go math 4th grade homework

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Go Math! Grade 4 Teacher Edition

Description: Go Math! Grade 4 Teacher Edition

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GRADE 4 Teacher Edition Currency and Coins Photos Courtesy of United States Mint, Bureau of Engraving, and Houghton Mifflin Harcourt 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 978-0-358-69486-1 1 2 3 4 5 6 7 8 9 10 XXXX 30 29 28 27 26 25 24 23 22 21 4500000000 r7.22 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.

3 or multiply 2 × 3. Check students’ drawings. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 3_mnlese694724_c03l01.indd 109 5/18/2022 11:00:31 AM Launch Activity 2 Three Reads First, listen to the problem. What is the math story about? Next, read the problem aloud with your class. How might numbers be used? Then, read the problem with a partner. What math questions can you ask about the problem? Izzy’s family is sending a box of oranges to his grandma. The box is packed so there are the same number of oranges in each row. The gift box contains 24 oranges. Launch Activity Multiplication A Taste of Sunshine! Oranges are citrus fruits. They grow best in tropical and subtropical climates, but are eaten and enjoyed all around the world. When oranges are ripe, they are picked and sent to a packing house. Oranges are graded on their color, shape, age, and freedom from defects. Most oranges are made into juice but the most perfect oranges are reserved for gift boxes, which are sent all over the world. Have you ever sent or received a gift box of oranges? More About Oranges • Oranges were first grown in China. • There are over 600 varieties of oranges in the world. • The word “orange” referred to a color first. The fruit was named after the color. Launch Activity • Multiplication 55 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Drobot Dean/Adobe Stock, (b) ©Tim UR/Shutterstock DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 3_mnlese694724_li02.indd 55 5/18/2022 10:28:05 AM Launch Activity lessons . . . are designed for exploration and collaboration among students. Look for these activities to occur multiple times per year, with contexts to engage your students. All students . . . will see themselves and the possibilities for their future success in the materials used as part of instruction. You will see questions that foster a growth mindset and help students reflect on the math taught in the lesson. Welcome to Go Math! The Interactive Student Edition . . . is structured to assist students in navigating through their lesson assignments. Students start their assigned lesson and are prompted at completion to review assignment boards or to check in with you. Interactive lessons include animations, learning pathways, and appropriate intervention options to encourage high engagement with students. T2 Go Math! Grade 4

AA MALE HISPANIC FEMALE CAUCASIAN MALE Bring the wonder of math . . . to your students through this program designed to help you, as a teacher, empower your students to become mathematicians through engaging activities and thought-provoking exploration of math in authentic contexts. The Go Math! program is designed to allow flexibility to solve problems using appropriate methods and strategies through discovery. The program supports exploration, rigor, fluency, and the application of real-world context. • Teachers have the flexibility of multi-grade access on Ed to provide prerequisite or challenge resources for students. • Students have access to a range of tools and resources to model their thinking. • Support for multilingual learners is included throughout the program. Go Math! supports you as an educator to implement standards for Mathematics with teacher-to-teacher notes, Teacher’s Corner, and other professional supports. Using these supports with Go Math!, you can meet the needs of each individual student. • Standards Helper, a resource document organized by benchmark to easily see lessons, resources, and commons errors for student learning. • Launch Activity, a lesson with engaging content that introduces new concepts. • Teacher’s Corner, an online and interactive resource center for professional support specific to Go Math!, as well as other researchbased supports. How am I supported as an educator? How can I ensure my students are engaged with the Mathematical Practices and Processes? The Go Math! lesson design integrates the Mathematical Practices and Processes throughout the Student and Teacher Editions. • MP An MP icon indicates where in a lesson an MP standard is addressed. How do I ensure my students have the flexibility to show what they know? GRADE BOOK 1 K K_MFLESE660170_BOOK1_CVR.indd 2 10/5/21 6:53 PM GRADE BOOK 1 1 1_MFLESE660880_BOOK1_CVR.indd 2 10/5/21 6:54 PM GRADE BOOK 1 2 2_MFLESE660958_BOOK1_CVR.indd 2 10/5/21 6:56 PM Welcome to Go Math! T3

Program Authors Edward B. Burger, PhD, is President & CEO of St. David’s Foundation and President Emeritus & Professor Emeritus of Mathematics at Southwestern University in Georgetown, Texas. He has authored or coauthored numerous articles, books, and video series; delivered many addresses and workshops throughout the world; and made many radio and television appearances. Thomasenia Lott Adams, PhD, is a mathematics teacher educator/researcher in the School of Teaching & Learning and the Associate Dean of Research (ADR) in the College of Education at the University of Florida (UF), Gainesville, FL. Dr. Adams is co-author of the Making Sense of Mathematics for Teaching series (Solution Tree) and Associate Editor of Mathematics Teacher: Learning and Teaching PreK-12 (NCTM). Juli K. Dixon, PhD, is a professor of mathematics education at the University of Central Florida (UCF). She has taught mathematics in urban schools at the elementary, middle, secondary, and postsecondary levels. Dr. Dixon has delivered keynotes and other presentations throughout the United States. Key areas of focus are deepening teachers’ content knowledge and communicating and justifying mathematical ideas. You can find her on social media at @TheStrokeOfLuck. Juli K. Dixon, PhD Edward B. Burger, PhD Thomasenia Lott Adams, PhD T4 Go Math! Grade 4

Program Contributors and Consultants Contributor Rena Petrello Professor, Mathematics Moorpark College Moorpark, CA English Language Learners Consultant Elizabeth Jiménez CEO, GEMAS Consulting Professional Expert on English Learner Education Bilingual Education and Dual Language Pomona, California Consultant Valerie Johse Math Consultant Houston, Texas Matthew R. Larson, PhD, is the associate superintendent for instruction at Lincoln Public Schools (Nebraska). A prolific speaker and writer, he is the coauthor of more than a dozen professional books. He was a member of the writing teams for the major publications Principles to Actions: Ensuring Mathematical Success for All (2014) and Catalyzing Change in High School Mathematics: Initiating Critical Conversations (2018). Key areas of focus include access and equity and effective stakeholder communication. He has taught mathematics at the secondary and college levels. You can find him on social media at @mlarson_math. Matthew R. Larson, PhD Program Authors and Consultants T5

ABOUT THE PROGRAM Learning Progression Lesson Design to Build Standards Mastery Go Math! builds mastery of all content areas and provides a focused approach to developing students’ mathematical understanding, procedural skills, and fluency. An emphasis is placed on making connections between concepts and skills as children move through a carefullysequenced learning experience. Building Procedural Mastery with the 5E Model Every Go Math! lesson follows the same lesson design based on the 5E model of instruction. Image Credit: ©HMH Small and Whole Group Explore In Explore, students build an understanding of new concepts through discovery and make sense of procedure using Investigate or Unlock the Problem. Math Talk questions provide entry points for mathematical discourse that explores the new concepts learned. Whole Group Engage Spark students curiosity with Engage to connect prior knowledge to new mathematical content. Small Group Explain In Explain, students apply their new knowledge of the lesson's mathematical concepts using Share and Show and On Your Own problems, increasing their conceptual understanding as they build towards procedural reliability. Teachers can assess differentiation needs, providing support with supplemental activities and materials for Intervention, Language Support, and Enrichment. Whole Group Elaborate The real-world problem solving in Elaborate gives students the opportunity to develop a deeper understanding of lesson concepts by practicing different solution methods. Evaluate Students summarize their thinking in Evaluate by connecting the I Can statement to the lesson objective. Practice and Homework problems support students’ newlylearned lesson skills in their progression towards procedural fluency and automaticity. T6 Go Math! Grade 4

HISPANIC FEMALE Three Reads First, listen to the problem. What is the math story about? Next, read the problem aloud with your class. How might numbers be used? Then, read the problem with a partner. What math questions can you ask about the problem? Muna helps her grandfather make a strawberry pie for dessert. There are 4 people who will eat the pie. Launch Activity Fractions More About Strawberries • A typical strawberry has about 200 seeds, all of which are on the outside. • The strawberry is native to North America. Native Americans ate strawberries in corn bread. • The strawberry is in the same plant family as the rose. Berry Beautiful! Sometimes towns have festivals to celebrate their fruit and vegetable harvests. One popular type of harvest festival is a berry festival. A festival will often have exhibits, crafts, and rides, but the main attractions are treats made from the crop. At a strawberry festival, you might find shortcakes, jam, milkshakes, sandwiches, pizzas, and even kettle corn, all made with fresh strawberries. Launch Activity 3 Launch Activity • Fractions 519 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (top, inset) ©focus finder/Adobe Stock, (bottom) ©baibaz/iStockPhoto.com DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 3_mnlese694731_li03.indd 519 10/13/2021 1:07:03 PM Launch Activity 2 Three Reads First, listen to the problem. What is the math story about? Next, read the problem aloud with your class. How might numbers be used? Then, read the problem with a partner. What math questions can you ask about the problem? Izzy’s family is sending a box of oranges to his grandma. The box is packed so there are the same number of oranges in each row. The gift box contains 24 oranges. Launch Activity Multiplication A Taste of Sunshine! Oranges are citrus fruits. They grow best in tropical and subtropical climates, but are eaten and enjoyed all around the world. When oranges are ripe, they are picked and sent to a packing house. Oranges are graded on their color, shape, age, and freedom from defects. Most oranges are made into juice but the most perfect oranges are reserved for gift boxes, which are sent all over the world. Have you ever sent or received a gift box of oranges? More About Oranges • Oranges were first grown in China. • There are over 600 varieties of oranges in the world. • The word “orange” referred to a color first. The fruit was named after the color. Launch Activity • Multiplication 55 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Drobot Dean/Adobe Stock, (b) ©Tim UR/Shutterstock DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 3_mnlese694724_li02.indd 55 5/18/2022 10:28:05 AM ABOUT THE PROGRAM Learning Tasks to Guide Instruction Go Math! lesson design supports standards-driven instruction. What are Launch Activity lessons? Each grade’s lessons are interspersed with Launch Activity lessons that introduce students to new, key areas of learning. Launch lessons highlight these important areas, and include professional development supports to help your class learn through productive perseverance and collaborative learning. Promoting Exploration The Listen and Draw and Unlock the Problem tasks are carefully crafted to promote reasoning and problem solving. Students can solve these puzzles using different strategies. These low-floor/ high-ceiling tasks give every student an entry point to be successful and build understanding. Each chapter is full of realworld situations. During these low floor/high ceiling tasks, students use their prior learning and choose manipulatives and models. Teachers provide just-in-time support, helping students engage in meaningful discourse to persevere when solving problems. Teachers lead the class to shared understanding in a student-centered environment, using the Math Talk feature to generate discussion. Becoming More Efficient The Share and Show tasks provide more opportunities for students to understand lesson concepts. Teachers can use the Quick Check to see if students are ready to go on, or determine how best to differentiate instruction. Teachers can assign the On Your Own problems to independently build fluency once students understand the lesson’s concepts. Building Procedural Fluency The Problem Solving lesson tasks include real-world problems to promote procedural understanding and fluency. Teachers help students understand why the procedures are efficient and how they can be applied to solve similar problem types. Then, using the Practice and Homework helps students continue to build procedural fluency. Launch Activity Lessons About the Program T7

> Lesson 1 Add or Subtract Parts of a Whole > Engage: Add or Subtract Parts of a Whole > Explore: Add or Subtract Parts of a Whole > Explain: Add or Subtract Parts of a Whole > Elaborate: Add or Subtract Parts of a Whole > Evaluate: Add or Subtract Parts of a Whole GRADE VOLUME 4 1 GRADE VOLUME 4 1 12/23/21 1:59 PM GRADE VOLUME 4 1 ACCELERATED ACCELERATED TC GRADE 4 VOLUME 1 GRADE VOLUME 4 1 4_mnlese_accelerated VOL1_CVR.indd All Pages 12/27/21 12:35 PM GRADE VOLUME 4 1 Teacher Edition Edition Teacher GRADE VOLUME 4 1 12/23/21 12:28 PM GRADE VOLUME 1828196 4 2 TEACHER EDITION GRADE 4 VOLUME 1 Teacher Edition Edition Teacher GRADE VOLUME 4 1 4_mnlete_9780358694861 VOL1_CVR.indd All Pages 12/23/21 12:28 PM PROGRAM TOUR Key Components for Learning For the Student For the Teacher Assessments Online Assessments Use a range of online assessments to benchmark student progress and inform instruction. Student Edition* Full-color, write-in Student Editions Online Student Experience Interactive practice with engaging Launch Activity lessons, hint, and corrective feedback. Teacher Edition* The Teacher Edition, with all the support you need to plan lessons, build understanding, and meet the needs of all your students. Online Teacher Experience Complete teacher support for lesson planning, assigning resources, viewing reports, and grouping, as well as flexible multi-grade access to provide both prerequisite and challenge content for standards progressions. * Some print and digital student-facing materials are available in Spanish for Grades K–5, with companion bilingual teacher materials. Growth Measure T8 Go Math! Grade 4

