practice and homework book grade 6 pdf

We’re fighting to restore access to 500,000+ books in court this week. Join us!

Internet Archive Audio

• This Just In
• Grateful Dead
• Old Time Radio
• 78 RPMs and Cylinder Recordings
• Audio Books & Poetry
• Computers, Technology and Science
• Music, Arts & Culture
• News & Public Affairs
• Spirituality & Religion
• Radio News Archive

• Flickr Commons
• Occupy Wall Street Flickr
• NASA Images
• Solar System Collection
• Ames Research Center

• All Software
• Old School Emulation
• MS-DOS Games
• Historical Software
• Classic PC Games
• Software Library
• Kodi Archive and Support File
• Vintage Software
• CD-ROM Software
• CD-ROM Software Library
• Software Sites
• Tucows Software Library
• Shareware CD-ROMs
• Software Capsules Compilation
• CD-ROM Images
• ZX Spectrum
• DOOM Level CD

• Smithsonian Libraries
• FEDLINK (US)
• Lincoln Collection
• American Libraries
• Canadian Libraries
• Universal Library
• Project Gutenberg
• Children's Library
• Biodiversity Heritage Library
• Books by Language
• Additional Collections

• Prelinger Archives
• Democracy Now!
• Occupy Wall Street
• TV NSA Clip Library
• Animation & Cartoons
• Arts & Music
• Computers & Technology
• Cultural & Academic Films
• Ephemeral Films
• Sports Videos
• Videogame Videos
• Youth Media

Search the history of over 866 billion web pages on the Internet.

Mobile Apps

• Wayback Machine (iOS)
• Wayback Machine (Android)

Browser Extensions

Archive-it subscription.

• Explore the Collections
• Build Collections

Save Page Now

Capture a web page as it appears now for use as a trusted citation in the future.

Please enter a valid web address

• Donate Donate icon An illustration of a heart shape

Math makes sense. 6

Bookreader item preview, share or embed this item, flag this item for.

• Graphic Violence
• Explicit Sexual Content
• Hate Speech
• Misinformation/Disinformation
• Marketing/Phishing/Advertising
• Misleading/Inaccurate/Missing Metadata

plus-circle Add Review comment Reviews

343 Previews

7 Favorites

DOWNLOAD OPTIONS

No suitable files to display here.

PDF access not available for this item.

IN COLLECTIONS

Uploaded by station54.cebu on February 26, 2022

SIMILAR ITEMS (based on metadata)

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice

Measurement

• Factoring & prime factors

Proportions

• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Sentences & passages
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

Download & Print From only $2.60

Sixth Grade Math Worksheets

Free grade 6 worksheets from k5 learning.

Our printable grade 6 math worksheets delve deeper into earlier grade math topics (4 operations, fractions, decimals, measurement, geometry) as well as introduce exponents, proportions, percents and integers .

Choose your grade 6 topic:

4 operations.

Place Value & Scientific Notation

Add & Subtract

Multiply & Divide

Decimals & Percents

Fractions to / from Decimals

Decimals - Add and Subtract

Decimals  - Multiply

Decimals - Divide

Add & Subtract Fractions

Multiply & Divide Fractions

Converting Fractions

Sample Grade 6 Math Worksheet

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

Join K5 to save time, skip ads and access more content. Learn More

• Forgot Password?

Return to Free Lessons

Practice Books, Grades K–5

Bridges Practice Books provide activities and worksheets for additional skill review, informal paper-and-pencil assessment, preparation for standardized testing, and differentiated instruction. Each volume also includes answer keys and a complete listing of the student pages grouped by skill. Although originally written to complement Bridges in Mathematics First Edition, these books may be used with any math program. Note: These materials were developed prior to the publication of the Common Core State Standards. While the content retains its educational value, the grade level alignment may have shifted for some lessons and activities.

Bridges Kindergarten Practice Book, 1st Edition

Grade level: k.

Numbers to 30, comparing and ordering sets, skip counting, early addition and subtraction, story problems.

Download English PDF Download Spanish PDF

Bridges Grade 1 Practice Book, 1st Edition

Grade level: 1.

Numbers to 100 and beyond, number patterns, place value, facts to 10, money, time, graphing, and problem solving.

Bridges Grade 2 Practice Book, 1st Edition

Grade level: 2.

Numbers to 1,000, skip counting and number patterns, facts to 18, place value, double-digit computation, money, time, and problem solving.

Bridges Grade 3 Practice Book, 1st Edition

Grade level: 3.

Numbers to 10,000, multi-digit addition and subtraction, multiplication and division concepts, fractions, equations, perimeter, time, money, and problem solving.

Bridges Grade 4 Practice Book, 1st Edition

Grade level: 4.

Multiplication and division facts, multi-digit addition, subtraction and multiplication, fractions and decimals, patterns and equations, area and perimeter, data analysis, and problem solving.

Bridges Grade 5 Practice Book, 1st Edition

Grade level: 5.

• Interactivity
• AI Assistant
• Digital Sales
• Online Sharing
• Offline Reading
• Custom Domain
• Branding & Self-hosting
• SEO Friendly
• Create Video & Photo with AI
• PDF/Image/Audio/Video Tools
• Art & Culture
• Food & Beverage
• Home & Garden
• Weddings & Bridal
• Religion & Spirituality
• Animals & Pets
• Celebrity & Entertainment
• Family & Parenting
• Science & Technology
• Health & Wellness
• Real Estate
• Business & Finance
• Cars & Automobiles
• Fashion & Style
• News & Politics
• Hobbies & Leisure
• Recipes & Cookbooks
• Photo Albums
• Invitations
• Presentations
• Newsletters
• Sell Content
• Fashion & Beauty
• Retail & Wholesale
• Presentation
• Help Center Check out our knowledge base with detailed tutorials and FAQs.
• Learning Center Read latest article about digital publishing solutions.
• Webinars Check out the upcoming free live Webinars, and book the sessions you are interested.
• Contact Us Please feel free to leave us a message.

Go Math! Grade 6 Student Edition

Description: Go Math! Grade 6 Student Edition

Read the text version.

No Text Content!

