interesting to note, dividing a whole number by a fraction smaller than one makes a quotient larger than the whole number Example: 2 ÷ ¼ = 8 Divide fractions - just enter the problem in the form and click divide! Unit 3 TIP #4 Fraction multiplication means taking part of a part; Fraction division is always rewritten as multiplication. .

Fraction-Decimal-Percent 3 ways to represent the same value Equivalents Fraction to Decimal Divide the N by the D 𝟑 𝟒 =𝟎.𝟕𝟓 Decimal to Percent Multiply by 100 Decimal to Fraction Read It-Write It-Reduce It This diagram summarizes how to convert fractions to decimals to percent Wisc-online slideshow f-d-% conversions Unit 3 TIP #5 Fraction Decimal Percent 3 ways to represent the same value .

UNIT 4 Tips & Strategies Evaluate expressions correctly by following the order of operations Equations are always balanced Inverse Operations ‘undo’ – useful for solving 1-step equations Number Patterns can be described by rules and represented by tables, with symbols, or on a graph

Always follow the order of operations when evaluating expressions Grouping Symbols parentheses ( ) brackets [ ] fraction bar 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 Exponents Multiplication or Division (L to R) Addition or Subtraction (L to R) Amby's Order of Operations Tutorial & Practice Unit 4 TIP #1 Always follow the order of operations when evaluating expressions .

Equations have two sides that are always balanced. Balanced Equations Can you find two different expressions that balance? Write the expressions with an equal sign between them to make an equation. Examples: 3 x 2 = 5 + 1 or for x = 2, 3(x+2) = 3 x 5 Pan Balance - Numbers Pan Balance – Algebraic Expressions with graph Unit 4 TIP #2 Equations have two sides that are always balanced. .

Inverse operations ‘undo’ useful for solving equations Addition - - - - - - - - - - - - Subtraction 2 + 3 = 5 5 – 3 = 2 x + 3 = 5 5 – 3 = x Subtraction - - - - - - - - - - - - Addition 8 – 3 = 5 5 + 3 = 8 x – 5 = 3 3 + 5 = x Multiplication - - - - - - - - - - Division 3 ∙ 4 = 12 12 ÷ 3 = 4 3 ∙ x = 12 12 ÷ 3 = x Division - - - - - - - - - - - - - Multiplication 28 ÷ 7 = 4 4 ∙ 7 = 28 x ÷ 7 = 4 4 ∙ 7 = x Unit 4 TIP #3 Inverse operations ‘undo’ useful for solving equations Inverse Operations in 1-Step Equations .

Patterns to Rules Pattern: Rule: Table: Symbols: (x, x÷2) Graph: Unit 4 TIP #4 Patterns to Rules Pattern: Rule: Table: Symbols: (x, x÷2) Graph: Four ways to describe what happens in a pattern: Rule- words Table- number pairs Symbols- notation such as diagrams, expressions and equations Graphs- ordered pairs on coordinate plane ThinkQuest Number Patterns 1st number 4 8 10 16 2nd number 2 5 ? .

UNIT 5 Tips & Strategies Regular polygons have the same number of lines of symmetry as number of sides Rotational Symmetry- Circle has 360 of turn Benchmark angles of a circle: 0, 90, 180, 270, 360 The degree of rotational symmetry for regular polygons is calculated as 360 (degrees in a circle) ÷ number of sides

An equilateral triangle has 3 lines of symmetry (3 sides = 3 lines) Unit 5 TIP #1 Line Symmetry An equilateral triangle has 3 lines of symmetry (3 sides = 3 lines) Line & Rotational Symmetry Review and Test @ Bitesize Maths Regular polygons (all sides congruent) have the same number of lines of symmetry as number of sides. How many lines of symmetry does a square have? .

Circles and Rotational Symmetry Practice estimating degrees of turn in a circle @ Banana Hunt Calculate rotational symmetry of figures with this Learning Math Interactivity (360 ÷ number of sides) Flipscript Ambigram Generator Create rotational symmetry with your name! Unit 5 TIP #2 Circles and Rotational Symmetry -Circle has 360 of turn -Benchmark angles- 90, 180, 270, 360 are reference points to estimate degrees of turn -Degree of rotational symmetry for regular polygons is equal to 360 ÷ number of sides .