1 = 10 units Compare: 10 units = 10 units So, Rectangle A has the same perimeter as Rectangle B. A B Compare the areas of Rectangle A and Rectangle B. Find the number of unit squares needed to cover each rectangle. Rectangle A: 2 rows of 3 = 2 × 3, or 6 square units Rectangle B: 1 row of 4 = 1 × 4, or 4 square units Compare: 6 square units > 4 square units So, Rectangle A has a greater area than Rectangle B. A B Find the perimeter and the area. Tell which rectangle has a greater area. 1 A B A: Perimeter = ; Area = B: Perimeter = ; Area = Rectangle has a greater area. 12 units 5 square units 12 units 9 square units B 2 A B A: Perimeter = ; Area = B: Perimeter = ; Area = Rectangle has a greater area. 14 units 10 square units 14 units 6 square units A LESSON 9.4 Reteach 66 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 3_mnlean1836902_c09r04.indd 66 13/05/22 6:36 PM Name Perimeter Puzzlers 1 The shaded rectangle has a perimeter of 18 cm. Draw a different rectangle that has a perimeter of 18 cm. Possible answers are shown. 2 Draw a square and find the perimeter. Then draw a rectangle that has the same perimeter as the square. Possible answers are shown. Perimeter: 16 cm Perimeter: 16 cm Find the unknown length for each rectangle. 3 Perimeter = 50 ft 4 Perimeter = 96 cm 15 ft ft 10 30 cm 18 cm LESSON 7.1 Enrich 39 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 4_mnlean1836903_c07e01.indd 39 13/05/22 7:24 PM for digital and interactive resources Go Online Teacher’s Corner TM Groups that have the same number of objects © Houghton Mifflin Harcourt Publishing Company grupos iguales equal groups DO NOT EDIT--Changes must be made through “File info” CorrectionKey=FL-B Groups that have the same number of objects © Houghton Mifflin Harcourt Publishing Company grupos iguales equal groups DO NOT EDIT--Changes must be made through “File info” CorrectionKey=FL-B PROGRAM TOUR Differentiation and Small-Group Instruction Professional Learning and Implementation Support Tabletop Flipchart Mini-lessons for math centers and small-group exploration. Readers* With Lexile® Measures Vocabulary Cards and Games* Fun, meaningful activities Differentiated Instruction* Resources for Reteach, Enrich, and Fluency to meet the needs of all students. Professional Learning Cards With Talk Moves and Language Routines Classroom Manipulatives Kit Hands-on materials for modeling and understanding Waggle* Interactive, adaptive practice with engaging tools and activities for students to develop fluency and mastery of the standards. Teacher’s Corner On-demand, bite-size articles, videos, and live events to tailor your professional learning to your specific needs. Program Tour T9

HISPANIC MALE PROGRAM TOUR Instructional Journey The instruction in Go Math! is designed from the ground up to help you nurture young mathematicians in your classroom. The small-group and whole-group activities in each lesson provide the flexibility to meet the needs of your students. While every classroom may look a little different, this instructional model provides a framework to organize small-group and wholegroup work for meaningful learning. How do I pace my lessons? Your Teacher Edition includes pacing recommendations for each lesson, which you can modify for your class and your teaching style. Small and Whole Group Explore 15–20 minutes Exploration • Investigate, Unlock the Problem • Multilingual Support and Strategy • Common Errors Whole Group Engage 5 minutes Readiness • Problem of the Day • Fluency Builder or Vocabulary Builder • Access Prior Knowledge Engagement • I Can • Making Connections • Learning Activity Small Group Explain 15–20 minutes Quick Check Share and Show Differentiated Instruction TM and Version 2.0 Differentiated Centers Kit Grab Intervention • Waggle • Reteach • Tier 2 and Tier 3 Resources Language Support • Vocabulary Activities • Language Routines • Multilingual Glossary Enrichment • Waggle Games • Ready for More • Enrich Whole Group Elaborate 5 minutes • Math on the Spot Videos • Higher-Order Thinking Problems Evaluate • I Can Reflection • Exit Ticket • Practice and Homework • Fluency Practice • Waggle T10 Go Math! Grade 4

12 = 24. • Which number marks the location where the time capsule is buried? 43 3_mnlete694847_c03co.indd 107 10/22/2021 11:00:20 AM PROGRAM TOUR Differentiated Instruction, Practice, and Fluency Effective instruction begins with knowing your students’ strengths and challenges, including knowing what your students understand about a topic before they begin a new chapter. Show What You Know These chapter opener assessments help you to zero in on students’ prerequisite knowledge, identify critical gaps, and make decisions about grouping. Differentiated Instruction Options Differentiation resources can be assigned to students who finish early (Enrich), or to students who are generally on grade level but who may need additional support (Reteach). Printable resources for differentiation are available in your teacher resources. Program Tour T11

20 = 40, so 4 × 10 = 40. 10 60 25 70 40 35 30 50 0 20 15 90 3 10¢ 3 10¢ 30¢ 30¢ DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 3_mnlese694724_c03l02.indd 116 5/18/2022 11:01:21 AM DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A T12 Go Math! Grade 4

8 2 × 8 = 16 Multiplication Properties Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. © Houghton Mifflin Harcourt Publishing Company • Image Credits: ©HMH Distributive Associative multiple 3_mnlese694724_c03o.indd 108 5/18/2022 10:58:30 AM Chapter 3 108 Use Show What You Know, Lesson Quick Check, and Assessments to diagnose students’ intervention levels. • Waggle Practice and Games For students who successfully complete lessons, use: For students who are generally at grade level but need early intervention with the lesson concepts, use: For students who need small group instruction to review concepts and skills needed for the chapter, use: For students who need one-on-one instruction to build foundational skills for the chapter, use: 1 2 3 Prerequisite Skills Activities 1 2 3 Tier 2 Activity • Reteach • Tabletop Flipchart Mini Lesson • Waggle 1 2 3 Tier 1 Activity 1 2 3 Prerequisite Skills Activities 1 2 3 Tier 3 Activity • Ready for More Activity for every lesson • Enrich School-Home Letter is available in English and Spanish online, and in multiple other languages. Have students complete the activities on this page by working alone or with partners. Visualize It A tree map helps to classify words. Start with the main idea, Multiplication Properties. The example in the box to the left shows the Identity Property. In the middle box, the example shows the Associative Property, and the example in the box to the right shows the Commutative Property. Understand Vocabulary Students can enhance their understanding of key chapter vocabulary through the use of the VOCABULARY CARDS. Have students cut out the cards and create their own deck of terms. You can use these cards to reinforce knowledge and reading across the content areas. Program Tour T13

HISPANIC FEMALE PROGRAM TOUR Waggle® FOCUSING ON THE WHOLE CHILD Go Math! with Waggle combines child-centered instruction with powerful personalization, immersing students in rigorous, skills-based practice that assesses knowledge in real time. Waggle provides flexibility in and out of the classroom. Teachers can leverage HMH Growth Measure to place children on personalized pathways of skills-based instruction and practice, or choose the assignments that extend their instruction. Waggle and Go Math! are two of the HMH solutions connected by HMH Growth Measure on Ed. Can I really fit all of this into my math block? • Plan for children to use Waggle for 20 minutes 2–3 times per week. • You can incorporate Waggle into rotations for targeted learning. • You can use Waggle to extend learning outside of your scheduled math block. • You can find Waggle content by standard, Growth Measure data, or the Go Math! table of contents inside Waggle. Go Math! ® Learning Model with Waggle® Independent Practice 5 min. 10-15 min. 5 min. 5-10 min./day 45-minute instructional block for 1 day or 90 minutes for 2 days Engage Explore Evaluate 5 min. Explain Independent Practice Guided Practice Collaborative Groups Adaptive Practice with Waggle 2-3 rotations per week Direct Instruction & Guided Practice Readiness: • Daily Routines • Access Prior Knowledge Engagement: • I Can Objective • Learning Activity Direct Instruction & Guided Practice • Explore Problems Elaborate Options: • I Can Reflection • Exit Ticket • Journal Writing Options: • Practice and Homework • Lesson Check • Spiral Review • Waggle Direct Instruction & Guided Practice • Share and Show T14 Go Math! Grade 4

PROGRAM TOUR Waggle Activities What They Are When to Use Them Skills Boosts • short, five-question exercises • same questions for all students • target a single skill • formative assessment Assign Skill Boosts before instruction for a quick assessment of each student's understanding of a particular skill. Assign Skill Boosts after instruction for a brief check of understanding. Learning Goals • dynamic and adaptive practice • personalized path for each student • target several related skills • provide scaffolded hints and personalized feedback Assign Learning Goals when you want students to follow a personalized path to reach proficiency. These can be used for enrichment or reteaching support. Lessons • automatically triggered when a student struggles in a Learning Goal • teach and model individual skills • conclude with a five-item skill check for students to apply what they have learned Lessons will automatically be assigned to students struggling with a Learning Goal. They can also be assigned manually when students need reintroductions or refreshers with certain skills. . Games • focus on fluency • fun, trackable practice • utilize an item generator for unlimited, skill-based gameplay Assign Games for fluency practice. CAUCASIAN MALE AA MALE • Practice activities are designed to follow core instruction and assess proficiency. • Learning activities combine instruction, practice, and formative assessments to accelerate learning. • Waggle identifies skill gaps as children work through practice and learning activities. • Formative assessments inform personalized pathways for children and provide powerful insights for teachers. • K–2 teachers assign Waggle's K–2 lessons, which set children on either an Enrich or Extend path that selects the best mix of instruction and practice items. Items are related to each skill based on children's understanding. Each K–2 lesson concludes with a section designed to allow children an opportunity to apply their knowledge. • 3–5 teachers can use Waggle's Growth Measure-powered auto-assign. With auto-assign, children progress down their own learning path based on skill gaps and priority standards. Or, 3–5 teachers can manually assign content based upon a particular Go Math! lesson, standard, or skill. How does Waggle work? How do I decide what to assign my students in Waggle? Program Tour T15

Authentic Partnerships Schoolwide Culture, Practices & Policies SEL Instruction & Classroom Climate Aligned Learning Opportunities SELFMANAGEMENTSELFAWARENESS RESPONSIBLE DECISIONMAKING SOCIAL AWARENESS SOCIAL & EMOTIONAL LEARNING RELATIONSHIP SKILLS © 2017 CASEL ALL RIGHTS RESERVED FAMILIES & CAREGIVERS SCHOOLS CLASSROOMS COMMUNITIES PROGRAM TOUR FOCUSING ON THE WHOLE STUDENT Social & Emotional Learning Social and Emotional Learning (SEL) is a critical aspect of students’ school experience. Inclusive and equitable mathematics environments cultivate the social, emotional, and academic competencies needed for students to contribute to a caring, thriving, and just society. • Cultivate a sense of belonging and community where students see themselves as mathematicians, collectively striving to develop a deep understanding of mathematics. • Provide structures for physical and emotional safety so that mathematical sense-making is cognitively possible. • Create space for student voice and agency as a means to productively shape students’ mathematical identities. • Provide tiered supports that meet the needs of all students to access and experience the joy, wonder, and beauty of mathematics. • Use engaging, relevant, and culturally responsive mathematics instruction built on an understanding of how students grow and develop socially, emotionally, and academically. • Offer frequent opportunities for students to discuss and practice anti-racism and develop collaborative solutions to address inequities using mathematics as a tool. • Engage in mathematics teaching practices that affirm diverse social, cultural, and linguistic identities. SELF-AWARENESS: The abilities to understand one’s own emotions, thoughts, and values and how they influence behavior across contexts. SELF-MANAGEMENT: The abilities to manage one’s emotions, thoughts, and behaviors effectively in different situations and to achieve goals and aspirations. RESPONSIBLE DECISION-MAKING: The abilities to make caring and constructive choices about personal behavior and social interactions across diverse situations. RELATIONSHIP SKILLS: The abilities to establish and maintain healthy and supportive relationships and to effectively navigate settings with diverse individuals and groups. SOCIAL AWARENESS: The abilities to understand the perspectives of and empathize with others, including those from diverse backgrounds, cultures, and contexts. ©2020 CASEL. All RIghts Reserved. CASEL's Student Competencies Adapted from Reunite, Renew, and Thrive: SEL Roadmap for Reopening School, CASEL, July 2020, https://casel.org/reopening-with-sel/. Mathematics Learning Environment A safe, supportive, and equitable learning environment calls on mathematics teachers to: T16 Go Math! Grade 4

Reflect on one’s cultural lens Recognize and redress bias in the system Model high expectations for all students Promote respect for student dierences Draw on students’ culture to shape curriculum and instruction Bring real-world issues into the classroom Communicate in lingusitically and culturally responsive ways Collaborate with families and the local community 8 Competencies for culturally responsive teaching PROGRAM TOUR FOCUSING ON THE WHOLE STUDENT The HMH Go Math! Commitment HMH is using this framework to guide our content and services. Created in 2019, it has been used by educators across the country as a tool to reflect on and strengthen their culturally responsive teaching practices. from Culturally Responsive Teaching: A Reflection Guide, New America, https://www.newamerica.org/education-policy/policy-papers/ culturally-responsive-teaching-competencies/. Image credit: © HMH Program Tour T17