6 GRADE DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

© Houghton Mifflin Harcourt Publishing Company Copyright © by Houghton Mifflin Harcourt Publishing Company All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system, without the prior written permission of the copyright owner unless such copying is expressly permitted by federal copyright law. Requests for permission to make copies of any part of the work should be submitted through our Permissions website at https://customercare.hmhco.com/contactus/Permissions. html or mailed to Houghton Mifflin Harcourt Publishing Company, Attn: K–12 School Permissions, 9400 Southpark Center Loop, Orlando, Florida 32819-8647. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National Governors Association Center for Best Practices and the Council of Chief State School Officers. Printed in the U.S.A. ISBN 978-0-358-78420-3 1 2 3 4 5 6 7 8 9 10 XXXX 31 30 29 28 27 26 25 24 23 22 4500000000 r12.22 If you have received these materials as examination copies free of charge, Houghton Mifflin Harcourt Publishing Company retains title to the materials and they may not be resold. Resale of examination copies is strictly prohibited. Possession of this publication in print format does not entitle users to convert this publication, or any portion of it, into electronic format. InCopy Notes 1. This is a list Bold, Italic, Strikethrough. 2. I replaced the hyphen with an en dash in "K-12." -RG 11/9/2022 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A

iii © Houghton Mifflin Harcourt Publishing Company • Image Credit: ©HMH Dear Students and Families, Welcome to Go Math! In this program, you will develop skills and make sense of mathematics by solving real-world problems, using hands-on tools and strategies, and collaborating with your classmates. With the support of your teacher and by engaging with meaningful practice, you will learn to persevere when solving problems. Go Math! will not only help you deepen your understanding of mathematics, but also build your confidence as a learner of mathematics. Even more exciting, you will write all your ideas and solutions right in your book. In your Go Math! book, writing and drawing on the pages will help you think deeply about what you are learning, help you truly understand math, and most important, help you become a confident user of mathematics! Sincerely, The Authors InCopy Notes 1. This is a list DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

iv © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Lee Dalton/Alamy Images; (bl) ©Image Plan/Corbis; (br) ©PixelsEffect/Getty Images Launch Activity 1 The Number System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 CHAPTER 1 Whole Numbers and Decimals Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Lesson 1 Divide Multi-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Lesson 2 Prime Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Lesson 3 Least Common Multiple . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Lesson 4 Greatest Common Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Lesson 5 Add and Subtract Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Lesson 6 Multipy Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Lesson 7 Divide Decimals by Whole Numbers . . . . . . . . . . . . . . . . . . 43 Lesson 8 Divide with Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 CHAPTER 2 Fractions Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Lesson 1 Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Lesson 2 Compare and Order Fractions and Decimals . . . . . . . . . . . 69 Lesson 3 Multiply Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Lesson 4 Simplify Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Lesson 5 Model Fraction Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Lesson 6 Divide Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Lesson 7 Divide Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 VOLUME 1 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

v © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Image Plan/Corbis; (b) ©Image Source/Corbis CHAPTER 3 Rational Numbers Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Lesson 1 Understand Positive and Negative Numbers . . . . . . . . . . 113 Lesson 2 Compare and Order Integers . . . . . . . . . . . . . . . . . . . . . . . 119 Lesson 3 Rational Numbers and the Number Line . . . . . . . . . . . . . 125 Lesson 4 Compare and Order Rational Numbers . . . . . . . . . . . . . . 131 Lesson 5 Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Lesson 6 Rational Numbers and the Coordinate Plane . . . . . . . . . 143 Lesson 7 Ordered Pair Relationships . . . . . . . . . . . . . . . . . . . . . . . . 149 Lesson 8 Distance on the Coordinate Plane . . . . . . . . . . . . . . . . . . . 155 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Launch Activity 2 Ratios and Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 CHAPTER 4 Ratios and Rates Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Lesson 1 Ratios and Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Lesson 2 Equivalent Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Lesson 3 Use Equivalent Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Lesson 4 Find Unit Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Lesson 5 Use Unit Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Lesson 6 Equivalent Ratios and Graphs . . . . . . . . . . . . . . . . . . . . . . 201 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

vi © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Digital Vision/Getty Images; (bl) ©shironosov/iStock/Getty Images; (br) ©Jgz/Adobe Stock CHAPTER 5 Percents Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Lesson 1 Model Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Lesson 2 Percents, Fractions, and Decimals . . . . . . . . . . . . . . . . . . . 221 Lesson 3 Percent of a Quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Lesson 4 Find the Whole from a Percent . . . . . . . . . . . . . . . . . . . . . 233 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 CHAPTER 6 Units of Measure Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Lesson 1 Convert Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Lesson 2 Transform Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Lesson 3 Distance, Rate, and Time Formulas . . . . . . . . . . . . . . . . . . 259 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

vii © Houghton Mifflin Harcourt Publishing Company

viii © Houghton Mifflin Harcourt Publishing Company • Image Credit: (t) ©Joe McBride/Getty Images; (m) ©jupiterimages/Getty Images; (b) ©Comstock/Getty Images Launch Activity 3 Expressions and Equations . . . . . . . . . . . . . . . . . . . 271 CHAPTER 7 Expressions Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Lesson 1 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Lesson 2 Evaluate Expressions Involving Exponents . . . . . . . . . . . . 281 Lesson 3 Write and Identify Parts of Algebraic Expressions . . . . . 287 Lesson 4 Evaluate Algebraic Expressions and Formulas . . . . . . . . . 293 Lesson 5 Use Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Lesson 6 Equivalent Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Lesson 7 Identify Equivalent Expressions . . . . . . . . . . . . . . . . . . . . . 311 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 CHAPTER 8 Equations and Inequalities Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Lesson 1 Solutions of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Lesson 2 Write Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Lesson 3 Solve Addition and Subtraction Equations . . . . . . . . . . . 337 Lesson 4 Solve Multiplication and Division Equations . . . . . . . . . . 343 Lesson 5 Solutions of Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Lesson 6 Write and Graph Inequalities . . . . . . . . . . . . . . . . . . . . . . . 355 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 VOLUME 2 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

ix CHAPTER 9 Relationships Between Variables Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Lesson 1 Independent and Dependent Variables . . . . . . . . . . . . . . 369 Lesson 2 Equations and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Lesson 3 Graph Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Lesson 4 Equations and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Launch Activity 4 Geometry and Statistics . . . . . . . . . . . . . . . . . . . . . . . 399 CHAPTER 10 Area Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 Lesson 1 Area of Parallelograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Lesson 2 Area of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Lesson 3 Area of Trapezoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Lesson 4 Area of Composite Figures . . . . . . . . . . . . . . . . . . . . . . . . . 421 Lesson 5 Figures on the Coordinate Plane . . . . . . . . . . . . . . . . . . . . 427 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 CHAPTER 11 Surface Area and Volume Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 Lesson 1 Three-Dimensional Figures and Nets . . . . . . . . . . . . . . . . . 441 Lesson 2 Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 Lesson 3 Volume of Rectangular Prisms . . . . . . . . . . . . . . . . . . . . . . 453 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 © Houghton Mifflin Harcourt Publishing Company • Image Credit: (t) ©Tetra Images - FBP/Getty Images; (b) ©Dleindec/Dreamstime DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

