# Cliffsnotes Grade 6 Common Core Math Review

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## Overview

Nearly half of adults, including parents of middle-school students, have never heard of the Common Core State Standards, let alone have a working knowledge of what exactly their children face when it comes to middle-school math. Even teachers acknowledge struggling with how best to teach their students these math standards.

CliffsNotes comes to the rescue with this Grade 6 Common Core Math Review. Aligned to the state standards, this book provides essential coverage of the Grade 6 CCSS math that's challenging middle-school students, teachers, and parents alike.

The material covers all of the math standards that comprise Grade 6 CCSS math:

- Ratios and proportional relationships

- The number system

- Geometry

- Expressions and equations

- Statistics and probability

Two practice tests round out the book, plus every review chapter includes example problems.

## Product Details

ISBN-13: 9780544373327 Houghton Mifflin Harcourt 06/01/2015 New edition 226 1,228,237 7.30(w) x 9.10(h) x 0.70(d) 10 - 12 Years

SANDRA LUNA McCUNE, Ph.D., is a former Regents Professor and math specialist in the Department of Elementary Education at Stephen F. Austin State University, where she received the Distinguished Professor Award. She now is a full-time author and consultant.

Introduction ix

Ratios and Proportional Relationships ix

Understand ratio concepts and use ratio reasoning to solve problems ix

The Number System x

Apply and extend previous understandings of multiplication and division to divide fractions by fractions x

Compute fluently with multi-digit numbers and find common factors and multiples x

Apply and extend previous understandings of numbers to the system of rational numbers xi

Expressions and Equations xii

Apply and extend previous understandings of arithmetic to algebraic expressions xii

Reason about and solve one-variable equations and inequalities xii

Represent and analyze quantitative relationships between dependent and independent variables xiii

Geometry xiii

Solve real-world and mathematical problems involving area, surface area, and volume xiii

Statistics and Probability xiv

Develop understanding of statistical variability xiv

Summarize and describe distributions xiv

Mathematical Practice xv

1 Ratios and Proportional Relationships 1

Understanding the Concept of a Ratio 1

(CCSS.Math.Content.6.RP.A. 1) Generating and Using Equivalent Ratios 3

(CCSS.Math.Content.6.RP.A. 1, CCSS.Math.Content.6.RP.A.3.A) Simplifying Ratios 6

(CCSS.Math.Content.6.RP.A. 1, CCSS.Math.Content.6.RP.A.3.A, CCSS.Math.Content.6.RP.A.3.D) Using the Value of a Ratio 7

(CCSS.Math.Content.6.RP.A.1, CCSS.Math.Content.6.RR.A.3.A) Writing Equations for Ratios 9

(CCSS.Math.Content.6.RP.A.1,CCSS.Math.Content.6.RP.A.3.A, CCSS.Math.Content.6.RP.A.3.D) Understanding the Concept of a Rate 14

(CCSS.Math.Content.6 RP.A.2) Using Unit Price for Comparison Shopping 16

(CCSS.Math.Content.6.RP.A.2, CCSS.Math.Content.6.RP.A.3.B) Converting Measurement Units 18

(CCSS.Math.Content.6.RR.A.2, CCSS.Math.Contenr.6.RP.A.3.D) Solving Unit Rate Problems 21

(CCSS.Math.Content.6.RP.A.2, CSS.Math.Content.6.RP.A.3.B, CCSS.Math.Content.6RP.A.3.D) Understanding Percent 24

(CCSS.Math.Content.6.RP.A.1, CCSS Math.Content.6.RP.A.3.C) Simplifying Percent Ratios 26

(CCSS.Math.Content.6.RP.A.1, CCSS.Math.Content.6.RP.A.3.C) Solving Percent Problems 27

(CCSS.Math.Content.6.RP.A.1, CCSS.Math.Content.6.RP.A.3.C) Finding the Part, Given the Percent and the Whole 27

Finding the Whole, Given the Percent and the Part 29

2 The Number System 33

Dividing Fractions by Fractions 33

(CCSS.Moth.Content.6.NS.A. 1, CCSS.Math.Content.6.NS.B.4) Dividing a Whole Number by a Fraction 33

Dividing Fractions (Like Denominators) 34

Dividing Fractions (Unlike Denominators) 37

Performing Operations with Multi-Digit Decimals Using Standard Algorithms 39

(CCSS.Math.Content.6.NS.B.2, CCSS.Math.Content.6.NS.B.3) Adding and Subtracting Multi-Digit Decimals 39

Multiplying Multi-Digit Decimals 42

Dividing Multi-Digit Decimals 43

Finding the Greatest Common Factor and Least Common Multiple of Two Whole Numbers (CCSS.Math.Content.6.N5.C.5) 47

Finding the Greatest Common Factor of Two Numbers 47

Finding the Least Common Multiple of Two Numbers 50

Understanding the Integers 51

(CCSS.Math.Content.6.NS.C.6.A, CCSS.Math.Content.6.NS.C.6.C) Understanding the Rational Numbers 53

(CCSS.Math.Content.6.NS.C.6.A, CCSS Math.Content.6.NS.C.6.C) Comparinq and Ordering Rational Numbers 56

(CCSS.Math.Content.6.NS.C.6.C, CCSS.Math.Content.6.NS.C.7.A) Common Inequality Symbols 56