• Look for strategies throughout the lesson to support multilingual learners. • Log on to ED to find additional multilingual activities and Vocabulary Cards. * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. Planning for Instruction Language Support Substantial (WIDA Level 1)* Moderate (WIDA Levels 2 & 3)* Light (WIDA Levels 4 & 5)* Student’s Use of Language • uses single words • uses common short phrases • heavily relies on visual supports and use of manipulatives • uses single words • uses some academic vocabulary • relies on visual supports and use of manipulatives • uses a variety of sentences • uses academic vocabulary • benefits from visual supports and manipulatives Ways to Assess Understanding Listening: points to pictures, words, or phrases to answer questions Speaking: answers yes/no questions Reading: matches symbols to math terms and concepts Writing: draws a visual representation of a problem Listening: matches, categorizes, or sequences information based on visuals Speaking: begins to explain reasoning, asks math questions, repeats explanations from peers Reading: identifies important information to solve a problem Writing: uses simple sentences and visual representations Listening: draws conclusions and makes connections based on what they heard Speaking: explains and justifies concepts and solutions Reading: understands information in math contexts Writing: completes sentences using some academic vocabulary Assessing your student’s understanding of mathematical concepts can be done by listening, speaking, reading, and writing. The level of support a student needs determines how best to assess that student’s understanding of mathematical concepts, and will help meet the needs of all your students. Strategies for Multilingual Learners CHAPTER 3 107G Go Math! Grade 3 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. In This Chapter Key Academic Vocabulary Current Development • Vocabulary Associative Property of Multiplication, Distributive Property, multiple Using Language Routines to Develop Understanding Language routines provide opportunities for students to develop an understanding of mathematical language and concepts by listening, speaking, reading, and writing. More information on these language routines can be found on the Language Support Cards. Compare and Connect Students share their work with a partner to compare and contrast their strategies. Language Support Substantial (WIDA Level 1)* Moderate (WIDA Levels 2 & 3)* Light (WIDA Levels 4 & 5)* Language Routine Differentiation Students will point out similarities and differences on visual representations. They may use short phrases to verbally compare and contrast their strategies. Students would rely on visual representations to inform their simplesentence discussions as they compare and contrast their strategies. Students would be able to use some academic vocabulary to compare and contrast their strategies with a partner or small group. Possible Student Work 4 × 8 = 32 8 × 4 = 32 Say: Compare. Are they the same? Student: Yes. They both equal 32. Say: Compare. Are they different? Student: Yes. The groups have different counters. Ask: What is 4 × 8? Show it with counters. Say: Use the counters to make another equation that shows 32. Say: Compare. How are they the same? Student: They both show equal groups. Say: Compare. How are they different? Student: The number of counters in the groups are different. Say: Write the equations. 4 × 8 = 32 8 × 4 = 32 Say: Compare. How are they the same? Student. They use the same factors. They both equal 32. Say: Compare. How are they different? Student: The factors are in a different order. Say: Write companion equations. Say: Compare. How did you know what to write? Chapter 3 107H DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A PROGRAM TOUR Supporting Multilingual Learners The Go Math! program includes print and online resources based on WIDA Language Support levels to provide examples of differentiated questions and strategies for multilingual learners. Chapter-Level Language Support The instruction highlights key academic vocabulary as well as language routines. The language routines provide opportunities for students to develop their understanding of mathematical language and concepts by listening, speaking, reading, and writing. Planning for Instruction Understanding the level of language support needed by your students is an important step in planning differentiation. The Planning for Instruction chart at the start of each chapter helps you explore your students’ current WIDA levels. Key Academic Vocabulary Multilingual learners are most successful when they learn key mathematical vocabulary throughout the lessons. Use the Language Routine Differentiations and Possible Student Work as a guide to better assess student's understanding of mathematical concepts based on their current level of language proficiency. T18 Go Math! Grade 4

____ = ____ Math Talk Construct arguments and critique reasoning of others. What do you notice about the product when you multiply by 2? MP Math Talk: Possible answer: When you multiply by 2, the product is always an even number. 6 6 8 5 5 3 3 4 4 10 6 8 12 16 7 9 7 9 14 18 3_mnlese694724_c03l01.indd 109 5/18/2022 11:00:31 AM PROGRAM TOUR Students can access a Glossary in their Student Editions, an Interactive Glossary online, as well as a Multilingual Glossary available in ten languages. Language Routines Language Routines Cards help teachers develop student reasoning and discourse during instruction. THREE READS Students read a problem three times with a specific focus each time: 1. Read What is the problem about? 2. Read What do each of the numbers describe? 3. Read What math questions could you ask about the problem? CRITIQUE, CORRECT, AND CLARIFY • Students analyze an incorrect explanation or solution. • Students work with a partner or small group to identify the error. • Students work together to correct the sample work. STRONGER AND CLEARER EACH TIME • Students show their thinking with math tools and visuals. • Students share their thinking and receive feedback with a partner or a group. • Students revoice feedback and revise their work. COMPARE AND CONNECT Students understand multiple solution strategies by relating other students’ approaches to their own approach. Lesson-Level Language Support Every lesson of Go Math! includes multilingual support. These are indicated by . Program Tour T19

PROGRAM TOUR Manipulatives and Tools Go Math! provides opportunities for students to choose manipulatives and tools to make sense of mathematics and express relationships. Flexible concrete and digital tools help students connect concepts to procedures and adapt their representations to different mathematical contexts. By seeing how students choose tools and which tools they choose, teachers also gain insight into the connections they’re making. In Go Math!, students have access to manipulatives for hands-on exploration, as well as digital manipulatives to supplement and extend that exploration. Both concrete and digital manipulatives support them in making sense of situations, solving problems, and checking their reasoning. Students experiment with a wide range of physical and visual representations of numbers and operations, including grouping, arrays, and number lines. Models like base ten blocks provide an ongoing foundation for students as they deepen their understanding of place value. The base ten number system becomes a flexible, extensible way to model their world. Students continue to build confidence and fluency with operations and their relationships to each other and to understand mathematical properties as tools. T20 Go Math! Grade 4

PROGRAM TOUR Students explore the many ways fractions can be represented and can represent situations in the world. They extend their understanding of shapes and the language they use to describe them, connecting that language with the different properties of shapes, how they relate, and how to measure them. Students use both measurement and modeling to understand a variety of units and to solve problems. TM and Version 2.0 Differentiated Centers Kit Grab Manipulatives are included in your Grab & Go kits. Kit contents are tailored to address the needs for each grade and may not be identical to what is shown here. Program Tour T21

Growth Measure PROGRAM TOUR Assessments to Drive Classroom Instruction Use a range of formative and summative assessments to measure students’ understanding as they develop mastery of the standards. Grade-Level Assessments Resource Assessment Features/Purpose Formats HMH Student Growth Measure 40 minutes Summative Growth Measure • Administered 3 times per year using items aligned to national assessments • Monitors student growth over time • Provides data reports to guide instructional decisions • Produces a Quantile Score grade level expectation against national assessments • Computer-adaptive digital assessment* • All items are multiple choice Beginning/ Middle/End of Year Test 40 minutes Diagnostic/ Summative • Administered at the beginning, middle, or end of the school year • All items aligned to national assessments • Measures mastery of content taught in Go Math! • Individual Record Forms show standards alignment, DOK, and intervention options for each item • PDF (Assessment Guide) Prerequisite Skills Inventory 40 minutes Diagnostic • Administered at the beginning of the school year • Assess core precursor skills associated with on-grade success • Review/intervention students may need to be successful in learning grade-level standards • Individual Record Forms show standards alignment, DOK, and intervention options for each item • PDF (Assessment Guide) Performance Tasks 30–40 minutes Performance Assessment (Formative/ Summative) • Assess students' ability to use what they have learned to solve everyday problems • Include a rubric for scoring purposes • Individual Record Forms show standards alignment, DOK, and intervention options for each item • PDF (Assessment Guide) • Constructed response format only Chapter-Level Assessments Resource Assessment Features/Purpose Formats Show What You Know 20 minutes Diagnostic • Administered at the beginning of the chapter • Assess prior knowledge from previous grades and content taught earlier in the grade • Intervention and individualized instructional recommendations are provided • Student Edition • Digital/interactive* • Mostly short answer items Chapter Review 20 minutes Summative/ Formative • Administered at the end of the chapter • Evaluates students' mastery of concept and skills taught in the module • Hints and corrective feedback are available for all items • All items aligned to content based on national assessments • Student Edition • Digital/interactive* Chapter Test 30–40 minutes Summative/ Formative • Administered at the end of the chapter • Evaluates students' mastery of concept and skills taught in the chapter • Digital/interactive* • PDF (Assessment Guide) • English and Spanish *These assessments provide data that can be accessed through Ed. T22 Go Math! Grade 4

PROGRAM TOUR Lesson-Level Assessments Resource Assessment Features/Purpose Formats Explain/Share and Show 15-20 minutes Formative • Formative assessment in every lesson • Teachers use data to determine which students need additional small-group support and which students can continue on to independent practice or math center challenges • Interactive Student Edition • Print Student Edition • Mostly short answer items Elaborate/ On Your Own 10 minutes Formative • As the lesson concludes, evaluates students’ mastery of concepts and skills taught in the lesson • Includes step-by-step methods for students to solve problems • Interactive Student Edition • Print Student Edition • Mix of item types from the lesson Evaluate/ Practice and Homework 20-30 minutes Formative • Administered at the end of the lesson • Evaluates students’ mastery of concepts and skills taught in the lesson • Contains Spiral Review problems • Print Student Edition • Digital/interactive • Mix of item types from the lesson Test Prep/Standards Mastery Resource Assessment Features/Purpose Formats StandardsBased Practice 20-30 minutes Test Prep • Administered when additional practice is needed to achieve standards mastery with a wide variety of ways in which the standard may be assessed, the standards-based practice helps students practice key standards and skills associated with grade-level success. • Hints and corrective feedback are available for all items • Individual Record Forms show standards alignment, DOK, and intervention options for each item • Digital/interactive* Getting Ready for HSA Practice Tests 40 minutes Test Prep • Administered to help students prepare for high stakes assessments • 3 practice tests available per grade • Digital/interactive* • Includes Constructed Response items Test Prep opportunities are also available in every More Practice problem set. DEPTH OF KNOWLEDGE (DOK) DOK Growth Measure Module Tests, Beginning, Middle, and End-of-Year, and Test Prep Lesson/Module Practice (Formative Assessments) Performance Assessments DOK 1 varies** 40–45% 50–55% 0–5% DOK 2 varies** 40–45% 40–45% 60–65% DOK 3 varies** 5–10% 0–5% 30–35% DOK 4 DOK 4 problems can be found in the Performance Tasks and Project Cards. All percentages are approximations. **The HMH Growth Measure is a computer-adaptive assessment. The DOKs of items will vary based on students’ individual experiences. Growth Measure *These assessments provide data that can be accessed through Ed. Program Tour T23

3 or multiply 2 × 3. Check students’ drawings. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 3_mnlese694724_c03l01.indd 109 10/8/2021 5:30:16 AM DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A DO NOT EDIT--Changes must CorrectionKey=NL-A 3_mnlete694847_c03l01.indd 109 10/22/2021 11:03:19 AM PROGRAM TOUR 1) National Council of Teachers of Mathematics, Principles to Actions: Ensuring Mathematical Success for All (Reston, VA: NCTM, 2014). Teacher Support Supporting Best Practices Go Math! helps students grow by providing teachers with instruction designed around proven-effective teaching practices, such as those described in Principles to Actions (NCTM, 2014)1. • Establish mathematics goals to focus learning • Implement tasks that promote reasoning and problem solving • Use and connect mathematical representations • Facilitate meaningful mathematical discourse • Pose purposeful questions • Build procedural fluency from conceptual understanding • Support productive struggle in learning mathematics • Elicit and use evidence of student thinking Carefully crafted tasks, student-centered learning, small groups, and hands-on manipulatives play important roles in a Go Math! classroom. Point-of-use support helps you facilitate learning and implement research-based best practices. Professional Learning Videos Every chapter includes a professional learning video featuring a teacher or HMH author working with real students who are engaging in similar activities. The videos include modeling and discussion of effective teaching practices, as well as Language Routines and Talk Moves strategies. These strategies are key supports for multilingual students, and for all students in expressing their thinking. Online Resources Teacher’s Corner Go online to Teacher’s Corner for on-demand, bite-size articles, videos, and other resources to tailor your professional learning to your specific needs. Image Credit: ©HMH T24 Go Math! Grade 4