/Getty Images DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Sweet Success When you think of trail mixes or fruit salad, you might think of nuts and dried fruits, such as apples, cherries, raisins, and cranberries. Many businesses have their own recipes for trail mix. These businesses need to order the correct amounts of each ingredient to make their products. A dried-fruit manufacturer sells fruit-and-nut mixes to bakeries, grocery stores, and other retailers. The manufacturer makes its AppleCherry Mix using the following recipe. Apple-Cherry Mix (1 bag) • _ 3 4 pound of dried apples • _ 1 2 pound of dried cherries • _ 1 4 pound of walnuts Three Reads First, read to understand the situation. Next, read to understand the math. Then, read to ask what mathematical questions could be asked about the problem. The manufacturer that sells Apple-Cherry Mix makes it in large batches. Each batch can be used to fill 250 bags. Launch Activity The Number System Launch Activity 1 More About Fruits and Nuts • Some of the earliest recorded mentions of dried fruits can be found in Mesopotamian tablets dating to about 1500 BCE. • When ancient Egyptian kings died, dried fruits were buried in their tombs, along with other treasures. • Dried fruits retain most of the nutritional value of fresh fruits. • The walnut is thought to be one of the oldest tree foods known to humanity and dates back to about 7000 BCE. © Houghton Mifflin Harcourt Publishing Company • Image credits: (t) ©Vladimir Konstantinov/Shutterstock; (b) ©Mark Roger Bailey/Shutterstock Launch Activity • The Number System 3 InCopy Notes 1. COMP: Fractions need to be stacked for all three bullet points. Done NL 11/21 2. LXD: After fact-check, I replaced ““The earliest recorded mention” with “Some of the earliest recorded mentions” and “1,500 B.C.” with “1500 BCE” (no comma and drop reference to the Christian-centric calendar, per HMH’s global style guide). -RG 11/18/21 LXD 11/21 3. LXD: After fact-check and some CEID, style, and grammatical issues, I replaced “Walnuts are the oldest tree food known to man, dating back to 7,000 B.C.” with “The walnut is thought to be one of the oldest tree foods known to humanity and dates back to about 7000 BCE.” -RG 11/18/22 LXD 11/21 4. LXD: I added a hyphen to “dried-fruit manufacturer.” -RG 11/18/22 LXD 11/21 5. LXD: I added a missing comma to “such as apples, cherries. . . .” -RG 11/18/22 LXD 11/21 6. LXD: I hyphenated “fruit-and-nut mixes” since the mix described is and mixture of fruit and nuts, not of one or the other. -RG 11/18/22 LXD 11/21 7. LXD: I replaced “They make their Apple Cherry mix using the fo” with “The manufacturer makes its” to avoid personifying a company (which would conflict with HMH style). -RG 11/18/22 LXD 11/21 8. LXD: I deleted “Ingredients in” in “Ingredients in Apple-Cherry Mix” because it’s unnecessary (after the introduction”the following recipe) and because the list gives not only the ingredients but their amounts, so describing the list as a list of ingredients could be considered imprecise. -RG 11/18/22 LXD 11/21 9. LXD: I hyphenated all instances of “Apple-Cherry Mix”. -RG 11/18/22 LXD 11/21 10. LXD: I deleted “an” in “A company sells an Apple-Cherry Mix” because the mix, when capitalized, is treated as a proper noun. (Alternatively, we could have “A company sells an apple-cherry mix” or “A company sells a trail mix of apples of cherries,” but this inconstant lowercasing might distract some readers who are unfamiliar with these nuances of capitalization). -RG 11/18/22 LXD 11/21 11. LXD: Query: Is the company selling apple-cherry mix supposed to be different from the manufacturer selling Apple-Cherry Mix? If so, the Apple-Cherry Mix (capitalized proper noun) should be sold by only one company. If it’s intended to be the same company, I suggest replacing “A company sells Apple-Cherry Mix and makes it in large batches.” with “The manufacturer that sells Apple-Cherry Mix makes it in large batches.” -RG 11/18/22 Updated problem to be “The manufacturer that sells Apple-Cherry Mix makes it in large batches.” NL 11/21 12. LXD: To avoid refering to a company as “They” and to avoid a remote relative pronoun “that” I revised the paragraph at the bottom of the left column. -RG 11/18/22 NL 11/21 13. LXD: I replaced “tombs with other treasures” with “tombs, along with other treasures.” -RG 11/18/22 NL 11/21 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

For the interactive lesson Go Online How did you find how many pounds of each ingredient to use? Is there another way to solve the problem? Compare how you solved the problem with the way other students in your class solved the problem. Discuss with a partner or in a group. Read the final question. Make a plan to solve the problem. The manufacturer that sells Apple-Cherry Mix makes it in large batches. Each batch can be used to fill 250 bags. How many pounds of each ingredient will be needed to make one batch of Apple-Cherry Mix? Write, model, or draw to solve the problem. Math Talk © Houghton Mifflin Harcourt Publishing Company • Image credit: ©Dionisvera/Adobe Stock 4 Go Math! Grade 6 InCopy Notes 1. This is a list Bold, Italic, Strikethrough. 2. LXD: I revised the problem at the top of the page so that it’s conistent with the revisions made to the same problem on the previous page. -RG 11/18/22 I updated the problem to match the updated that was queried about in the previous page. NL 11/21 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

MATH in the World Real Wor Show What You Know Chapter 1 5 Name Chapter 1 Uncle Max saved $18 to buy a fingerprinting kit that costs $49. He spent 0.25 of his savings to buy a magnifying glass. Help Uncle Max find out how much more he needs to save to buy the fingerprinting kit. Whole Numbers and Decimals Factors Find all of the factors of the number. 1. 16 ____ 2. 27 ____ 3. 30 ____ 4. 45 ____ Round Decimals Round to the place of the underlined digit. 5. 0.323 ___ 6. 4.096 ___ 7. 10.67 ___ 8. 5.278 ___ Multiply 3-Digit and 4-Digit Numbers Multiply. 9. 2,143 __ × 6 ___ 10. 375 ×_ 8 ___ 11. 3,762 ×__ 7 ___ 12. 603 _ × 9 ___ © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Vocabulary Builder Go Online For more help Estimation 80 20 4 Division 84.15 18.7 4.5 ÷ = ÷ = 6 Go Math! Grade 6 Connect to Vocabulary Review Words ✓ compatible numbers decimal ✓ dividend divisible ✓ divisor factor prime number ✓ quotient Preview Words common factor greatest common factor least common multiple prime factorization Understand Vocabulary Complete the sentences using the preview words. 1. The least number that is a common multiple of two or more numbers is the _____. 2. The greatest factor that two or more numbers have in common is the _____. 3. A number that is a factor of two or more numbers is a _____. 4. A number written as the product of its prime factors is the _____ of the number. Visualize It Complete the Flow Map using the words with a ✓. © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

