CRCT Test-takingTips & Strategies

UNIT 1 TIPS & STRATEGIESBefore 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?

Unit 1

TIP #2Read 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) 21B) 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 #1To find factors of a number, test divisibility by numerical order starting with 1, then 2, then 3 and so on. Record factors in pairs.

48

48 ÷ 1 = 48

48 ÷ 2 = 24

48 ÷ 3 = 16

48 ÷ 4 = 12

48 ÷ 6 = 8

48 ÷ 8 = 6

STOPwhen the factors

‘turn around’

Factors of 48:• 1, 48, 2, 24, 3,

16, 4, 12, 6, 8 or

• 1, 2, 3, 4, 6, 8, 12, 16, 24, & 48

Unit 2

TIP #2GCF- Starting with the greatest factor of the smallest number, see if the larger number is also divisible by the smallest number’s factors.

GCF of 48 and 72 Factors of 48:48 ÷ 1 = 48 1, 4848 ÷ 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 72GCF Venn Diagram

Unit 2

TIP #3LCM- Starting with the least multiple of the greatest number, see if the greatest number’s multiples are also multiples of the smaller number.

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

Unit 2

TIP #4Prime 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

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

Unit 3

TIP #1Equivalent Fractions

• Simplest Form/Lowest Terms

= =

GCF of is 1• Higher Terms (used in + & -) Numerator & denominator are multiplied by a fraction form of one*

Funbrain Equivalent Fractions Choose medium to hard difficulty!

Fractions can be written in

lowest terms

or higher terms

by multiplying

or dividing by

a fraction

form of 1*

Unit 3

TIP #2Comparing Fractions

• Same N

• Same D

• Different N & D 1st 2nd

MathPlayground Compare applet

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

Unit 3

TIP #3Estimate b4u Operate

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.

Unit 3

TIP #4Fraction

Multiplication & Divisionmultiplicationalgorithm

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!

divisionalgorithm

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!

Fraction multiplication

means taking part of a part;

Fraction division is always rewritten

as multiplication.

Unit 3

TIP #5Fraction-Decimal-Percent

Equivalents

Fraction to Decimal Divide the N by the D

Decimal to PercentMultiply by 100

Decimal to FractionRead It-Write It-Reduce It

This diagram summarizes how to convert fractions to decimals to percent

Wisc-online slideshow f-d-% conversions

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

Unit 4

TIP #1Order of Operations• Grouping Symbols

– parentheses ( ) – brackets [ ] – fraction bar

• Exponents• Multiplication or Division (L to R)• Addition or Subtraction (L to R)

Amby's Order of Operations Tutorial & Practice

Always follow the order of operations

when evaluating

expressions

Unit 4

TIP #2Balanced 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 - NumbersPan Balance – Algebraic Expressions with graph

Equations have two sides that are always balanced.

Unit 4

TIP #3Inverse Operations

Addition - - - - - - - - - - - - Subtraction2 + 3 = 5 5 – 3 = 2x + 3 = 5 5 – 3 = xSubtraction - - - - - - - - - - - - Addition8 – 3 = 5 5 + 3 = 8x – 5 = 3 3 + 5 = x Multiplication - - - - - - - - - - Division3 4 = 12 12 ÷ 3 = 4 3 x = 12 12 ÷ 3 = x Division - - - - - - - - - - - - - Multiplication28 ÷ 7 = 4 4 7 = 28x ÷ 7 = 4 4 7 = x

Inverse operations

‘undo’ useful for solving equations

Inverse Operations in 1-Step Equations

Unit 4

TIP #4 Patterns to RulesPattern: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 4 5 ?

3 4 5 6 7 8 9 10 110

1

2

3

4

5

6

f(x) = 0.5 x

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

Unit 5

TIP #1 Line SymmetryAn 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?

Unit 5

TIP #2Circles 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

Practice estimating degrees of turn in a circle @ Banana Hunt

Calculate rotational symmetryof figures with this Learning Math Interactivity (360 ÷ number of sides)

Flipscript Ambigram Generator Create rotational symmetry with your name!

UNIT 6 TIPS & STRATEGIES• Keys to reading a ruler-

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

Unit 6

TIP #1Metric

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 inch click to see

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 termsRead A Ruler GameFunBrain measurement

3.3 cm

1 in.

Unit 6

TIP #2Corresponding

Parts & ProportionsSimilar Triangles ABC and A’B’C’

The ratio of the side lengths of

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 lessonSimilar 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

Unit 7

TIP #1Memorize

common equivalents

NLVM Converting Units InteractivityMatching customary equivalentsMatching metric equivalents

Corresponding units keep the same position in both ratios of a proportion when converting measures within a system

Unit 7

TIP #2

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.com9-3 Interactive Practice Quiz9-4 Interactive Practice Quiz7-3 Proportion Interactivity

Unit 7

TIP #3

Graph Mole- 3 versionsFunBrain What’s the Point?Billy Bug game

Math-play Coordinate plane game

GraphingOrdered 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)

Unit 7

TIP #4 Map Scale Direct Variation

Representations of

Direct Variation- rule - table- equation- graphTo learn more look in your Holt textbook @ the Chapter 11 Extension, Direct Variation, pp652-653 or watchDirect Variation video tutorial about weights on the moon and on earth.

Can you find . . .the number of miles 2 inches represents using the equation? the table? the graph?

Number of inches

Number of miles

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

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)