Integrating Language Routines Into Instruction © Houghton Mifflin Harcourt Publishing Company Grades 3–5 From the Classroom PRESENT Ms. G: Look up here [directing students to look at the board where she has written: For any square, the area and perimeter are the same]. Do you agree or disagree? Study this individually, writing down any questions, ideas, or reasoning that you have about it. Try to use complete sentences. PREPARE Students Pre-Write [Ms. G pauses for a full minute while students write their thoughts.] Think Time Ms. G: In a moment, you will partner up to discuss if you agree or disagree and why. You won’t take your papers with you, so pause now and study your notes. PARTNER Structured Pairing Ms. G: To start, you will partner up. When you talk with your partner, explain your ideas like a mathematician, and partners ask questions to clarify. It is important to be clear in your explanations. The purpose is to borrow ideas from your partner to make your argument stronger and clearer. In Pairs Ms. G: Find your first partner, and start your discussion. [Ms. G circulates while students discuss and listen for common justifications. After one minute, she signals for students to switch listener/speaker roles.] Rotate Partners Ms. G: Rotate to a new partner, and repeat the sharing and listening. Incorporate ideas you heard as you make your arguments stronger and clearer. [Ms. G circulates again while students discuss and listen for common justifications. She has students switch one more time for a total of three partner discussions.] PROCESS Post-Write Ms. G: Head back to your seats. You have 2 minutes to revise your original argument. Take things you heard from your partners, and strengthen and clarify your original thoughts. Compare Ms. G: Now that you’ve refined your arguments, look at what you first wrote and your final draft. What do you notice? Raaqim: In my first draft, I said that it was not true because I tried squares with side lengths of 2 and 6. When I was talking with my second partner, she said it was true because she tested out a square that has a side length of 4. I decided to change my final draft to say that it is not always true. [Ms. G continues to facilitate the class discussion. Students share how their arguments are improved after their partner discussions.] © Houghton Mifflin Harcourt Publishing Company Into Instruction Integrating Language Routines (continued) Grades 3–5 Stronger and Clearer Each Time Mathematical understandings and language competence develop interdependently. When students discuss mathematical ideas with one another, they strengthen and clarify their academic thoughts. Language Routine: Stronger and Clearer Each Time This routine is well-suited for circumstances that call for students to construct a mathematical argument or defend an idea. Each time students talk with partners, they build from and borrow the ideas and language of previous partners. Routine PRESENT Teacher poses a problem/question to students PREPARE Students Pre-Write • Students study the problem individually, writing down any questions or ideas/reasoning about how to solve the problem, using complete sentences if possible. • Scaffolding: Provide sentence frames or a skeletal paragraph framework to support students with the language structures, while leaving room for their independent mathematical reasoning. Think Time • Provide a minute for students to think about what they will say to their first partner, considering what they are currently doing (or did) to solve the problem. • Students cannot look at what they wrote during their partner conversations. PARTNER STRUCTURED PAIRING: PARTNER ROTATIONS Students • Listener asks clarifying questions, especially related to justifying (Why did you do that?). • Partners switch roles. Each person shares and each person listens, asking clarifying questions. • Rotate to additional partners, strengthening and clarifying their ideas each time Teacher • Circulates and listens during student discussions • Prompts students at each turn to emphasize strength (focus on math concepts and skills) or clarity (how to describe the math to others) • Removes scaffolds with each successive pairing to build student independence PROCESS Post-Write • Students return to seats and write down their final explanations using sentences or drawings supported with sentences. Compare • Students analyze their pre-writes and post-writes, noticing how their ideas were strengthened and/or clarified during partner discussions. TM and Version 2.0 Differentiated Centers Kit Grab CHAPTER 3 LESSON 3.1 • 1 Day LESSON 3.2 • 1 Day LESSON 3.3 • 1 Day Lesson at a Glance Multiply with 2 and 4 . . . . . . . . . . . . . 109A Multiply with 5 and 10 . . . . . . . . . . . . 115A Multiply with 3 and 6 . . . . . . . . . . . . . 121A I Can I can multiply with 2 and 4. I can multiply with 5 and 10. I can multiply with 3 and 6. Learning Goal Draw a picture, count by 2s, or use doubles to multiply with the factors 2 and 4. Use skip counting, a number line, or a bar model to multiply with the factors 5 and 10. Draw a picture, use 5s facts and addition, doubles, or a multiplication table to multiply with the factors 3 and 6. Vocabulary multiple Multilingual Support Strategy: Illustrate Understanding Strategy: Elicit Prior Knowledge Strategy: Develop Meanings Practice and Fluency LESSON 3.1 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* LESSON 3.2 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* LESSON 3.3 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 3 .1 ◆ ■ Tier 2 Intervention Skill S57 ◆ ■ Tier 3 Intervention Skill E57 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 3 .1 ■ Waggle ◆ ■ Reteach 3 .2 ◆ ■ Tier 2 Intervention Skill S55/S56 ◆ ■ Tier 3 Intervention Skill E55/E56 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 3 .2 ■ Waggle ◆ ■ Reteach 3 .3 ◆ ■ Tier 2 Intervention Skill S62 ◆ ■ Tier 3 Intervention Skill E62 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 3 .3 See the Grab-and-Go!™ Centers Kit for more small-group activities. ◆ Print/Printable Resource ■ Interactive Resource Multiplication Facts and Strategies Chapter at a Glance The kit provides literature, games, and activities for small-group learning. 107A Go Math! Grade 3 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A Chapter Pacing Chart Introduction Instruction Assessment Total 1 day 10 days 2 days 13 days LESSON 3.4 • 1 Day LESSON 3.5 • 1 Day LESSON 3.6 • 1 Day Lesson at a Glance Understand the Distributive Property . . . . . . . . . . 127A Multiply with 7 . . . . . 133A Understand the Associative Property of Multiplication . . . . 139A I Can I can use the Distributive Property to find products. I can use multiple strategies to multiply with 7. I can use the Associative Property of Multiplication to find products. Learning Goal Use the Distributive Property to find products by breaking apart arrays. Use the Commutative or Distributive Property or known facts to multiply with the factor 7. Use the Associative Property of Multiplication to multiply with three factors. Vocabulary Distributive Property Associative Property of Multiplication Multilingual Support Strategy: Rephrase Strategy: Model Concept Strategy: Illustrate Understanding Practice and Fluency LESSON 3.4 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* LESSON 3.5 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* LESSON 3.6 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment     ■ Waggle ◆ ■ Reteach 3 .4 ◆ ■ Tier 2 Intervention Skill S69 ◆ ■ Tier 3 Intervention Skill E69 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 3 .4     ■ Waggle ◆ ■ Reteach 3 .5 ◆ ■ Tier 2 Intervention Skill S70 ◆ ■ Tier 3 Intervention Skill E70 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 3 .5     ■ Waggle ◆ ■ Reteach 3 .6 ◆ ■ Tier 2 Intervention Skill S68 ◆ ■ Tier 3 Intervention Skill E68 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 3 .6 ◆ Print/Printable Resource ■ Interactive Resource *For individual and class practice with counting automaticity and operational fluency, go to Achieving Facts Fluency pages located online. Chapter 3 107B DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A LESSON 3.10 • 1 Day Lesson at a Glance Multiply with 11 and 12 . . . . . . . . . . . . 163A I Can I can use multiple strategies to multiply with 11 and 12. Learning Goal Use the Distributive Property with addition or subtraction or patterns to multiply with the factor 11 or 12. Vocabulary Multilingual Support Strategy: Develop Meaning Practice and Fluency LESSON 3.10 ◆ ■ Practice and Homework ■ ■ Waggle ◆ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment     ■ Waggle ◆ ■ Reteach 3 .10 ◆ ■ Tier 2 Intervention Skill S70 ◆ ■ Tier 3 Intervention Skill E70 ◆ ■ Enrich 3 .10 ◆ Print/Printable Resource ■ Interactive Resource Consider the active and participatory communication styles of linguistically diverse children and how they engage in Math Talk. SUPPORTING ALL LEARNERS Embrace and honor the linguistic diversity of children by engaging them in relevant mathematics tasks with multiple paths for success. Image Credit: ©HMH *For individual and class practice with counting automaticity and operational fluency, go to Achieving Facts Fluency pages located online. Chapter 3 107D DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A Chapter pacing and pacing for each lesson is conveniently located. PROGRAM TOUR When students verbalize their thoughts and hear what classmates are thinking, they become stronger mathematicians. Math Talk tools for teachers and students help children achieve different communication aims and deepen their understanding. Professional Learning Cards The Go Math! Professional Learning Cards include teacher supports for Talk Moves and Language Routines. Talk Moves encourage children to verbalize their thoughts. Language Routines provide opportunities for students to internalize their mathematical thinking and describe their knowledge through writing, discourse, and engagement. Image Credit: ©HMH The Chapter at a Glance pages provide the details and resources for each lesson, starting with Lesson at a Glance, the I Can statement, and the lesson learning goal. Multilingual Support strategies help you to plan ahead, as do lists of resources for Practice and Fluency, and Intervention and Enrichment. Program Tour T25

32 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A PROGRAM TOUR Teaching for Depth Teaching for Depth gives you background about the best practices and research related to the lesson’s concepts. Identify ways the chapter lessons and activities can be extended into opportunities for students to achieve mathematical thinking and reasoning. Gain understandings of common errors and misunderstandings students may have as they begin the work in the chapter. Then identify tools and strategies that they can use to become proficient. Explore more deeply the research behind the strategies used in the Go Math! lessons. T26 Go Math! Grade 4

 3. Pídale a su hijo que le diga cuáles son las operaciones de dobles. Agregue otro artículo a uno de los grupos y pida a su hijo que nombre la operación de dobles más uno. Literature Busque estos libros en una biblioteca. Señale ejemplos de operaciones de dobles y de contar uno hacia delante en las imágenes. 12 Ways to Get to 11 por Eve Merriam. Aladdin, 1996. Two of Everything: A Chinese Folktale por Lily Toy Hong. Albert Whitman and Company, 1993. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=FL-A PROGRAM TOUR Connect with Families and Community Go Math! provides resources teachers can use to engage families throughout the school year. Math on the Spot video tutorials provide instruction of the math concepts covered and allow for family involvement in learning. In addition, the write-in format of the print Student Edition gives families a front-row seat to their child’s thinking and progress over time, encouraging a strong home-school connection. School-Home Letters inform families about the skills, strategies, and topics students are encountering at school, extending rich dialogue beyond the classroom. The School Home Letters are available in English, Spanish, Portuguese, and Haitian Creole. Image Credit: ©HMH Program Tour T27

PROGRAM TOUR Ashlock, R. (2010). Error patterns in computation: Using error patterns to help each student learn (10th ed.). Boston, MA: Allyn & Bacon. Bahr, D. L. & de Garcia, L. A. (2010). Elementary mathematics is anything but elementary. Belmont, CA: Wadsworth. Baldi, S., Jin, Y., Skemer, M., Green, P. J. & Herget, D. (2007). Highlights from PISA 2006: Performance of U.S. 15-year-old students in science and mathematics literacy in an international context (NCES 2008–016). National Center for Education Statistics, Institute of Education Sciences. Washington, DC: U.S. Department of Education. Bartell, T. G., Bieda, K. N., Putnam, R. T., Bradfield, K., & Dominguez, H. (Eds.). (2015). Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University. Battista, M. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: 2 (pp. 843–908). Charlotte, NC: Information Age Publishing. Beckmann, S. (2008). Mathematics for elementary teachers. Boston, MA: Pearson Education. Carroll, W. M., & Porter, D. (1998). Alternative algorithms for wholenumber operations. In J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics: 1998 yearbook. (pp. 106–114). Reston, VA: National Council of Teachers of Mathematics. Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2011). Learning mathematics in elementary and middle schools. Columbus, OH: Pearson. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann and Reston, VA: National Council of Teachers of Mathematics. Casa, T. M., & Gavin, M. K. (2009). Advancing students’ understanding of quadrilaterals. In T. V. Craine & R. Rubenstein (Eds.), Understanding geometry for a changing world (pp. 205–220). Reston, VA: National Council of Teachers of Mathematics. Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. New York: Routledge, Taylor and Francis. de Groot, C., & Whalen, T. (2006). Longing for division. Teaching children mathematics 12(8), pp. 410–418. de Villiers, M., Govender, R., & Patterson, N. (2009). Defining in geometry. In T. V. Craine & R. Rubenstein (Eds.), Understanding geometry for a changing world: Seventy-first yearbook (pp. 189–203). Reston, VA: National Council of Teachers of Mathematics. Flores, A. (2002). Profound understanding of division of fractions. In B. H. Litwiller (Ed.), Making sense of fractions, ratios, and proportions, 2002 Yearbook (pp. 237–246). Reston, VA: National Council of Teachers of Mathematics. Franke, M. L., Carpenter, T. P., & Battey, D. (2008). Content matters: Algebraic reasoning in teacher professional development. In J. J. Kaput, D. W. Carraher, and M. L. Blanton (Eds.), Algebra in the early grades (pp. 333–359). New York: Lawrence Erlbaum Associates/ National Council of Teachers of Mathematics. Frykholm, J. (2010). Learning to think mathematically with the number line: A resource for teachers, a tool for young children. Retrieved from https://www.mathlearningcenter.org/sites/default/files/pdfs/LTM_ Numberline.pdf. Furhman, S. H., Resnick, L., & Shepard, L. (2009). Standards aren’t enough. Education Week 29(7), p. 28. Fuson, K. C. (2003). Developing mathematical power in whole number operations. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 68–94). Reston, VA: National Council of Teachers of Mathematics. Fuson, K. C., SanGiovanni, J., & Adams, T. L. (2009). Focus in grade 5: Teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics. Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Katsberg, D., & Brenwald, S. (2008). Highlights from TIMSS 2007: Mathematics and science achievement of U.S. fourth- and eighth-grade students in an international context (NCES 2009–001 Revised). National Center for Education Statistics, Institute of Education Sciences. Washington, DC: U.S. Department of Education. Gravemeijer, K. & van Galen, F. (2003). Facts and algorithms as products of students’ own mathematical activity. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.) A research companion to principles and standards for school mathematics (pp. 114–122). Reston, VA: National Council of Teachers of Mathematics. Hatfield, M. M., Edwards, N. T., Bitter, G. G., & Morrow, J. (2008). Mathematics methods for elementary and middle school teachers. Hoboken, NJ: John Wiley & Sons. Heddens, J. W., & Speer, W. R. (2006). Today’s mathematics: Concepts, methods, and instructional activities (11th ed.). Hoboken, NJ: John Wiley & Sons. Hiebert, J. (1999). Relationships between research and the National Council of Teachers of Mathematics standards. Journal for Research in Mathematics Education 30(1), pp. 3–19. Huinker, D. (2002). Examining dimensions of fraction operation sense. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 yearbook (pp. 1–48). Reston, VA: National Council of Teachers of Mathematics. Irwin, K. C. (2001). Using everyday knowledge of decimals to enhance understanding. Journal for Research in Mathematics Education, 32(4), 399–420. Kamii, C., & Warrington, M. A. (1999). Teaching fractions: Fostering children’s own reasoning. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12: 1999 yearbook (pp. 82–92). Reston, VA: National Council of Teachers of Mathematics. Professional Learning References T28 Go Math! Grade 4

