McGraw Hill Math Grade 8, Third Edition

By McGraw Hill

An engaging math workbook to help your 8th grade student master the skills necessary to perform better in class and on standardized tests

Colorful, dynamic, and filled with engaging activities, McGraw Hill Math Grade 8, Third Edition provides maximum educational value, giving your 8th grader a student-friendly learning experience to learn and practice the skills they need to do well in school and on standardized tests.

Based on the curriculum standards followed by states across the U.S., McGraw Hill Math Grade 8 covers key topics with easy-to-follow instructions, helpful examples, and more than 1,000 practice problems with answers. End-of-chapter tests allow your child to see where mastery has been gained and what they need to focus on. As they master each concept, you child will sharpen their problem-solving skills and build the confidence they need to succeed in eighth grade math.

Features include:

• NEW Addition of “real-world” questions and multi-step problems
• A state-by-state guide shows you how to focus your child’s lessons
• The guide shows which states have adopted Common Core State Standards, how each state has implemented the standards for math, and outlines the standards for non-Common Core states
• 1,000+ math problems with explanations for answers
• A 10-Week Summer Study Plan shows you how to create the best study schedule for your child
• A pretest helps your child determine which skills require more attention
• End-of-chapter tests helps your child assess if they’ve mastered the chapter’s concepts
• Posttest at the end of the book shows your child how well they understand key concepts
• A glossary explains key terms that students will encounter in the book

Topics covered:

• Solving problems with rational numbers
• Approximating irrational numbers
• Ratios, proportions, and percents
• Roots and exponents
• Performing operations with scientific notation
• Analyzing and solving linear equations and pairs of linear equations
• Graphing proportional relationships and functions
• Customary and metric units of measure, including conversions
• Geometric transformations
• Using the Pythagorean Theorem
• Solving problems involving volume of cones and spheres
• Analyzing patterns in bivariate data, including probability

• Language: English
• Publisher: McGraw-Hill Education
• Release date: Aug 11, 2022
• ISBN: 9781264285723