12,749 Divide the tens. Divide the ones. STEP 1 Divide. STEP 2 Check your answer. So, 12,749 ÷ 18 = __. Multiply the whole number part of the quotient by the divisor. Add the remainder. r5 2 92 ‾2,208 − 1 84 368 − 70 18‾12,749 − 12 6 14 − 0 149 − Estimate using compatible numbers. __÷ _= _ Example 1 Divide 12,749 ÷ 18. Math Idea You can write a remainder with an r, as a fractional part of the divisor, or as a decimal. For 131 ÷ 5, the quotient can be written as 26 r1, 261_ 5 , or 26.2. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Math Share and Show Board 8 Go Math! Grade 6 © Houghton Mifflin Harcourt Publishing Company Example 2 MP Describe two ways to check your answer in Example 2. Divide 59,990 ÷ 280. Write the remainder as a fraction. Estimate using compatible numbers. __÷ _= _ 280 ‾59,990 − − − 70 Compare your estimate with the quotient. Since the estimate, _ is close to _, the answer is reasonable. So, 59,990 ÷ 280 = _. Write the remainder over the divisor. Simplify. Think: 30 × 3 = 90 Estimate. Then find the quotient. Write the remainder, if any, with an r. 1. 29‾986 ___ 2. 37‾3,786 ___ STEP 1 Divide. STEP 2 Write the remainder as a fraction. remainder ________ divisor = ____ 280 _________ 70 ÷ 280 ÷ = ___ DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

On Your Own Chapter 1 • Lesson 1 9 Name © Houghton Mifflin Harcourt Publishing Company Estimate. Then find the quotient. Write the remainder, if any, as a fraction. 3. 6,114 ÷ 63 ___ 4. 11,050 ÷ 26 ___ Estimate. Then find the quotient. Write the remainder, if any, as a fraction. 10. The group of 128 engineers volunteer 12,480 hours in 26 weeks. On average, how many hours do they all volunteer per week? On average, how many hours does each engineer volunteer per week? ____ 11. A factory produces 30,480 bolts in 12 hours. If the same number of bolts are produced each hour, how many bolts does the factory produce in 5 hours? ____ 8. Find the greatest whole number that can replace ■ to make the statement true. ■ 3,744 ÷ 52 2 × ■ < 1,800 ÷ 12 ____ 5. 3,150 ÷ 9 ___ 6. 2,115 ÷ 72 ___ 7. 20,835 ÷ 180 ___ Math Talk Attend to precision. Explain why you can use multiplication to check a division problem. MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Spot on the Demonstrate Your Thinking Demonstrate Your Thinking Show the Math 10 Go Math! Grade 6 Problem Solving · Applications World Real Wor © Houghton Mifflin Harcourt Publishing Company • Image Credits: © PhotoDisc/Getty Images Airplane Passenger Seats Type of Plane Seats Jet Set 298 Smooth Flight 403 Blue Skies 160 Cloud Mover 70 Use the table for 12–15. 12. A Smooth Flight jet carried 6,045 passengers last week, and all of its flights were full. How many flights did the jet make last week? 13. Last month an airline made 6,322 passenger reservations from Newark, New Jersey, to Frankfurt, Germany. If there were 21 full flights and 64 reservations cancelled, which airplane made the flights? 14. An airline carries about 750 passengers from Houston to Chicago each day. How many Blue Sky jets would be needed to carry this many passengers, and how many empty seats would there be? 15. Refer back to Problem 12. Use the information in the table to write a similar problem involving airplane passenger seats. 16. For numbers 16a–16d, choose Yes or No to indicate whether the equation is correct. 16a. 1,350 ÷ 5 = 270 ● Yes ● No 16b. 3,732 ÷ 4 = 933 ● Yes ● No 16c. 4,200 ÷ 35 = 12 ● Yes ● No 16d. 1,586 ÷ 13 = 122 ● Yes ● No DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

World Real Problem Solving Chapter 1 • Lesson 1 11 © Houghton Mifflin Harcourt Publishing Company Name LESSON 1.1 Practice and Homework Divide Multi-Digit Numbers Estimate. Then find the quotient. Write the remainder, if any, with an r. Estimate. Then find the quotient. Write the remainder, if any, as a fraction. Find the greatest whole number that can replace to make the statement true. 1. 2. 19‾800 3. 68‾1,025 7. 5,601 ÷ 7 > 8. 274 ÷ 21 > 9. < 6,001 ÷ 400 4. 20‾1,683 5. 14,124 ÷ 44 6. 11,629 ÷ 29 10. A plane flew a total of 2,220 miles. Its average speed was 555 miles per hour. How many hours did the plane fly? 11. A van is carrying 486 pounds. There are 27 boxes in the van. What is the average weight of each box in the van? Estimate: 700 ÷ 50 = 15 12. Write Math Find 56,794 ÷ 338. Write the quotient twice, once with the remainder as a fraction and once with an r. 13 55‾715 55 165 165 0 Interactive Examples Go Online DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

12 Go Math! Grade 6 Lesson Check © Houghton Mifflin Harcourt Publishing Company Spiral Review 15. Hank bought 2.4 pounds of apples. Each pound cost $1.95. How much did Hank spend on the apples? 16. Gavin bought 4 packages of cheese. Each package weighed 1.08 kilograms. How many kilograms of cheese did Gavin buy? 17. Mr. Thompson received a water bill for $85.98. The bill covered three months of service. He used the same amount of water each month. How much did Mr. Thompson pay for water each month? 18. Layla used 0.482 gram of salt in her experiment. Maurice use 0.51 gram of salt. Who used the greater amount of salt? 13. A caterer’s fee is based on the number of meals she provides. How much is the price per meal if the total fee is $1,088 for 64 meals? 14. Nana Emelia needs 24 grams of beads to make a bracelet. She has 320 grams of beads. How many bracelets can she make? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