PROGRAM TOUR Konold, C. & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.) A research companion to principles and standards for school mathematics (pp. 193–215). Reston, VA: National Council of Teachers of Mathematics. Lamon, S. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates. Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurements in the elementary grades. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 100–121). Reston, VA: National Council of Teachers of Mathematics. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates. Marzano, R. J. (2003). What works in schools: Translating research into action. Alexandria, VA: ASCD. Monk, S. (2003). Representation in school mathematics: Learning to graph and graphing to learn. In J. Kilpatrick, W. G. Martin, and D. Schifter (Eds.), A research companion to principles and standards for school mathematics. (pp. 250–262). Reston, VA: National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics. (2005). Standards and curriculum: A view from the nation—A joint report by the National Council of Teachers of Mathematics (NCTM) and the Association of State Supervisors of Mathematics (ASSM). J. W. Lott & K. Nishimura (Eds.). Reston, VA: Author. National Council of Teachers of Mathematics (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: Author. National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U. S. Department of Education. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Washington, DC: National Academy Press. Outhred, L., Mitchelmore, M., McPhail, D., & Gould, P. (2003). Count me into measurement: A program for the early elementary school. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 81–99). Reston, VA: National Council of Teachers of Mathematics. Reed, D. S. (2009). Is there an expectations gap? Educational federalism and the demographic distribution of proficiency cut scores. American Educational Research Journal 46(3), pp. 718–742. Reys, B. J., Chval, K., Dingman, S., McNaught, M., Regis, T. P., & Togashi, J. (2007). Grade-level learning expectations: A new challenge for elementary mathematics teachers. Teaching Children Mathematics 14(1), pp. 6–11. Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., & Suydam, M. N. (2009). Helping children learn mathematics (9th ed.). Hoboken, NJ: John Wiley & Sons. Ross, S. H. (1989). Parts, wholes, and place value: A developmental view. Arithmetic Teacher 36(6), pp. 47–51. Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: A study of the efficacy of a lesson sequence that uses the number line as the principal representational context. The International Journal on Mathematics Education 45(3), pp. 343–364. doi:10.1007/s11858-012- 0466-2. Schielack, J. (2009). Focus in grade 4: Teaching with curriculum focal points. Reston, VA: National Council of Teachers of Mathematics. Schifter, D. (1999). Reasoning about operations: Early algebraic thinking in grades K–6. In L. Stiff (Ed.), Developing mathematical reasoning in grades K–12: 1999 yearbook of the National Council of Teachers of Mathematics (pp. 62–81). Reston, VA: National Council of Teachers of Mathematics. Schmoker, M. (2011). Focus: Elevating the essentials to radically improve student learning. Alexandria, VA: ASCD. Schneider, M. (2007). National Assessment of Education Progress: Mapping 2005 state proficiency standards onto the NAEP scales. Washington, DC: IES National Center for Education Statistics. Sobel, M., & Maletsky, E. (1999). Teaching mathematics: A sourcebook for aids, activities, and strategies (3rd ed.). Boston, MA: Allyn & Bacon. Stephan, M. & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics. Taber, S. B. (2002). Go ask Alice about multiplication of fractions. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 yearbook (pp. 61–71). Reston, VA: National Council of Teachers of Mathematics. Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson. van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press. van Hiele, P. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics 5(6), pp. 310–316. Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Reston, VA: National Council of Teachers of Mathematics. WIDA (2020). WIDA English language development standards framework, 2020 edition: Kindergarten–grade 12. Board of Regents of the University of Wisconsin System. Program Tour T29

PROGRAM TOUR VOLUME 1 TABLE OF CONTENTS CHAPTER 1 Whole Number Place Value Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3C Daily Classroom Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Lesson 1 Model Place-Value Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Lesson 2 Read and Write Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Lesson 3 Compare and Order Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Lesson 4 Round Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34A CHAPTER 2 Addition and Subtraction Within 10,000 Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Lesson 1 Use Expanded Form to Add . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Lesson 2 Use Place Value to Add . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Lesson 3 Use Place Value to Subtract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Lesson 4 Combine Place Values to Subtract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Lesson 5 Model and Solve Two-Step Addition and Subtraction Problems . . . . . 61 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A Image credit: (t) ©Design Pics Inc./Patrick Endres/Alamy, (b) ©Diego Cervo/Shutterstock.com i Go Math! Grade 4

PROGRAM TOUR Launch Activity 1 Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73A CHAPTER 3 Multiply by 1-Digit Numbers Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Lesson 1 Multiplication Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Lesson 2 Comparison Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Lesson 3 Multiply Tens, Hundreds, and Thousands . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Lesson 4 Estimate Products by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Lesson 5 Multiply Using the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . 101 Lesson 6 Multiply Using Expanded Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Lesson 7 Multiply Using Partial Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Lesson 8 Multiply Using Mental Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Lesson 9 Multi-Step Multiplication Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Lesson 10 Multiply 3-Digit and 4-Digit Numbers with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Lesson 11 Solve Multi-Step Problems Using Equations . . . . . . . . . . . . . . . . . . . . . . 137 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148A Image credit: © (t) ©Ron Levine/Getty Images, (b) ©LIGHTFIELD STUDIOS/Adobe Stock Program Tour ii

PROGRAM TOUR CHAPTER 4 Multiply by 2-Digit Numbers Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Lesson 1 Multiply by Tens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Lesson 2 Estimate Products by 2-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Lesson 3 Area Models and Partial Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Lesson 4 Multiply Using Partial Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Lesson 5 Multiply with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Lesson 6 Choose a Multiplication Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Lesson 7 Multiply by 2-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198A CHAPTER 5 Division Strategies Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Lesson 1 Investigate Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Lesson 2 Interpret Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Lesson 3 Divide Tens, Hundreds, and Thousands . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Lesson 4 Estimate Quotients Using Compatible Numbers . . . . . . . . . . . . . . . . . . . 219 Lesson 5 Division and the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236A iii Go Math! Grade 4

PROGRAM TOUR CHAPTER 6 Divide by 1-Digit Numbers Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Lesson 1 Divide Using Repeated Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Lesson 2 Divide Using Partial Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Lesson 3 Model Division with Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Lesson 4 Place the First Digit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Lesson 5 Divide by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Lesson 6 Multi-Step Division Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280A Image credit: (bl) ©Billion Photos/Shutterstock, (l) ©george doyle/Getty Images; (r) © Samuel Borges Photography/Shutterstock Program Tour iv

PROGRAM TOUR CHAPTER 7 Apply Multiplication to Perimeter and Area Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Lesson 1 Apply the Perimeter Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Lesson 2 Apply the Area Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Lesson 3 Find Unknown Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Lesson 4 Find the Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312A CHAPTER 8 Factors, Multiples, and Number Patterns Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Lesson 1 Factors and Divisibilty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Lesson 2 Factors and Multiples..............................................321 Lesson 3 Prime and Composite Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Lesson 4 Number Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344A Image credit: © george doyle/Getty Images; © Rosemary Calvert/Getty Images v Go Math! Grade 4

PROGRAM TOUR Launch Activity 2 Parts of a Whole Amount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345A CHAPTER 9 Fraction Equivalence Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Lesson 1 Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Lesson 2 Generate Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 Lesson 3 Use Division to Generate Equivalent Fractions......................361 Lesson 4 Find Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Lesson 5 Write Fractions as Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Lesson 6 Rename Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390A Image Credit: ©HMH Program Tour vi

PROGRAM TOUR VOLUME 2 TABLE OF CONTENTS CHAPTER 10 Compare Fractions Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Lesson 1 Compare Fractions Using Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Lesson 2 Compare Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 Lesson 3 Compare and Order Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416A Image credit: © Blend Images/JR Carvey/Streetfly Studio/Getty images vii Go Math! Grade 4

PROGRAM TOUR CHAPTER 11 Add and Subtract Fractions Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 Lesson 1 Add and Subtract Parts of a Whole . . . . . . . . . . . . . . . . . . . . . . . 419 Lesson 2 Add Fractions Using Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Lesson 3 Subtract Fractions Using Models . . . . . . . . . . . . . . . . . . . . . . . . . 431 Lesson 4 Use Benchmarks to Determine Reasonableness . . . . . . . . . . . . . . 437 Lesson 5 Add and Subtract Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 Lesson 6 Add and Subtract Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . 449 Lesson 7 Use Properties of Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466A CHAPTER 12 Multiply Fractions and Whole Numbers Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 Lesson 1 Multiples of Unit Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Lesson 2 Multiples of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Lesson 3 Multiply a Fraction by a Whole Number Using Models . . . . . . . . . 481 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492A Image credit: ©Petra Wegner/Alamy Images Program Tour viii

PROGRAM TOUR CHAPTER 13 Relate Fractions and Decimals Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Lesson 1 Model Tenths and Hundredths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Lesson 2 Relate Tenths and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 Lesson 3 Relate Hundredths and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 Lesson 4 Equivalent Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Lesson 5 Relate Fractions, Decimals, and Money . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Lesson 6 Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Lesson 7 Add Fractional Parts of 10 and 100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Lesson 8 Compare Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 Lesson 9 Order Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554A Image Credit: ©HMH ix Go Math! Grade 4

PROGRAM TOUR Launch Activity 3 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555A CHAPTER 14 Two-Dimensional Figures Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 Lesson 1 Lines, Rays, and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 Lesson 2 Classify Triangles by Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 Lesson 3 Parallel Lines and Perpendicular Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 Lesson 4 Classify Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 Lesson 5 Line Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 Lesson 6 Find and Draw Lines of Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 Lesson 7 Shape Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606A CHAPTER 15 Measure Angles Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 Lesson 1 Explore Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 Lesson 2 Degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Lesson 3 Measure and Draw Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 Lesson 4 Join and Separate Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 Lesson 5 Unknown Angle Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644A Image credit: (t) ©Scol22/Adobe Stock; (bl) ©Adobe Stock Program Tour x

PROGRAM TOUR CHAPTER 16 Customary and Metric Measures Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646 Lesson 1 Measurement Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647 Lesson 2 Customary Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Lesson 3 Customary Units of Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 Lesson 4 Customary Units of Liquid Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Lesson 5 Mixed Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671 Lesson 6 Metric Units of Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677 Lesson 7 Metric Units of Mass and Liquid Volume . . . . . . . . . . . . . . . . . . . . . . . . . . 683 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694A Image credit: (l) ©Creatas/Jupiterimages/Getty Images, (r) ©Vasyl Syniuk/Shutterstock xi Go Math! Grade 4

PROGRAM TOUR CHAPTER 17 Temperature and Time Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695C Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695D Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695E Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696 Lesson 1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 Lesson 2 Units of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 Lesson 3 Elapsed Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720A Launch Activity 4 Measuring the Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721A CHAPTER 18 Represent and Interpret Data Chapter at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723A Teaching for Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723E Instructional Journey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723F Strategies for Multilingual Learners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723G Show What You Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Vocabulary Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 Lesson 1 Frequency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Lesson 2 Use Frequency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Lesson 3 Determine Mode, Median, and Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 Lesson 4 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743 Lesson 5 Use Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749 Lesson 6 Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755 Lesson 7 Use Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767 Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772A Image credit: © Esin Deniz/Shutterstock Program Tour xii

TM and Version 2.0 Differentiated Centers Kit Grab CHAPTER 1 Chapter at a Glance Whole Number Place Value LESSON 1.1 • 1 Day LESSON 1.2 • 1 Day LESSON 1.3 • 1 Day Lesson at a Glance Model Place-Value Relationships . . . . . . . . 5A Read and Write Numbers . . . . . . . . . . . 11A Compare and Order Numbers . . . . . . . . . . . 17A I Can I can describe the value of a digit. I can read and write numbers up to 1,000,000 using standard form, expanded form, and word form. I can use number lines and symbols to compare and order numbers. Learning Goal Model the 10-to-1 relationship among place-value positions in the base-ten number system. Read and write whole numbers in standard form, word form, and expanded form. Compare and order whole numbers based on the values of the digits in each number. Vocabulary expanded form, period, standard form, word form Multilingual Support Strategy: Illustrate Understanding Strategy: Elicit Prior Knowledge Strategy: Model Language Practice and Fluency LESSON 1.1 ◆ ■ Practice and Homework ■ ■ Waggle LESSON 1.2 ◆ ■ Practice and Homework ■ ■ Waggle LESSON 1.3 ◆ ■ Practice and Homework ■ ■ Waggle MTSS RtI Intervention and Enrichment ◆ ■ Waggle ◆ ■ Reteach 1.1 ◆ ■ Tier 2 Intervention Skill S1 ◆ ■ Tier 3 Intervention Skill E1 ◆ ■ Tabletop Flipchart ◆ ■ Enrich1.1 ◆ ■ Waggle ◆ ■ Reteach 1.2 ◆ ■ Tier 2 Intervention Skill S4 ◆ ■ Tier 3 Intervention Skill E4 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 1.2 ◆ ■ Waggle ◆ ■ Reteach 1.3 ◆ ■ Tier 2 Intervention Skill S8/S9 ◆ ■ Tier 3 Intervention Skill E8/E9 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 1.3 See the Grab-and-Go!™ Centers Kit for more small-group activities. The kit provides literature, games, and activities for small-group learning. ◆ Print/Printable Resource ■ Interactive Resource 3A Go Math! Grade 4