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Table of Contents

Letter to Parents and Students

Eighth Grade National and State Math Standards

Pretest

Answers and Explanations for Pretest

Unit 1: Operations with Rational Numbers

Chapter 1: Fundamentals

Lesson 1.1     Order of Operations

Lesson 1.2     Properties

Chapter 2: Negative Numbers

Lesson 2.1     Negative Numbers

Lesson 2.2     Adding and Subtracting Negative Numbers

Lesson 2.3     Multiplying and Dividing Negative Numbers

Chapter 3: Fractions and Mixed Numbers

Lesson 3.1     Changing Improper Fractions to Mixed Numbers

Lesson 3.2     Changing Mixed Numbers to Improper Fractions

Lesson 3.3     Adding and Subtracting Fractions with Like Denominators

Lesson 3.4     Adding or Subtracting Fractions with Unlike Denominators

Lesson 3.5     Adding or Subtracting Mixed Numbers with Unlike Denominators

Lesson 3.6     Reducing Fractions

Chapter 4: Multiplying Fractions

Lesson 4.1     Multiplying Fractions and Whole Numbers

Lesson 4.2     Multiplying Two Fractions; Reciprocals

Lesson 4.3     Multiplying Fractions and Mixed Numbers

Lesson 4.4     Multiplying Mixed Numbers

Chapter 5: Dividing Fractions

Lesson 5.1     Dividing Fractions by Whole Numbers

Lesson 5.2     Dividing Whole Numbers by Fractions

Lesson 5.3     Dividing Fractions by Fractions

Lesson 5.4     Dividing Mixed Numbers

Chapter 6: Understanding Decimals

Lesson 6.1     Place Value and Rounding

Lesson 6.2     Changing Fractions to Decimals

Lesson 6.3     Changing Decimals to Fractions

Lesson 6.4     Comparing and Ordering Decimals

Chapter 7: Adding and Subtracting Decimals

Lesson 7.1     Adding Decimals

Lesson 7.2     Subtracting Decimals

Chapter 8: Multiplying and Dividing Decimals

Lesson 8.1     Multiplying with Decimals

Lesson 8.2     Dividing with Decimals

Review     Rational Numbers

Unit 1 Test

Unit 2: Ratios, Proportions, and Percents

Chapter 9: Ratios & Proportions

Lesson 9.1     Ratios

Lesson 9.2     Proportions and Cross-Multiplying

Lesson 9.3     Rates

Chapter 10: Percents

Lesson 10.1   Proportions and Percent

Lesson 10.2   Percent Change, Mark-up, and Discount

Lesson 10.3   Percents and Fractions

Lesson 10.4   Multiplying Percents and Fractions

Lesson 10.5   Percents and Decimals

Lesson 10.6   Simple and Compound Interest

Unit 2 Test

Unit 3: Exponents & Roots

Chapter 11: Exponents

Lesson 11.1   Multiplying and Dividing Exponents

Lesson 11.2   Powers

Lesson 11.3   More about Exponents

Chapter 12: Roots

Lesson 12.1   Squares and Square Roots

Lesson 12.2   Irrational Numbers

Chapter 13: Scientific Notation

Lesson 13.1   Understanding Scientific Notation

Lesson 13.2   Estimation and Comparison

Unit 3 Test

Unit 4: Equations & Inequalities

Chapter 14: Variable Expressions

Lesson 14.1   Understanding Variable Expressions

Lesson 14.2   Solving Equations with Addition and Subtraction

Lesson 14.3   Solving Equations with Multiplication and Division

Lesson 14.4   Solving 2-Step Equations

Lesson 14.5   Equations with Infinite or No Solutions

Chapter 15: Inequalities

Lesson 15.1   Understanding Inequalities

Lesson 15.2   Solving Inequalities by Addition and Subtraction

Lesson 15.3   Solving Inequalities by Multiplication and Division

Unit 4 Test

Unit 5: The Coordinate Plane

Chapter 16: Functions

Lesson 16.1   Plotting Ordered Pairs

Lesson 16.2   Function Tables

Chapter 17: Graphing Lines and Relationships

Lesson 17.1   Solve Equations by Graphing

Lesson 17.2   Slope

Lesson 17.3   Graphing Relationships

Unit 5 Test

Unit 6: Measurement

Chapter 18: Customary Units of Measure

Lesson 18.1   Customary Units of Length

Lesson 18.2   Customary Units of Liquid Volume

Lesson 18.3   Customary Units of Weight

Lesson 18.4   Perimeter with Customary Units

Lesson 18.5   Area with Customary Units

Chapter 19: Metric Units of Measure

Lesson 19.1   Metric Units of Length

Lesson 19.2   Metric Units of Liquid Volume

Lesson 19.3   Metric Units of Mass

Lesson 19.4   Calculating Perimeter and Area with Metric Units

Chapter 20: Equivalent Measures

Lesson 20.1   Changing from Customary Units to Metric Units

Lesson 20.2   Changing from Metric Units to Customary Units

Lesson 20.3   Customary and Metric Units of Temperature

Unit 6 Test

Unit 7: Geometry

Chapter 21: Basic Concepts of Geometry

Lesson 21.1   Points and Lines

Lesson 21.2   Line Segments and Rays

Lesson 21.3   Measuring and Naming Angles

Lesson 21.4   Types of Angles

Lesson 21.5   Finding Missing Angle Measurements

Chapter 22: Triangles

Lesson 22.1   Types of Triangles

Lesson 22.2   Congruent and Similar Triangles

Lesson 22.3   Right Triangles and Pythagorean Theorem

Chapter 23: Geometric Figures

Lesson 23.1   Quadrilaterals

Lesson 23.2   Polygons

Lesson 23.3   Circles

Lesson 23.4   Symmetry and Transformations

Chapter 24: Solid Figures

Lesson 24.1   Surface Area of Solid Figures

Lesson 24.2   Volume of Solid Figures

Unit 7 Test

Unit 8: Data & Statistics

Chapter 25: Data Presentation

Lesson 25.1   Bar Graphs

Lesson 25.2   Line Graphs

Lesson 25.3   Double-Line Graphs

Lesson 25.4   Circle Graphs

Chapter 26: Visualizing Statistics and Probabilities

Lesson 26.1   Measures of Central Tendency

Lesson 26.2   Stem-and-Leaf Plots

Lesson 26.3   Box-and-Whisker Plots

Lesson 26.4   Tree Diagrams

Lesson 26.5   Venn Diagrams

Lesson 26.6   Calculating Probabilities

Unit 8 Test

Posttest

Answers and Explanations for Posttest

Glossary

Answers and Explanations

Letter to Parents and Students

Welcome to McGraw Hill’s Math!