3 180 2 2 2 3 6 180 2 2 10 Remember UNLOCK the Problem Chapter 1 • Lesson 2 13 Name © Houghton Mifflin Harcourt Publishing Company • Image Credits: © PhotoDisc/Getty Images Prime Factorization I Can write the prime factorization of a number. Lesson 2 CHAPTER 1 Secret codes are often used to send information over the Internet. Many of these codes are based on very large numbers. For some codes, a computer must determine the prime factorization of these numbers to decode the information. The prime factorization of a number is the number written as a product of all of its prime factors. One Way Use a factor tree. The key for a code is based on the prime factorization of 180. Find the prime factorization of 180. Choose any two factors whose product is 180. Continue finding factors until only prime factors are left. 180 = _× _× _× _× _ List the prime factors from least to greatest. So, the prime factorization of 180 is _× _× _× _× _. A. Use a basic fact. Think: 10 times what number is equal to 180? 10 × _= 180 B. Use a divisibility rule. Think: 180 is even, so it is divisible by 2. 2 × _= 180 A prime number is a whole number greater than 1 that has exactly two factors: itself and 1. Math Talk Construct arguments and critique reasoning of others. How can you apply divisibility rules to make the factor tree on the left? MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

7 140 70 2 140 ÷ 2 = 70 prime factors 10 2 1 2 5 140 14 2 3 2 42 7 18 6 Math Share and Show Board 14 Go Math! Grade 6 Another Way Use a ladder diagram. Find the prime factorization. The key for a code is based on the prime factorization of 140. Find the prime factorization of 140. Choose a prime factor of 140. Continue dividing by prime factors until the quotient is 1. 140 = _× _× _× _ List the prime factors from least to greatest. So, the prime factorization of 140 is _× _× _× _. 1. 18 2. 42 18 = _× _× _ 42 = _× _× _ A Use the divisibility rule for 2. Think: 140 is even, so 140 is divisible by 2. B Use the divisibility rule for 5. Think: The last digit is 0, so 140 is divisible by 5. Math Talk Reason abstractly and quantitatively. Describe a different strategy you could use to find the prime factorization of 140. MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

On Your Own Chapter 1 • Lesson 2 15 Name Find the prime factorization. Write the number whose prime factorization is given. Find the prime factorization. 6. 2 × 2 × 2 × 7 7. 2 × 2 × 5 × 5 8. 2 × 2 × 2 × 2 × 3 × 3 15. The area of a rectangle is the product of its length and width. A rectangular poster has an area of 260 square inches. The width of the poster is greater than 10 inches and is a prime number. What is the width of the poster? 16. Dani says she is thinking of a secret number. As a clue, she says the number is the least whole number that has three different prime factors. What is Dani’s secret number? What is its prime factorization? MP 3. 75 4. 12 5. 65 9. 45 10. 50 11. 32 12. 76 13. 108 14. 126 Math Talk Attend to precision. Explain why a prime number cannot be written as a product of prime factors. MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Code Number Rules 1. The code is a 4-digit number. 2. Each digit is a prime number. 3. The prime numbers are entered from least to greatest. 4. The code number is changed at the beginning of each month. 36 6 Spot on the Demonstrate Your Thinking Demonstrate Your Thinking Show the Math 16 Go Math! Grade 6 © Houghton Mifflin Harcourt Publishing Company Problem Solving · Applications World Real Wor 20. Use the numbers to complete the factor tree. You may use a number more than once. 2 3 6 9 18 Write the prime factorization of 36. Use the table for 17–19. Agent Sanchez must enter a code on a keypad to unlock the door to her office. 17. In August, the digits of the code number are the prime factors of 150. What is the code number for the office door in August? 18. In September, the fourth digit of the code number is 2 more than the fourth digit of the code number based on the prime factors of 225. The prime factors of what number were used for the code in September? 19. One day in October, Agent Sanchez enters the code 3477. How do you know that this code is incorrect and will not open the door? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

World Real Problem Solving 44 2 2 4 11 11 6_MNLAEPB392691_C01_001T.ai Chapter 1 • Lesson 2 17 © Houghton Mifflin Harcourt Publishing Company Name LESSON 1.2 Practice and Homework Prime Factorization Find the prime factorization. 1. 44 2 ∙ 2 ∙ 11 2. 90 ____ 3. 48 ____ 4. 204 ____ 5. 400 ____ 6. 112 ____ 7. A computer code is based on the prime factorization of 160. Find the prime factorization of 160. 8. The combination for a lock is a 3-digit number. The digits are the prime factors of 42 listed from least to greatest. What is the combination for the lock? 9. Write Math Describe two methods for finding the prime factorization of a number. Interactive Examples Go Online DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

18 Go Math! Grade 6 Lesson Check © Houghton Mifflin Harcourt Publishing Company Spiral Review 10. Maritza remembers her PIN because it is between 1,000 and 1,500 and it is the product of two consecutive prime numbers. What is her PIN? 11. Brent knows that the 6-digit number he uses to open his computer is the prime factorization of 5,005. If each digit of the code increases from left to right, what is his code? 12. Piano lessons cost $15. What expressions could be used to find the cost in dollars of 5 lessons? 13. A jet plane costs an airline $69,500,000. What is the place value of the digit 5 in this number? 14. A museum has 13,486 butterflies, 1,856 ants, and 13,859 beetles. What is the order of the insects from least number to greatest number? 15. Juan is reading a 312-page book for school. He reads 12 pages each day. How long will it take him to finish the book? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Prime factors of 6 Prime factors of 8 Common prime factors 3 2 UNLOCK the Problem World Real Wor Chapter 1 • Lesson 3 19 Name Least Common Multiple I Can find the least common multiple of two whole numbers. Lesson 3 CHAPTER 1 One Way Use a list. Make a list of the first eight nonzero multiples of 6 and 8. Circle the common multiples. Then find the least common multiple. Another Way Use prime factorization and a Venn diagram. Multiples of 6: 6, 12, 18, _,_,_,_,_ Multiples of 8: 8, 16, 24, _,_,_,_,_ The least common multiple, or LCM, is _. In an experiment, each flower pot will get one seed. If the flower pots are in packages of 6 and the seeds are in packets of 8, what is the least number of plants that can be grown without any seeds or pots left over? The least common multiple, or LCM, is the least number that is a common multiple of two or more numbers. Write the prime factorization of each number. So, the least number of plants is _. List the common prime factors of the numbers, if any. Place the prime factors of the numbers in the appropriate parts of the Venn diagram. To find the LCM, find the product of all of the prime factors in the Venn diagram. 3 × 2 × 2 × 2 = _ The LCM is _. 6 = 2 × _ 8 = 2 × _× _ 6 and 8 have one prime factor of _ in common. © Houghton Mifflin Harcourt Publishing Company Image Credits: (cr) ©C Squared Studios/Photodisc/Getty Images Math Talk Model with mathematics. How does the diagram help you find the LCM of 6 and 8? MP • Explain why you cannot buy the same number of packages of each item. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Math Share and Show Board Math Idea Try This! Find the LCM. 20 Go Math! Grade 6 Example Use prime factorization to find the LCM of 8 and 12. A 10 and 11 Use prime factorization. 10 = ___ 11 = ___ ____ The LCM is _. B 3 and 12 Use a list. Multiples of 3: ___ Multiples of 12: ___ The LCM is _. Write the prime factorization of each number. Line up the common factors. Multiply one number from each column. So, the LCM of 8 and 12 is _. 8 = 2 × 2 × _ 12 = 2 × 2 × _ 2 × 2 × 2 × 3 = 24 1. How can you tell whether the LCM of a pair of numbers is one of the numbers? Give an example. 2. MP Explain one reason why you might use prime factorization instead of making a list of multiples to find the LCM of 10, 15, and 25. 1. List the first six nonzero multiples of 6 and 9. Circle the common multiples. Then find the LCM. Multiples of 6: ____ Multiples of 9: ____ The LCM of 6 and 9 is _. The factors in the prime factorization of a number are usually listed in order from least to greatest. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