Chapter Pacing Chart Introduction Instruction Assessment Total 1 day 4 days 2 days 7 days LESSON 1.4 • 1 Day Lesson at a Glance Round Numbers . . . . . 23A I Can I can round multi-digit whole numbers to any place. Learning Goal Round a whole number to any place. Vocabulary estimate, round Multilingual Support Strategy: Cooperative Grouping Practice and Fluency LESSON 1.4 ◆ ■ Practice and Homework ■ ■ Waggle MTSS RtI Intervention and Enrichment ◆ ■ Waggle ◆ ■ Reteach 1.4 ◆ ■ Tier 2 Intervention Skill S10 ◆ ■ Tier 3 Intervention Skill E10 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 1.4 Reflect on how you are communicating implicit and explicit expectations for students achievement in mathematics. SUPPORTING ALL LEARNERS Student Learning Hold productive beliefs about each student’s mathematical potential, set high expectations through ambitious and equitable mathematics teaching practices, and allow students to develop productive perseverance. Image Credit: ©HMH ◆ Print/Printable Resource ■ Interactive Resource Chapter 1 3B

CHAPTER 1 Teaching for Depth Whole Number Place Value The Number System Our number system is known as a base-ten positional number system. • The value of each digit is determined by its position. • For whole numbers, the digit farthest to the right is in the ones place. • Moving to the left, each digit has a place value 10 times the value of the place to the right. • Focusing on this pattern in place value during instruction helps students build understanding. • The millions period is to the left of the thousands. PERIOD MILLIONS THOUSANDS ONES Hundreds Tens Ones Hundreds Tens Ones Hundreds Tens Ones 9 5 5, 6 2 8 Connecting to Algorithms Standard algorithms in the U.S. work as they do because of the base-ten number system and other properties of numbers. Student mastery of the algorithms for computation is enhanced when students possess deep conceptual understanding of the place-value system. From the Research “The base-10 place-value system is very efficient. It allows one to write very large numbers using only 10 symbols, the digits 0 through 9. The same digit has a different meaning depending on its place in the numeral. Although this system is familiar and seems obvious to adults, its intricacies are not so obvious to children.” (NRC, 2001, p. 199) Different Number Forms Expressing numbers in different forms helps students develop understanding of the place-value meaning for each of the digits in a numeral. • Writing numbers in expanded form is a particularly useful strategy when teaching for understanding because it helps students partition numbers and develop a deeper understanding of the value of each digit. 395,604 300,000 ∙ 90,000 ∙ 5,000 ∙ 600 ∙ 4 • One indicator that students lack a deep understanding of place value is that they do not associate a digit with its place value. (Ross, 1989) Mathematical Practices and Processes Look for and make use of structure. Our place-value system provides many opportunities for students to see structure. Students can use patterns in the place-value system to deepen their understanding of a number. This understanding leads students to expect structure. For more professional learning, go online to Teacher’s Corner. 3C Go Math! Grade 4

TM and Version 2.0 Differentiated Centers Kit Grab Chapter 1 3D Instructional Journey While every classroom may look a little different, this instructional model provides a framework to organize small-group and whole-group learning for meaningful student learning. Whole Group Engage 5 minutes Readiness • Problem of the Day • Fluency Builder or Vocabulary Builder • Access Prior Knowledge Engagement • I Can • Making Connections • Learning Activity Small and Whole Group Explore 15–20 minutes Exploration • Investigate, Unlock the Problem • Multilingual Support and Strategy • Common Errors Small Group Explain 15–20 minutes Quick Check Share and Show Differentiated Instruction TM and Version 2.0 Grab Intervention • Waggle • Reteach • Tier 2 and Tier 3 MTSS • Tabletop Flipchart Mini Lessons Language Support • Vocabulary Activities • Language Routines • Multilingual Glossary Enrichment • Waggle Games • Ready for More • Enrich Whole Group Elaborate 5 minutes • Math on the Spot Videos • Higher-Order Thinking Problems Evaluate • I Can Reflection • Exit Ticket • Practice and Homework • Fluency Practice • Waggle Assessment Diagnostic Formative Summative • Show What You Know • Lesson Quick Check • Chapter Review • Chapter Test • Performance Assessment Task The kit provides literature, games, and activities for small-group learning.

CHAPTER 1 Strategies for Multilingual Learners Assessing your student’s understanding of mathematical concepts can be done by listening, speaking, reading, and writing. The level of support a student needs determines how best to assess that student’s understanding of mathematical concepts and will help meet the needs of all your students. Planning for Instruction Language Support Substantial (WIDA Level 1)* Moderate (WIDA Levels 2 & 3)* Light (WIDA Levels 4 & 5)* Student’s Use of Language • uses single words • uses common short phrases • heavily relies on visual supports and use of manipulatives • uses single words • uses some academic vocabulary • relies on visual supports and use of manipulatives • uses a variety of sentences • uses academic vocabulary • benefits from visual supports and manipulatives Ways to Assess Understanding Listening: points to pictures, words, or phrases to answer questions Speaking: answers yes/no questions Reading: matches symbols to math terms and concepts Writing: draws a visual representation of a problem Listening: matches, categorizes, or sequences information based on visuals Speaking: begins to explain reasoning, asks math questions, repeats explanations from peers Reading: identifies important information to solve a problem Writing: uses simple sentences and visual representations Listening: draws conclusions and makes connections based on what they heard Speaking: explains and justifies concepts and solutions Reading: understands information in math contexts Writing: completes sentences using some academic vocabulary * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. • Look for strategies throughout the lesson to support multilingual learners. • Log on to ED to find additional multilingual activities and Vocabulary Cards. 3E Go Math! Grade 4

In This Chapter Key Academic Vocabulary Current Development • Vocabulary expanded form, period, standard form, word form, estimate, round Using Language Routines to Develop Understanding Language routines provide opportunities for students to develop an understanding of mathematical language and concepts by listening, speaking, reading, and writing. More information on these language routines can be found on the Language Support Cards. Critique, Correct, and Clarify 1 Students analyze an incorrect explanation or solution. 2 Students work with a partner or small group to identify the error. 3 Students work together to correct the sample work. Language Support Substantial (WIDA Level 1)* Moderate (WIDA Levels 2 & 3)* Light (WIDA Levels 4 & 5)* Language Routine Differentiation 1 Students determine that the visual representation of a provided solution is incorrect. 2 Students identify the error by circling, underlining, or pointing. 3 Students correct the visual representation of the sample. 1 Students analyze an incorrect visual representation of a provided solution. 2 Students work with a partner or small group to identify the error using simple sentences. 3 Students work together to correct the sample work. 1 Students analyze an incorrect explanation or solution. 2 Students work with a partner or small group to identify the error using some academic language. 3 Students work together to correct the sample work. Possible Student Work True? 516,280 516,820 THOUSANDS ONES Hundreds Tens Ones Hundreds Tens Ones 5 1 6, 2 8 0 5 same samesamedifferent 1 6, 8 2 0 Fix. 516,280 516,820 True? 516,280 516,820 Prove. THOUSANDS ONES Hundreds Tens Ones Hundreds Tens Ones 5 1 6, 2 8 0 5 1 6, 8 2 0 200 < * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. Chapter 1 3F

INTERVENE If NO . . . then INTERVENE If YES . . . then use INDEPENDENT ACTIVITIES TM and Version 2.0 Differentiated Centers Kit Grab World MATH Real in the World Real CHAPTER 1 Assessing Prior Knowledge Use Show What You Know to determine if students need intensive or strategic intervention. Fans love the neon Liberty Bell that is part of the Philadelphia ballpark. After every home run scored by the home team, the bell swings and rings. Students are given a set of clues to find a 5-digit number. Discuss solution strategies, and then ask: • Which place values are the digits of the number in? ten thousands place: 4, thousands place: 3, hundreds place: 6, tens place: 5, and ones place: 1 Show What You Know • Diagnostic Assessment Use to determine if students need intervention for the chapter’s prerequisite skills. Were students successful with Show What You Know? TIER 3 TIER 2 TIER 2 Skill Missed More Than Tens and Ones 0 Regroup Hundreds as Tens 0 Round Whole Numbers 1 Intervene With Intensive Intervention Skill E1 Strategic Intervention Skill S7 Strategic Intervention Skill S10 Use the Reteach or Enrich Activities online or the independent activities in the Grab-and-Go 2.0™ Differentiated Centers Kit. 3 Go Math! Grade 4 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (b) ©Universal Images Group North America LLC/Alamy Chapter 1 3 Chapter 1 Name Whole Number Place Value Show What You Know Tens and Ones Write the missing numbers. 1. 27 = _ tens_ ones 2. 93 = _ tens _ ones Regroup Hundreds as Tens Regroup. Write the missing numbers. 3. 5 hundreds 4 tens = _ tens 4. 8 hundreds 9 tens = _ tens Round Whole Numbers Round the whole number to the nearest 10 or 100. 5. Round 334 to the nearest 10. _ 6. Round 579 to the nearest 100. _ 7. Round 209 to the nearest 10. _ MATH in the World Real Use the following clues to find the maximum seating capacity of a baseball stadium. • The 5-digit number has a 4 in the greatest place-value position and a 1 in the least place-value position. • The digit in the thousands place has a value of 3,000. • The digit in the hundreds place is twice the digit in the thousands place. • There is a 5 in the tens place. 2 7 9 3 54 89 330 600 210 43,651 gg CorrectionKey=NL-A 4_mnlese694748_c01co.indd 3 6/7/2022 7:40:49 PM

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Unit 1: Place value

Unit 2: addition, subtraction, and estimation, unit 3: multiply by 1-digit numbers, unit 4: multiply by 2-digit numbers, unit 5: division, unit 6: factors, multiples and patterns, unit 7: equivalent fractions and comparing fractions, unit 8: add and subtract fractions, unit 9: multiply fractions, unit 10: understand decimals, unit 11: plane figures, unit 12: measuring angles, unit 13: area and perimeter, unit 14: units of measurement.

4th Grade Go Math- Chapter 6 Classwork/Homework

Description

This resource is closely aligned to the 4th Grade Go Math Chapter 6 lessons. I use this resource as an independent classwork station after students meet with me during teacher-guided instruction. This resource could easily be used as homework as well. It takes the main concept/skill from each lesson and puts it into a one-page practice. Many of the problems are taken directly from the Go Math homework pages. Couple things to note:

* I combined lesson 6.1 and 6.2, that's why there is one combined page for those lessons.

* I create the resource on Google Docs and always have a hard time adding the circles for comparing so after I print I draw them myself before copying, you will need to do the same!

Make sure to check out my word problem resource to supplement your curriculum. This resource is designed to enhance student learning and mathematical understanding!

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Go Math! Florida 4th Grade, Grade: 4 Publisher: Houghton Mifflin Harcourt

Go math florida 4th grade, title : go math florida 4th grade, publisher : houghton mifflin harcourt, isbn : 153802650, isbn-13 : 9780153802652, use the table below to find videos, mobile apps, worksheets and lessons that supplement go math florida 4th grade..

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Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8

Go Math Answer Key:  HMH Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8 are provided helps students to have learning targets and achieve success at chapter and lesson level and makes learning visible.

Download Go Math Answer Key for Grades K-8 | HMH Go Math Solution Key for Grades Kindergarten, 1, 2, 3, 4, 5, 6, 7, 8

All the Concepts in the CCSS Go Math Answer Key for Grades Kindergarten, 1, 2, 3, 4, 5, 6, 7, 8 are given with straightforward and detailed descriptions.

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Free Download Go Math Answer Key from Kindergarten to 8th Grade

Students can find Go Math Answer Keys right from  Primary School to High School all in one place. You just need to tap on the quick links available in order to access them and learn all the Chapters in each grade. Once you tap on the quick link you will be directed to the respective Grade Solutions Key wherein you can access the complete information. You can find Solutions for all the Go Math Textbook Questions free of cost and we don’t charge any amount.

• Go Math Kindergarten Answer Key

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Go math grade 2 answer key, go math grade 3 answer key, go math grade 4 answer key, go math grade 5 answer key, go math grade 6 answer key.