Understanding Absolute Value of Rational Numbers 61

(CCSS.Math.Content.6.NS.C.6A,CCSS.Math.Content.6.NS.C.7.C,CCSS.Math.Content.6.NS.C.7.D) Using-Rational Numbers in the Real World 63

(CCSS.Math.Content.6.NS.C.5, CCSS.Math.Content.6.NS.C.7.B,CCSS.Math.Content.6.NS.C.7.C, CCSS.Math.Content.6.NS C.7.D)

Plotting Points and Finding Distances Between Points in the Coordinate Plane 66

(CCSS.Math.Content.6.NS.C.6.A, CCSS.Math.Content.6.NS.C.6.B, CCSS.Math.Content.6.NS.C.6.C, CCSS.Math.Content.6NS.C.8)

Plotting Points in the Coordinate Plane 67

Finding Distances Between Points in the Coordinate Plane 75

3 Expressions and Equations 81

Understanding and Evaluating Exponential Expressions Involving Whole-Number Exponents 81

(CCSS.Math.Content.6.EE.A.1) Evaluating Numerical Expressions (CCSS.Math.Content.6.EE.A.1) 83

Understanding Variables and Expressions in Which Letters Stand for Number (CCSS.Math.Content.6.EE.A.2.B, CCSS.Math.Content.6.EE.B.6) 85

Writing and Reading Expressions in Which Letters Stand for Numbers (CCSS.Math.Content.6.EE.A.2.A,CCSS.Math.Content.6.EE.A.2.B,CCSS.Math Content.6.EE.B.6) 87

Writing and Reading Subtraction Expressions 89

Writing and Reading Multiplication Expressions 92

Writing and Reading Division Expressions 94

Evaluating Expressions at Specific Values of Their Variables (CCSS.Math.Content.6.EE.A.2.C) 97

Identifying and Generating Equivalent Expressions (CCSS.Math.Content.6.EE.A.3, CCSS.Math.Content.6.EE.A.4) 99

Solving One-Step Single-Variable Mathematical and Real-World Equations 103

(CCSS.Math.Content.6.EE.B.5, CCSS.Math.Content.6.EE.B.6, CCSS.Math.Content.6.EE.B.7) 103

Solving One-Step Mathematical Equations of the Forms x + p = q and x - p = q 105

Solving One-Step Mathematical Equations of the Forms px = q and x/p = q 108

Solving Real-World One-Step Equations of the Forms x + p = q, x - p = q, px = q, and x/p = q 111

Understanding and Using Inequalities of the Form x < c and x > c (CCSS.Math.Content.6.EE.B.8) 114

Representing and Analyzing Relationships Between Two Variables (CCSS.Math.Content.6.EE.C.9) 116

4 Geometry 119

Finding the Area of Triangles (CCSS.Math.Content.6.G.A.1) 119

Finding the Area of Parallelograms and Rectangles (CCSS.Math.Content.6.G.A.1) 122

Finding the Area of Special Quadrilaterals and Other Polygons by Composing or Decomposing into Rectangles, Triangles, and Other Shapes (CCSS.Math.Content.6.G.A.1) 124

Finding Perimeter and Area of Polygons in the Coordinate Plane (CCSS Math.Content.6.G.A.3) 128

Finding the Volume of Right Rectangular Prisms (CCSS.Math.Content.6.G.A.2) 135

Using Nets to Find the Surface Area of Three-Dimensional Figures (CCSS.Math.Content.6.G.A.4) 137

5 Statistics and Probability 143

Recognizing Statistical Questions (CCSS.Math.Content.6.SP.A.1) 143

Graphically Representing Data (CCSS.Math.Content.6.SP.A.2, CCSS.Math.Content.6.SP.B.4, CCSS.Math.Content.6.SP.B.5A, CCSS.Math Content.6.SP.B.5.B) 144

Understanding and Creating Dot Plots 145

Understanding and Creating Histograms 146

Understanding and Determining Measures of Center (CCSS.Math.Content.6.SP.A.2, CCSS.Math.Content.6.SP.A.3, CCSS.Math.Content.6.SP.B.4, CCSS.Math.Content.6.SP.B.S.B,CCSS.Math.Content.6.SP.B.5.C, CCSS.Math.Content.6.SP.B.5.D) 150

Understanding and Determining the Mean of a Data Set 151

Understanding and Determining the Median of a Data Set 152

Understanding and Determining the Mode of a Data Set 153

Choosing Among the Mean, Median, and Mode 154

Understanding and Determining Measures of Variation (CCSS.Math.Content.6.SP.A.2, CCSS.Math.Content.6.SP.A.3, CCSS.Math.Content.6.SP.B.4, CSS.Math.Contentt.6.SP.B.5.B, CCSS.Math.Content.6.SP.B.5.D) Understanding and Determining the Range 158

Understanding and Determining the Mean Absolute Deviation (MAD) 159

Understanding and Determining the interquartile Range (IQR) 160

Determining the Five-Number Summary and Creating Box Plots 163

(CCSS.Math.Content.6.SP.A.4, CCSS.Math.Content.6.SP.B.A, CCSS.Math.Content.6.SP.B.5.C) 163

6 Practice Test 1 167

7 Practice Test 2 187