On Your Own Chapter 1 • Lesson 3 21 Name 8. 5, 8 LCM: ■ ■ = __ 9. ■, 6 LCM: 42 ■ = __ MP Write the unknown number for the ■. 5. 5, 10 __ 6. 3, 8 __ 7. 9, 12 __ 11. MP Mr. Haigwood is shopping for a school picnic. Veggie burgers come in packages of 10, and buns come in packages of 6. He wants to serve veggie burgers on buns and wants to have no items left over. Mr. Haigwood says that he will have to buy at least 60 of each item, since 6 × 10 = 60. Do you agree with his reasoning? Explain. Find the LCM. 2. 3, 5 __ 3. 3, 9 __ 4. 4, 6 __ Find the LCM. 10. How can you tell when the LCM of two numbers will equal one of the numbers or equal the product of the numbers? Math Talk Attend to precision. Explain what the LCM of two numbers represents. MP 12. A deli has a special one-day event to celebrate its anniversary. On the day of the event, every eighth customer receives a free drink. Every twelfth customer receives a free sandwich. If 200 customers show up for the event, how many of the customers will receive both a free drink and a free sandwich? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

UNLOCK the Problem Spot on the 22 Go Math! Grade 6 © Houghton Mifflin Harcourt Publishing Company 13. Sister Katie is making hair clips to sell at the craft fair. To make each hair clip, she uses 1 barrette and 1 precut ribbon. The barrettes are sold in packs of 12, and the precut ribbons are sold in packs of 9. How many packs of each item does she need to buy to make the least number of hair clips with no supplies left over? a. What information are you given? b. What problem are you being asked to solve? c. Show the steps you use to solve the problem. d. Complete the sentences. The least common multiple of 12 and 9 is _. Sister Katie can make _ hair clips with no supplies left over. To get 36 barrettes and 36 ribbons, she needs to buy _ packs of barrettes and _ packs of precut ribbons. 14. Reptile stickers come in sheets of 6 and fish stickers come in sheets of 9. Antonio buys the same number of each type of sticker, and he buys at least 100 of each type. What is the least number of sheets of each type he might buy? 15. For numbers 15a–15d, choose Yes or No to indicate whether the LCM of the two numbers is 12. 15a. 2, 8 ● Yes ● No 15b. 4, 6 ● Yes ● No 15c. 4, 8 ● Yes ● No 15d. 6, 12 ● Yes ● No DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

World Real Problem Solving Chapter 1 • Lesson 3 23 © Houghton Mifflin Harcourt Publishing Company Name Least Common Multiple LESSON 1.3 Practice and Homework Find the LCM. 1. 2, 7 LCM: _ 2. 4, 12 LCM: _ 3. 6, 9 LCM: _ 10. Abuela Juana is making necklaces to give as presents. She plans to put 12 beads on each necklace. Beads are sold in packages of 10. What is the least number of packages she can buy to make necklaces and have no beads left over? _______ 11. Pencils are sold in packages of 10, and erasers are sold in packages of 6. What is the least number of pencils and erasers you can buy so that there is one pencil for each eraser with none left over? _______ 4. 5, 4 LCM: _ 5. 5, 8 LCM: _ 6. 12, 8 LCM: _ Write the unknown number for the . 7. 3, LCM: 21 = _ 8. , 7 LCM: 63 = _ 9. 10, 5 LCM: = _ Multiples of 2: 2, 4, 6, 8, 10, 12, 14 Multiples of 7: 7, 14 14 12. Write Math Explain when you would use each method (finding multiples or prime factorization) for finding the LCM and why. Interactive Examples Go Online DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

24 Go Math! Grade 6 © Houghton Mifflin Harcourt Publishing Company Spiral Review Lesson Check 13. The teacher is buying hot dogs and buns for the class barbecue. The hot dogs come in packages of 10. The buns come in packages of 12. What is the least number he can buy of each so that he has exactly the same number of hot dogs and buns? How many packages of each should he buy? 14. Kevin makes snack packs that each contain a box of raisins and a granola bar. Each package of raisins contains 9 boxes. The granola bars come 12 to a package. What is the least number he can buy of each so that he has exactly the same number of granola bars and boxes of raisins? How many packages of each should he buy? 15. Grandpa has 2,456 coins in his coin collection. He has the same number of coins in each of 3 boxes. Estimate to the nearest hundred the number of coins in each box. 16. What is the distance around a triangle that has sides measuring 21_ 8 feet, 31_ 2 feet, and 21_ 2 feet? 17. $15,575 was collected at a fundraiser. The organization hosting the fundraiser plans to give the same amount of money to each of 35 charitable groups. How much will each group receive? 18. Jean needs 1_ 3 cup of walnuts for each serving of salad she makes. She has 2 cups of walnuts. How many servings can she make? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