Parents, this book will help your child succeed in eighth grade mathematics. It will give your eighth grader:

•   A head start in the summer before eighth grade

•   Extra practice during the school year

•   Helpful preparation for standardized mathematics exams

The book is aligned to National and State Standards. A chart beginning on the next page summarizes those standards and shows how each state that does not follow the national standards differs from those standards. The chart also includes comparisons to Canadian standards.

If you live in a state that has adopted the national Common Core standards, you won’t need the information in this table, although you may find its summary of Common Core standards helpful. Parents who live in Canada or states that have not adopted Common Core standards will find the table a useful tool and can be reassured that most of these regions have standards that are very similar to the national standards. This book contains ample instruction and practice for students in any state or in Canada.

Students, this book will help you do well in mathematics. Its lessons explain math concepts and provide lots of interesting practice activities.

Open your book and look at the Table of Contents. It tells what topics are covered in each lesson. Work through the book at your own pace.

Begin with the Pretest, which will help you discover the math skills you need to work on.

Each group of lessons ends with a Unit Test. The results will show you what skills you have learned and what skills you may need to practice more. A Posttest completes your work in this book and will show how you have done overall.

Take time to practice your math. Practicing will help you use and improve your math skills.

Good luck!

Eighth Grade National and State Math Standards

Pretest

Complete the following test items.

Kathy runs 16 miles a week. If she continues to run at this rate, how many miles will she run in a year?

_________________________

The women’s clothing department at Ms. Smith’s store had a sale on jeans. There were 945 jeans in stock at the beginning of the sale and another 254 jeans were ordered. At the end of the sale the store still had 245 jeans in stock. How many jeans were sold during the sale?

_________________________

Jack has 16 lengths of rope. Each is meters long. How much rope does Jack have to divide among 20 people?

_________________________

How much rope will each person receive?

_________________________

David has 176 ounces of hot sauce to divide among the 32 contestants in a chicken-wing eating contest. How many cups is that per contestant?

_________________________

_________________________

_________________________

Solve for x: x − 7 = 14

_________________________

Solve for x: 2x + 6 = 18

_________________________

Solve: 10 + (8 − 6)² − (12 ÷ 4) + 5(6 × 2) + 3(7 − 4) =

Restate in exponent form, then solve: 5 × 5 + 2 × 2 × 2 + 3 × 3 =

__________________________________________________

3.55 meters = _______ inches (Use 2.54 cm = 1 inch)

10 yards = _______ centimeters

What is the area of the rectangle? ________

What is the perimeter?

_________________________

What is the perimeter, in inches, using the conversion factor of 2.54 cm to the inch?

_________________________

What is the area of the circle? _______ (Use 3.14 for π.)

What is the circumference of the circle?

_________________________

Identify each angle as obtuse, acute, or right.

Identify each triangle as scalene, isosceles, or equilateral.

Calculate and reduce the fractions.

Give the coordinates for points on the grid.

What is the slope of a line drawn between points A and B?

_________________________

What is the measure of angle DBC?

_________________________

What is 40% of 0.775? ____________

What is of 72%? ____________

Restate 4.25 as an improper fraction and a mixed number.

Improper Fraction _______________ Mixed Number _______________

Put the following numbers in order from least to greatest. 1.162, 1.161, 2.16302, 2.163, 2.8022, 1.90688, 1.9122, 1.099

__________________________________________________

Solve for x. _______________

Restate as a decimal. _______________

Sarah manufactured surfboards at a cost of $45.00 each. She wants to sell the surfboards at a 50% markup. What will be the selling price for each?

_________________________

Dexter deposits $200 in a bank account that earns 3% simple interest. How much money