UNIT 6 Tips & Strategies Keys to reading a ruler- Similar figures- identifying units as metric or customary finding number of equal parts in each unit knowing how to write parts of a unit Similar figures- corresponding parts have the same ratio which means sides are ‘proportional’ measures of corresponding parts keep the same position in both ratios of a proportion

Customary (aka standard) Unit 6 TIP #1 Metric What is the length of the line to the nearest tenth of a cm? click to see Customary (aka standard) What is the length of the line to the nearest 𝟏 𝟏𝟔 inch Reading a ruler: -Metric lengths less than one cm are measured in tenths (each cm is divided into ten equal parts) & written in decimal form; - Customary lengths less than one inch are measured as halves, fourths, eighths, or sixteenths (each inch is divided into 2, 4, 8, or 16 equal parts) and written as fractions in lowest terms Read A Ruler Game FunBrain measurement 3.3 cm . 1 𝟓 𝟏𝟔 in.

Corresponding Parts & Proportions Similar Triangles ABC and A’B’C’ Unit 6 TIP #2 Corresponding Parts & Proportions Similar Triangles ABC and A’B’C’ 𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ𝑠 𝑜𝑓 ∆𝐴 𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ𝑠 𝑜𝑓 ∆𝐵 = 4 20 = 6 30 = 9 45 The ratio of the side lengths of ∆𝐴 :∆𝐵 is 1:5 Similar Figures * corresponding parts have the same ratio which means side lengths are ‘proportional’ * measures of corresponding parts keep the same position in each ratio Math.com lesson Similar Triangles applet ∆𝐴 ∆𝐵 .

UNIT 7 Tips & Strategies Memorize common measurement equivalents Corresponding units keep the same position in both ratios of a proportion when converting measures within a system Graphing Ordered Pairs (x, y) x is first in the ordered pair and graphed on the horizontal axis (left to right) y is second in the ordered pair and graphed on the vertical axis (up and down) A direct variation may be represented in an input-output table on the coordinate plane as the graph of a line as an equation y=kx

Memorize common equivalents NLVM Converting Units Interactivity Matching customary equivalents Matching metric equivalents Unit 7 TIP #1 .

Unit 7 TIP #2 Corresponding units keep the same position in both ratios of a proportion when converting measures within a system Take Lessons 9-3 and 9-4 Interactive Practice Quizzes and learn more about proportions in Lesson 7-3 using the online textbook resources @ myhrw.com 9-3 Interactive Practice Quiz 9-4 Interactive Practice Quiz 7-3 Proportion Interactivity

Unit 7 TIP #3 Graphing Ordered Pairs (x, y) Graph Mole- 3 versions FunBrain What’s the Point? Billy Bug game Math-play Coordinate plane game Unit 7 TIP #3 Graphing Ordered Pairs (x, y) - x comes first in the ordered pair and is graphed on the horizontal axis (left to right) - y is second in the ordered pair and is graphed on the vertical axis (up and down) .

Representations of Direct Variation Map Scale Direct Variation Unit 7 TIP #4 Representations of Direct Variation rule table equation graph To learn more look in your Holt textbook @ the Chapter 11 Extension, Direct Variation, pp652-653 or watch Direct Variation video tutorial about weights on the moon and on earth. Number of inches Number of miles . Can you find . . . the number of miles 2 inches represents using the equation? the table? the graph?

UNIT 8 Tips & Strategies Classify prisms, pyramids, cylinders, and cones and recognize their nets using properties of solids Faces Bases Edges Practice applying formulas for: Area of rectangles, triangles, and circles Volume of prisms and cylinders Surface area is total area of all faces and bases Use the correct units for what is being measured

Unit 8 TIP #1 Solids- cylinders, cones, prisms, and pyramids- are classified by their common properties: Faces Bases Edges 3-D Interactivity with 2-D nets Which 3-D solid will this 2-D net form when folded? click here for answer: . Square pyramid

Practice applying formulas for surface area and volume of solids. Unit 8 TIP #2 Practice applying formulas for surface area and volume of solids. Don’t forget to check the front page of the CRCT Test for formulas! formulas practice (scroll down for lesson links)