12 inches 18 inches 6_MNLAESE587783_233A.ai Sam Valentino 1.21.11 1st pass Prime factors of 12 Prime factors of 18 Common prime factors 2 3 Remember UNLOCK the Problem World Real Wor Chapter 1 • Lesson 4 25 © Houghton Mifflin Harcourt Publishing Company Name Greatest Common Factor I Can find the greatest common factor of two whole numbers. Lesson 4 CHAPTER 1 One Way Use a list. Factors of 12: 1, 2, _, _, _, 12 Factors of 18: 1, _, _, _, _, _ The greatest common factor, or GCF, is _. Another Way Use prime factorization. Jim is cutting two strips of wood to make picture frames. The wood strips measure 12 inches and 18 inches. He wants to cut the strips into equal lengths that are as long as possible. Into what lengths should he cut the wood? A common factor is a number that is a factor of two or more numbers. The numbers 16 and 20 have 1, 2, and 4 as common factors. Factors of 16: 1, 2, 4, 8, 16 Factors of 20: 1, 2, 4, 5, 10, 20 The greatest common factor, or GCF, is the greatest factor that two or more numbers have in common. The greatest common factor of 16 and 20 is 4. Write the prime factorization of each number. 12 = 2 × _× 3 18 = _× 3 × _ Place the prime factors of the numbers in the appropriate parts of the Venn diagram. To find the GCF, find the product of the common prime factors. 2 × 3 = _ The GCF is _. Find the greatest common factor, or GCF, of 12 and 18. So, Jim should cut the wood into _-inch lengths. A number that is multiplied by another number to find a product is a factor. Factors of 6: 1, 2, 3, 6 Factors of 9: 1, 3, 9 Every number has 1 as a factor. Math Talk Reason abstractly and quantitatively. Into what other lengths could Jim cut the wood to obtain equal lengths? MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

27 as a product. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

12 __ Math Talk Look for and make use of structure. Describe how to use the prime factorization of two numbers to find their GCF. MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

Spot on the Prime factors of 6 Prime factors of 12 Common prime factors 28 Go Math! Grade 6 Problem Solving · Applications World Real Wor Scott School of Music Instrument Number of Students Bass 20 Cello 27 Viola 30 Violin 36 22. Write Math Explain how you could use the GCF and the Distributive Property to express the sum of the number of bass students and the number of violin students as a product. 23. The prime factorization of each number is shown. 6 = 2 × 3 12 = 2 × 2 × 3 Using the prime factorization, complete the Venn diagram and write the GCF of 6 and 12. GCF = ______ Use the table for 19–22. Teachers at the Scott School of Music teach only one instrument in each class. No students take classes for more than one instrument. 19. Señor Gil teaches group lessons to all of the violin and viola students at the Scott School of Music. All of his classes have the same number of students. What is the greatest number of students he can have in each class? 20. Jamila teaches all of the bass and viola students. All her classes have the same number of students. Each class has the greatest possible number of students. How many of these classes does she teach? 21. Ms. Harris teaches jazz classes. She has 9 students in each class, and she teaches all the classes for two of the instruments. Which two instruments does she teach, and how many students are in her classes? © Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Hill Street Studios/Blend Images/Getty Images DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

45 ____ 4. 14, 18 ____ 5. 6, 48 ____ 6. 16, 100 ____ 10. A trophy case at Riverside Middle School holds 18 basketball trophies and 24 soccer trophies. The coach wants to place the same number of trophies on each shelf. What is the greatest number of trophies that can be on each shelf? 11. There are 24 sixth graders and 40 seventh graders. Mr. Chan wants to divide both grades into groups of equal size, with the greatest possible number of students in each group. How many students should be in each group? 1. 25 and 10 ____ 2. 36 and 90 ____ 3. 45 and 60 1, 5 ____ 12. Write Math Write a short paragraph to explain how to use prime factorization and the Distributive Property to express the sum of two whole numbers as a product. Interactive Examples Go Online DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

30 Go Math! Grade 6 Lesson Check © Houghton Mifflin Harcourt Publishing Company Spiral Review 13. There are 15 jazz dancers and 10 tap dancers in Miss Li’s class. She wants to group all the students so that each group has the same number of jazz and tap dancers. What is the greatest number of groups she can have? 14. A pet shop manager wants the same number of birds in each cage. He wants to use as few cages as possible, but can only have one type of bird in each cage. If he has 42 parakeets and 18 canaries, how many birds will he put in each cage? 17. The Cramer Company had a profit of $8,046,890 and the Coyle Company had a profit of $8,700,340 last year. Which company had the greater profit? 18. There are 111 guests attending a party. There are 15 servers. Each server has the same number of guests to serve. Jess will serve any extra guests. How many extra guests will Jess be serving? 15. There are 147 people attending a dinner party. If each table can seat 7 people, how many tables are needed for the dinner party? 16. Sammy has 3 pancakes. He cuts each one in half. How many pancake halves are there? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

_= _ © Houghton Mifflin Harcourt Publishing Company • Image Credits: (c) ©Rubberball/Alamy DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

3.461 You can place zeros to the right of a decimal without changing its value. 4.91 = 4.910 = 4.9100 Math Talk Model with mathematics. Explain how to use inverse operations to check your answer to 5 − 1.836. MP Math Talk Look for and make use of structure. Describe how adding and subtracting decimals is like adding and subtracting whole numbers. MP © Houghton Mifflin Harcourt Publishing Company • Image Credits: (cr) ©Lee Dalton/Alamy Images (cl) Courtesy, United States Mint DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

(9.2 − 1.413) 11. 21.3 − (19.1 − 3.22) Math Talk Attend to precision. Why is it important to align the decimal points when you add or subtract decimals? MP DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

1.8 = 4.32 ● True ● False 14c. 2.01 – 1.33 = 0.68 ● True ● False 14d. 51 – 49.2 = 1.8 ● True ● False Comparing Eggs Different types of birds lay eggs of different sizes. Small birds lay eggs that are smaller than those that are laid by larger birds. The table shows the average lengths and widths of five different birds’ eggs. Average Dimensions of Bird Eggs Bird Length (m) Width (m) Canada Goose 0.086 0.058 Hummingbird 0.013 0.013 Raven 0.049 0.033 Robin 0.019 0.015 Turtledove 0.031 0.023 Use the table for 15–17. 15. What is the difference in average length between the longest egg and the shortest egg? 16. Which egg has a width that is eight thousandths of a meter shorter than its length? 17. How many robin eggs, laid end to end, would be about equal in length to two raven eggs? Justify your answer. Canada Goose © Houghton Mifflin Harcourt Publishing Company Image Credits: (c) ©David R. Frazier Photolibrary, Inc./Alamy Images DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

4.9) ____ 9. (32.45 − 4.8) − 2.06 ____ 10. The average annual rainfall in Clearview is 38 inches. This year, 29.777 inches fell. How much less rain fell this year than falls in an average year? _______ 11. At the theater, the Worth family spent $18.00 on adult tickets, $16.50 on children’s tickets, and $11.75 on refreshments. How much did they spend in all? _______ 40 ∙ 30 ∙ 70 Evaluate using the order of operations. 12. Write Math Write a word problem that involves adding or subtracting decimals. Include the solution. 43.53 ∙__27.67 71.20 Interactive Examples Go Online DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