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Go Math Grade K Answer Key

• Chapter 1 Represent, Count, and Write Numbers 0 to 5
• Chapter 2 Compare Numbers to 5
• Chapter 3 Represent, Count, and Write Numbers 6 to 9
• Chapter 4 Represent and Compare Numbers to 10
• Chapter 5 Addition
• Chapter 6 Subtraction
• Chapter 7 Represent, Count, and Write 11 to 19
• Chapter 8 Represent, Count, and Write 20 and Beyond
• Chapter 9 Identify and Describe Two-Dimensional Shapes
• Chapter 10 Identify and Describe Three-Dimensional Shapes
• Chapter 11 Measurement
• Chapter 12 Classify and Sort Data
• Chapter 1 Addition Concepts
• Chapter 2 Subtraction Concepts
• Chapter 3 Addition Strategies
• Chapter 4 Subtraction Strategies
• Chapter 5 Addition and Subtraction Relationships
• Chapter 6 Count and Model Numbers
• Chapter 7 Compare Numbers
• Chapter 8 Two-Digit Addition and Subtraction
• Chapter 9 Measurement
• Chapter 10 Represent Data
• Chapter 11 Three-Dimensional Geometry
• Chapter 12 Two-Dimensional Geometry
• Chapter 1 Number Concepts
• Chapter 2 Numbers to 1,000
• Chapter 3 Basic Facts and Relationships
• Chapter 4 2-Digit Addition
• Chapter 5 2-Digit Subtraction
• Chapter 6 3-Digit Addition and Subtraction
• Chapter 7 Money and Time
• Chapter 8 Length in Customary Units
• Chapter 9 Length in Metric Units
• Chapter 10 Data
• Chapter 11 Geometry and Fraction Concepts

Grade 3 HMH Go Math – Answer Keys

• Chapter 1: Addition and Subtraction within 1,000
• Chapter 2: Represent and Interpret Data
• Chapter 3: Understand Multiplication
• Chapter 4: Multiplication Facts and Strategies
• Chapter 5: Use Multiplication Facts
• Chapter 6: Understand Division
• Chapter 7: Division Facts and Strategies
• Chapter 8: Understand Fractions
• Chapter 9: Compare Fractions
• Chapter 10: Time, Length, Liquid Volume, and Mass
• Chapter 11: Perimeter and Area
• Chapter 12:Two-Dimensional Shapes

Grade 3 HMH Go Math – Extra Practice Questions and Answers

• Chapter 1: Addition and Subtraction within 1,000 Extra Practice
• Chapter 2: Represent and Interpret Data Extra Practice
• Chapter 3: Understand Multiplication Extra Practice
• Chapter 4: Multiplication Facts and Strategies Extra Practice
• Chapter 5: Use Multiplication Facts Extra Practice
• Chapter 6: Understand Division Extra Practice
• Chapter 7: Division Facts and Strategies Extra Practice
• Chapter 8: Understand Fractions Extra Practice
• Chapter 9: Compare Fractions Extra Practice
• Chapter 10: Time, Length, Liquid Volume, and Mass Extra Practice
• Chapter 11: Perimeter and Area Extra Practice
• Chapter 12: Two-Dimensional Shapes Extra Practice

Common Core Grade 4 HMH Go Math – Answer Keys

• Chapter 1 Place Value, Addition, and Subtraction to One Million
• Chapter 2 Multiply by 1-Digit Numbers
• Chapter 3 Multiply 2-Digit Numbers
• Chapter 4 Divide by 1-Digit Numbers
• Chapter 5 Factors, Multiples, and Patterns
• Chapter 6 Fraction Equivalence and Comparison
• Chapter 7 Add and Subtract Fractions
• Chapter 8 Multiply Fractions by Whole Numbers
• Chapter 9 Relate Fractions and Decimals
• Chapter 10 Two-Dimensional Figures
• Chapter 11 Angles
• Chapter 12Relative Sizes of Measurement Units
• Chapter 13 Algebra: Perimeter and Area

Grade 4 Homework Practice FL.

Common Core – Grade 4 – Practice Book

• Chapter 1 Place Value, Addition, and Subtraction to One Million  (Pages 1- 20)
• Chapter 2 Multiply by 1-Digit Numbers  (Pages 21 – 47)
• Chapter 3 Multiply 2-Digit Numbers  (Pages 49- 65)
• Chapter 4 Divide by 1-Digit Numbers  (Pages 67 – 93)
• Chapter 5 Factors, Multiples, and Patterns  (Pages 95 – 109)
• Chapter 6 Fraction Equivalence and Comparison  (Pages 111 – 129)
• Chapter 7 Add and Subtract Fractions  (Pages 131 – 153)
• Chapter 8 Multiply Fractions by Whole Numbers  (Pages 155- 167)
• Chapter 9 Relate Fractions and Decimals  (Pages 169- 185)
• Chapter 10 Two-Dimensional Figures  (Pages 187- 204)
• Chapter 11 Angles  (Pages 205- 217)
• Chapter 12 Relative Sizes of Measurement Units  (Pages 219- 244)
• Chapter 13 Algebra: Perimeter and Area  (Pages 245- 258)

Grade 4 Homework FL. – Answer Keys

• Chapter 2 Multiply by 1-Digit Numbers Review/Test
• Chapter 3 Multiply 2-Digit Numbers Review/Test
• Chapter 4 Divide by 1-Digit Numbers Review/Test
• Chapter 5 Factors, Multiples, and Patterns Review/Test
• Chapter 6 Fraction Equivalence and Comparison Review/Test
• Chapter 7 Add and Subtract Fractions Review/Test
• Chapter 8 Multiply Fractions by Whole Numbers Review/Test
• Chapter 9 Relate Fractions and Decimals Review/Test
• Chapter 10 Two-Dimensional Figures Review/Test
• Chapter 11 Angles Review/Test
• Chapter 12 Relative Sizes of Measurement Units Review/Test
• Chapter 13 Algebra: Perimeter and Area Review/Test
• Chapter 1: Place Value, Multiplication, and Expressions
• Chapter 2: Divide Whole Numbers
• Chapter 3: Add and Subtract Decimals
• Chapter 4: Multiply Decimals
• Chapter 5: Divide Decimals
• Chapter 6: Add and Subtract Fractions with Unlike Denominators
• Chapter 7: Multiply Fractions
• Chapter 8: Divide Fractions
• Chapter 9: Algebra: Patterns and Graphing
• Chapter 10: Convert Units of Measure
• Chapter 11: Geometry and Volume
• Chapter 1: Divide Multi-Digit Numbers
• Chapter 2: Fractions and Decimals
• Chapter 3: Understand Positive and Negative Numbers
• Chapter 4: Model Ratios
• Chapter 5: Model Percents
• Chapter 6: Convert Units of Length
• Chapter 7: Exponents
• Chapter 8: Solutions of Equations
• Chapter 9: Independent and Dependent Variables
• Chapter 10: Area of Parallelograms
• Chapter 11: Surface Area and Volume
• Chapter 12: Data Displays and Measures of Center
• Chapter 13: Variability and Data Distributions

Go Math Answer Key for Grade 7

• Chapter 1: Adding and Subtracting Integers
• Chapter 2: Multiplying and Dividing Integers
• Chapter 3: Rational Numbers
• Chapter 4: Rates and Proportionality
• Chapter 5: Percent Increase and Decrease
• Chapter 6: Algebraic Expressions
• Chapter 7: Writing and Solving One-Step Inequalities
• Chapter 8: Modeling Geometric Figures
• Chapter 9: Circumference, Area, and Volume
• Chapter 10: Random Samples and Populations
• Chapter 11: Analyzing and Comparing Data
• Chapter 12: Experimental Probability
• Chapter 13: Theoretical Probability and Simulations
• Chapter 1 Real Numbers
• Chapter 2 Exponents and Scientific Notation
• Chapter 3 Proportional Relationships
• Chapter 4 Nonproportional Relationships
• Chapter 5 Writing Linear Equations
• Chapter 6 Functions
• Chapter 7 Solving Linear Equations
• Chapter 8 Solving Systems of Linear Equations
• Chapter 9 Transformations and Congruence
• Chapter 10 Transformations and Similarity
• Chapter 11 Angle Relationships in Parallel Lines and Triangles
• Chapter 12 The Pythagorean Theorem
• Chapter 13 Volume
• Chapter 14 Scatter Plots
• Chapter 15 Two-Way Tables

Give your kid the right amount of knowledge he needs as a part of your preparation by taking the help of our HMH Go Math Answer Key for Grades K-8. Resolve all your queries and assess your preparation standard using the Common Core Go Math Solution Key.

Practicing from the Go Math Answer Key for Grades K to 8 will provide a grade by grade roadmap and prepares students for College Readiness. Gradewise HMH Go Math Answer Key provided will develop problem-solving skills among students thereby helping them to Think, Explore and Grow. The Diverse Opportunities provided helps Kids to master the content with engaging activities.

Characteristics of Go Math Answer Key for Grades K to 8

Go through the below-listed features of referring to the HMH Go Math Anwer Key for Grades K to 8. They are outlined as follows

• All the Go Math Answer Key for Grades K to 8 are easy to download and we don’t charge any penny from you.
• Step by Step Solutions provided in the HMH Go Math Practice Key is aligned as per the College and Career Expectations.
• Solving from the Math 101 Practice Key helps you inculcate Higher Order Thinking Skills and you can answer any Question from your Homework, Assessment, or Review Test.
• More Rigorous Content made available meets the Common Core State Standards Initiative.
• You can gain a deeper knowledge of mathematical concepts and find solutions to all the Questions from Go Math Textbooks for Grades K, 1, 2, 3, 4, 5, 6, 7, 8

FAQs on Common Core HMH Go Math Answer Key

1. When Can I use the Go Math Answer Key for Grades K-8?

You can use the HMH Go Math Answer Key for Grades K to 8 while practicing the Go Math Textbook Questions as a part of your Homework or Assessment and make the most out of them.

2. Is there any site that provides the Common Core Go Math Solutions Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8?

Yes, you can find Go Math Answer Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8 all in one place i.e. ccssmathanswers.com a trusted and reliable portal.

3. Can I download HMH Go Math Answer Key PDF for free?

Yes, you can download the HMH Math 101 Practice Key for free on our page via quick links available and we don’t charge any amount for it.

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 13: Algebra: Perimeter and Area

Are you viewing for Go Math Grade 4 Answer Key Homework Practice FL Chapter 13 Algebra: Perimeter and Area? This is the correct page for you. We have listed chapterwise Go math grade 4 practice FL Answer key along with homework practice FL solution Key on our site. So, you can learn the concepts in an understanding manner & score maximum scores in the assessments and standardized tests. Hence, download the HMH Go Math 4th Grade Chapter 13 Perimeter and Area Answer key to find out the area & perimeter of the rectangle & square quickly & easily.

Go Math Grade 4 Ch 13 Answer Key includes topics covered in Algebra: Perimeter and Area. Students who are pursuing 4th grade can find the HMH Go Math Grade 4 Solution Key Chapter 13 Algebra: Perimeter and Area extremely useful. Simply identify your preparation level and weak areas by practicing and solving the questions from 4th Grade Go Math Answer Key Chapter 13 Algebra: Perimeter and Area. Tap on the below provided links and check the detailed explanation for each and every question covered here.

Lesson: 1 – Perimeter

Common Core – Algebra: Perimeter and Area – Page No. 247

Common core – algebra: perimeter and area – page no. 248.

Lesson: 2 – Area

Common Core – Algebra: Perimeter and Area – Page No. 249

Common core – algebra: perimeter and area – page no. 250.

Lesson: 3 – Area of Combined Rectangles

Common Core – Algebra: Perimeter and Area – Page No. 251

Common core – algebra: perimeter and area – page no. 252.

Lesson: 4 – Find Unknown Measures

Common Core – Algebra: Perimeter and Area – Page No. 253

Common core – algebra: perimeter and area – page no. 254.

Lesson: 5 – Problem Solving Find the Area

Common Core – Algebra: Perimeter and Area – Page No. 255

Common core – algebra: perimeter and area – page no. 256, common core – algebra: perimeter and area – page no. 257.

• Common Core – Algebra: Perimeter and Area – Page No. 258

Find the perimeter of the rectangle or square.

Explanation: Given, sides = 8 m we know that the perimeter of a square is 4×s P = 4 × s P = 4 × 8m P = 32m Therefore the perimeter of the above square is 32m

Explanation: Given, Length (L) = 10 ft Width (W) = 12 ft we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 10 ft + 10 ft + 12 ft + 12 ft P = 44 ft Therefore the perimeter of the above Rectangle is 44 ft

Remember: The perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a rectangle, opposite sides are equal in length, so the perimeter is twice its width plus twice its height.

Answer: 108

Explanation: Given, Length (L) = 30 cm Width (W) = 24 cm we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 30 cm + 30 cm + 24 cm + 24 cm P = 108 cm Therefore the perimeter of the above Rectangle is 108 cm

Answer: 216

Explanation: Given, Length (L) = 25 in. Width (W) = 83 in. we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 25 in. + 25 in. + 83 in. + 83 in. P = 216 in. Therefore the perimeter of the above Rectangle is 216 in.

Answer: 240

Explanation: Given, sides = 60 m we know that the perimeter of a square is 4×s P = 4×s P = 4×60 m P = 240 m Therefore the perimeter of the above square is 240 m

Problem Solving

Question 7. Troy is making a flag shaped like a square. Each side measures 12 inches. He wants to add ribbon along the edges. He has 36 inches of ribbon. Does he have enough ribbon? Explain. _____

Answer: no. He needs 48 inches of ribbon.