(6 × 4). What property does the equation illustrate? 18. Cups come in packages of 12 and lids come in packages of 10. What is the least number of cups and lids that Gabby can buy if she wants to have the same number of cups and lids? 13. Alden fills his backpack with 0.45 kg of apples, 0.18 kg of cheese, and a water bottle that weighs 1.4 kg. How heavy are the contents of his backpack? 14. Josina plans to hike 6.3 kilometers to see a waterfall. She stops to rest after hiking 4.75 kilometers. How far does she have left to hike? DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

$ © Houghton Mifflin Harcourt Publishing Company • Image Credits: ©HMH DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

_, or _ decimal places Example 2 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

1.27) × 6.4 Estimate. Then find the product. MP Evaluate using the order of operations. 12. Paman Bima is buying ingredients to make a large batch of granola to sell at the food bazaar. He buys 3.2 pounds of walnuts for $4.40 per pound and 2.4 pounds of cashews for $6.25 per pound. How much change will he receive if he pays with two $20 bills? 12.42 × __28.6 Estimate. Think: The estimate is about _, so the decimal point should be placed after _. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

UNLOCK the Problem Spot on the 40 Go Math! Grade 6 Item Calculation Cost Gasoline 12.4 × $3.80 Water bottles 4 × $1.99 Snacks 2 × $1.55 14. At a convenience store, the Amani family puts 12.4 gallons of gasoline in their van at a cost of $3.80 per gallon. They also buy 4 water bottles for $1.99 each, and 2 snacks for $1.55 each. Complete the table to find the cost for each item. Mrs. Amani says the total cost for everything before tax is $56.66. Do you agree with her? Explain why or why not. b. How will you use the table to solve the problem? c. Complete the sentences. 40 U.S. dollars were worth __ Canadian dollars in 2009. So, Cameron would receive __ __ Canadian dollars in 2009. a. What do you need to find? Major Dawes found some international currency in a suitcase. The table shows some currency exchange rates for 2009. Major Currency Exchange Rates in 2009 Currency U.S. Dollar Japanese Yen European Euro Canadian Dollar U.S. Dollar 1 88.353 0.676 1.052 Japanese Yen 0.011 1 0.008 0.012 European Euro 1.479 130.692 1 1.556 Canadian Dollar 0.951 83.995 0.643 1 13. When Major Dawes went to Canada in 2007, she exchanged 40 U.S. dollars for 46.52 Canadian dollars. If Major Dawes exchanged 40 U.S. dollars in 2009, did she receive more or less than she received in 2007? How much more or less? Denominations of Euro © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Comstock/Getty Images DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A

The book owner has disabled this books.

Explore Others

Amanda Cupelli

Related publications.

• 888-309-8227
• 732-384-0146

New User Registration

Forgot Password

Go Math! 6 Common Core Edition, Grade: 6 Publisher: Houghton Mifflin Harcourt

Go math 6 common core edition, title : go math 6 common core edition, publisher : houghton mifflin harcourt, isbn : 547587783, isbn-13 : 9780547587783, use the table below to find videos, mobile apps, worksheets and lessons that supplement go math 6 common core edition..

textbook resources

• Call us toll-free
• FAQs – Frequently Asked Questions
• Contact Lumos Learning – Proven Study Programs by Expert Teachers

Follow us: Lumos Learning -->

• 2024 © Lumos Learning
• Privacy Policy - Terms of Service - Disclaimers

PARCC® is a registered trademark of PARCC, Inc. Lumos Learning, is not owned by or affiliated in any fashion with PARCC, Inc... Read More

PARCC® is a registered trademark of PARCC, Inc. Lumos Learning, is not owned by or affiliated in any fashion with PARCC, Inc., the Partnership for the Assessment of Readiness for College and Careers, nor any state of the Union. Neither PARCC, Inc., nor The Partnership for the Assessment of Readiness for College and Careers, nor any member state has endorsed this product. No portion of any fees or charges paid for any products or services Lumos Learning offers will be paid or inure to the benefit of PARCC, Inc., or any state of the Union

SBAC is a copyright of The Regents of the University of California – Smarter Balanced Assessment Consortium, which is not aff... Read More

SBAC is a copyright of The Regents of the University of California – Smarter Balanced Assessment Consortium, which is not affiliated to Lumos Learning. The Regents of the University of California – Smarter Balanced Assessment Consortium, was not involved in the production of, and does not endorse these products or this site.

ACT® Aspire™ is a registered trademark of ACT Aspire LLC., which is not affiliated to Lumos Learning. ACT Aspire LLC, was not... Read More

ACT® Aspire™ is a registered trademark of ACT Aspire LLC., which is not affiliated to Lumos Learning. ACT Aspire LLC,was not involved in the production of, and does not endorse these products or this site.

Florida Department of Education is not affiliated to Lumos Learning. Florida department of education, was not involved in the... Read More

Florida Department of Education is not affiliated to Lumos Learning. Florida department of education, was not involved in the production of, and does not endorse these products or this site.

Indiana Department of Education is not affiliated to Lumos Learning. Indiana department of education, was not involved in the... Read More

Indiana Department of Education is not affiliated to Lumos Learning. Indiana department of education, was not involved in the production of, and does not endorse these products or this site.

Mississippi Department of Education is not affiliated to Lumos Learning. Mississippi department of education, was not involved... Read More

Mississippi Department of Education is not affiliated to Lumos Learning. Mississippi department of education, was not involved in the production of, and does not endorse these products or this site.

Ohio Department of Education is not affiliated to Lumos Learning. Ohio department of education, was not involved in the prod... Read More

Ohio Department of Education is not affiliated to Lumos Learning. Ohio department of education, was not involved in the production of, and does not endorse these products or this site.

Tennessee Department of Education is not affiliated to Lumos Learning. Tennessee department of education, was not involved... Read More

Tennessee Department of Education is not affiliated to Lumos Learning. Tennessee department of education, was not involved in the production of, and does not endorse these products or this site.

Georgia Department of Education is not affiliated to Lumos Learning. Georgia department of education, was not involved... Read More

Georgia Department of Education is not affiliated to Lumos Learning. Georgia department of education, was not involved in the production of, and does not endorse these products or this site.

Missouri Department of Education is not affiliated to Lumos Learning. Missouri department of education, was not involved... Read More

Missouri Department of Education is not affiliated to Lumos Learning. Missouri department of education, was not involved in the production of, and does not endorse these products or this site.

Louisiana Department of Education is not affiliated to Lumos Learning. Louisiana department of education, was not involved... Read More

Louisiana Department of Education is not affiliated to Lumos Learning. Louisiana department of education, was not involved in the production of, and does not endorse these products or this site.

Report an Error