Explanation: Since each side is 12 inches, then multiply 12 by 4 since it’s a square and has 4 sides which make 48. 48 is bigger than 36. Therefore, Troy does not have enough ribbon.

Question 8. The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter of the pool? _____ feet

Answer: 120

Explanation:

Width of the Ochoa community pool = 20 feet Length is twice as long as its width = 2(20) = 40 feet Use this formula to get perimeter = 2(w) + 2(L) then the perimeter equals to = 2(20)+ 2(40) P = 40 feet + 80 feet  = 120 feet Therefore The perimeter of the pool is 120 feet.

Lesson Check

Question 1. What is the perimeter of a square window with sides 36 inches long? Options: a. 40 inches b. 72 inches c. 144 inches d. 1,296 inches

Answer: 144 inches

Explanation: Perimeter of a square = L + L + L + L = 4L From the question given L=36 inches substitute the value of L into the formula Perimeter of a square (P)= L + L + L + L P = 36 in. + 36 in.. +36 in.+ 36 in. P =144 inches Therefore the perimeter of a square window with sides 36 inches long is 144 inches.

Answer: 18 meters

Explanation: Given, Length (L) = 5 m Width (W) = 4 m we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 5 m + 5 m + 4 m + 4 m P = 18 m Therefore the perimeter of the above Rectangle is 18 m Thus the correct answer is option c.

Spiral Review

Answer: 90°

Explanation: Right angle: An angle of 90°, as in a corner of a square or at the intersection of two perpendicular straight lines. As we can see in the figure, that an angle is made at the intersection of the two perpendicular straight lines, thus the figure will be definitely a right-angled figure. Therefore, the measure of the angle Natalie draw is 90°. Thus the correct answer is option b.

Question 4. Ethan has 3 pounds of mixed nuts. How many ounces of mixed nuts does Ethan have? Options: a. 30 ounces b. 36 ounces c. 48 ounces d. 54 ounces

Answer: 48 ounces

Explanation: Since we have given that Number of pounds of mixed nuts = 3 As we know that 1 pound = 16 ounces So, we need to find the number of ounces of mixed nuts Ethan has. So, the number of ounces of mixed nuts Ethan have is given by = 3 × 16 = 48 ounces Thus the correct answer is option c.

Explanation: It has only one line of symmetry on the horizontal axis because it is an arrow. Thus the correct answer is option b.

Question 6. Which of the following comparisons is correct? Options: a. 0.70 > 7.0 b. 0.7 = 0.70 c. 0.7 < 0.70 d. 0.70 = 0.07

Answer: 0.7 = 0.70 The decimal 0.7 and 0.70 are the same so the correct answer is option b.

Find the area of the rectangle or square.

Answer: 108 Square feet

Explanation: Given, Height (h) = 9 ft. Breath (b) = 12 ft. Area of the rectangle  A = b×h A = 12 ft × 9 ft A = 108 Square feet. Therefore the Area of the rectangle is 108 Square feet.

Explanation: Given, Sides (s) = 8 yd Area of the square. A = s×s A = 8 yd × 8 yd A = 64 Square yards Therefore the Area of the square is 64 Square yards.

Explanation: Given, Height (h) = 3 m Breath (b) = 15 m Area of the rectangle or square. A = b×h A = 3 m× 15 m A = 45 Square meters Therefore the Area of the rectangle is 45 Square meters

Explanation: Given, Height (h) = 6 in. Breath (b) = 13 in. Area of the rectangle =  A = b×h A = 6 in. × 13 in. A = 78 square inches Therefore the Area of the rectangle is 78 square inches.

Answer: 150 square cm

Explanation: Given, Height (h) = 5 cm Breath (b) = 30 cm Area of the rectangle or square. A = b×h A =  5 cm × 30 cm A = 150 square centimeters Therefore the Area of the rectangle is 150 square centimeters.

Answer: 56 square ft

Explanation: Given, Height (h) = 4 ft Breath (b) = 14 ft Area of the rectangle or square. A = b×h A = 4 ft × 14 ft A = 56 square feet Therefore the Area of the rectangle is 56 square feet.

Question 7. Meghan is putting wallpaper on a wall that measures 8 feet by 12 feet. How much wallpaper does Meghan need to cover the wall? _____ square feet wallpaper

Answer: 96 square feet wallpaper

Explanation: Given, Length = 8 feet. Width = 12 feet. the area (area=length × width) area=8 × 12 area=96 square feets. Therefore the area is always expressed in units squared it would be 96 square feet of wallpaper.

Question 8. Bryson is laying down sod in his yard to grow a new lawn. Each piece of sod is a 1-foot by 1-foot square. How many pieces of sod will Bryson need to cover his yard if his yard measures 30 feet by 14 feet? _____ pieces

Answer: 420 pieces

Explanation: Given, length (l) = 30 ft Breath (b) = 14 ft Area of the rectangle or square. A = l×b A = 30 ft × 14 ft A = 420 Therefore 420 pieces of sod will Bryson need to cover his yard if his yard measures 30 feet by 14 feet.

Question 1. Ellie and Heather drew floor models of their living rooms. Ellie’s model represented 20 feet by 15 feet. Heather’s model represented 18 feet by 18 feet. Whose floor model represents the greater area? How much greater? Options: a. Ellie; 138 square feet b. Heather; 24 square feet c. Ellie; 300 square feet d. Heather; 324 square feet

Answer: Heather; 24 square feet

Given, Ellie’s model represented 20 feet by 15 feet. Heather’s model represented 18 feet by 18 feet. Length of Ellie’s model = 20 feet Width of Ellie’s model = 15 feet Area = Length × Breadth A = 20 × 15 A = 300 ft² Length of Heather’s model = 18 feet Width of Heather’s model = 18 feet Area = Length × Breadth A= 18 × 18 A= 324 ft² Therefore Heather’s model has a greater area by (324-300)= 24 sq.ft. Thus the correct answer is option b.

Question 2. Tyra is laying down square carpet pieces in her photography studio. Each square carpet piece is 1 yard by 1 yard. If Tyra’s photography studio is 7 yards long and 4 yards wide, how many pieces of square carpet will Tyra need? Options: a. 10 b. 11 c. 22 d. 28

Explanation: Given, Tyra’s photography studio  length is 7 yards Tyra’s photography studio width is  4 yards Area = Length × Breadth Area = 7 yards × 4 yards Area = 28 square yards Therefore as Each square carpet piece is 1 yard by 1 yard. No.of pieces of square carpet Tyra needed is 28. Thus the correct answer is option d.

Question 3. Typically, blood fully circulates through the human body 8 times each minute. How many times does blood circulate through the body in 1 hour? Options: a. 48 b. 240 c. 480 d. 4,800

Answer: 480

Explanation: Given, blood fully circulates through the human body 8 times each minute one hour = 60 minutes blood circulates through the body in 1 hour = 8 times × 60 minutes. = 480 Times. Therefore blood circulates through the body in 1 hour is 480 times. Thus the correct answer is option c.

Question 4. Each of the 28 students in Romi’s class raised at least $25 during the jump-a-thon. What is the least amount of money the class raised? Options: a. $5,200 b. $700 c. $660 d. $196

Answer: $700

explanation: If each of the 28 students made at least $25, you would multiply 28 and 25 together to obtain the least amount of money the class raised. That gets, 28×25 = 700. Therefore The class made at least $700. Thus the correct answer is option b.

Answer: 28 feet

Explanation: From the above figure we can observe that there area 2 rows and 12 columns. L = 12 feet W = 2 feet We know that perimeter of the rectangle is 2l + 2w P = 2l + 2w P = 2(12) + 2(2) P = 24 feet + 4 feet P = 28 feet Thus the correct answer is option d.

Question 6. Ryan is making small meat loaves. Each small meat loaf uses \(\frac{3}{4 }\) pound of meat. How much meat does Ryan need to make 8 small meat loaves? Options: a. 4 pounds b. 6 pounds c. 8 pounds d. 10 \(\frac{2}{3}\) pounds

Answer: 6 pounds

Explanation: Given, 3/4 pound=1 small meatloaf So Multiply 3/4 pound by 8 because he wants to make 8 small meatloaves. = 3/4 × 8 = 24/4 (24 divided by 4) = 6 pounds Therefore Ryan need 6 pounds to make 8 small meat loaves. Thus the correct answer is option b.

Area of Combined Rectangles

Find the area of the combined rectangles.

Answer: 143

Explanation: Divide the figure into two parts Figure 1: L = 9 ft W = 5 ft Area of the rectangle = l × w A = 9 ft × 5 ft = 45 sq. ft Figure 2: L = 14 ft W = 7 ft Area of the rectangle = l × w A = 14 ft × 7 ft = 98 sq. ft Area of the combined rectangles = 98 sq. ft + 45 sq. ft = 143 sq. ft.

Explanation: Divide the figure into two parts Figure 1: L = 9 in. W = 5 in. Area of the rectangle = l × w A = 9 in. × 5 in. = 45 sq. in. Figure 2: L = 3 in. W = 6 in. Area of the rectangle = l × w A = 3 in. × 6 in. = 18 sq. in. Area of the combined rectangles = 45 sq. in + 18 sq. in = 63 square inches.

Answer: 50 square feet

Explanation: Divide the figure into two parts Figure 1: L = 4 ft W = 2 ft Area of the rectangle = l × w A = 4 ft × 2 ft = 8 sq. ft Figure 2: L = 6 ft W = 7 ft Area of the rectangle = l × w A = 6 ft × 7 ft = 42 sq. ft Area of the combined rectangles = 8 sq. ft + 42 sq. ft = 50 sq. ft.

Answer: 180 square centimeters

Explanation: Divide the figure into two parts Figure 1: L = 12 cm W = 7 cm Area of the rectangle = l × w A = 12 cm × 7 cm = 84 sq. cm. Figure 2: L = 16 cm W = 6 cm Area of the rectangle = l × w A = 16 cm × 6 cm = 96 sq. cm Area of the combined rectangles = 84 sq. cm + 96 sq. cm = 180 square centimeters

Explanation: Divide the figure into two parts Figure 1: L = 20 yd W = 1 yd Area of the rectangle = l × w A = 20 yd × 1 yd = 20 sq. yd. Figure 2: L = 6 yard W = 8 yard Area of the rectangle = l × w A = 6 yard × 8 yard = 48 sq. yard Area of the combined rectangles = 20 sq. yd + 48 sq. yd = 68 square yards

Use the diagram for 7–8.

Question 7. What is the area of the space that Nadia has shown for scrapbooking? _____ square feet

Explanation: The length of the Scrapbooking is 13 ft Width of the Scrapbooking is 4 ft Area of the rectangle = l × w A = 13 ft × 4 ft = 52 square feet Thus the area of the space that Nadia has shown for scrapbooking is 52 square feet.

Question 8. What is the area of the space she has shown for painting? _____ square feet

Explanation: The area of the space shown for painting is square. side = 5 ft The area of the square is 5 ft × 5 ft = 25 sq. ft Thus the area of the space she has shown for painting is 25 square feet.

Answer: 76 square yards

Explanation: Divide the figure into two parts Figure 1: L = 8 yd W = 5 yd Area of the rectangle = l × w A = 8 yd × 5 yd = 40 sq. yd. Figure 2: L = 12 yard W = 3 yard Area of the rectangle = l × w A = 12 yard × 3 yard = 36 sq. yard Area of the combined rectangles = 40 sq. yd + 36 sq. yd = 76 square yards Therefore the correct option is c.

Question 2. Marquis is redecorating his bedroom. What could Marquis use the area formula to find? Options: a. how much space should be in a storage box b. what length of wood is needed for a shelf c. the amount of paint needed to cover a wall d. how much water will fill up his new aquarium

Answer: the amount of paint needed to cover a wall The correct answer is option c.

Question 3. Giraffes are the tallest land animals. A male giraffe can grow as tall as 6 yards. How tall would the giraffe be in feet? Options: a. 2 feet b. 6 feet c. 12 feet d. 18 feet

Answer: 18 feet

Explanation: Given, Giraffes are the tallest land animals. A male giraffe can grow as tall as 6 yards. we have to find How tall would the giraffe be in feet Converting from Yards to feet. one Yard = 3 Feet. So 6 yards = 6 × 3 feet = 18 feet Therefore the correct option is d.

Question 4. Drew purchased 3 books for $24. The cost of each book was a multiple of 4. Which of the following could be the prices of the 3 books? Options: a. $4, $10, $10 b. $4, $8, $12 c. $5, $8, $11 d. $3, $7, $14

Answer: $4, $8, $12

Explanation: Given, Drew purchased 3 books for $24. The cost of each book was a multiple of 4. To find the prices of the 3 books The cost of one book is $4 the cost of two books is $4 × 2 = $8 The cost of three books is $4 × 3 = $12 Therefore the correct option is b.

Question 5. Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long. What is the perimeter of her magnet? Options: a. 3 inches b. 7 inches c. 9 inches d. 12 inches

Answer: 12 inches

Explanation: Given, Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long. To find the perimeter of her magnet P = 4 × s P = 4 × 3 in. P = 12 in. Therefore the correct option is d.

Answer: 63 square feet

Explanation: Given, Height (h) = 7 ft. Breath (b) = 9 ft. Area of the rectangle  A = b×h A = 7 ft × 9 ft A = 63 Square feet. The Area of the rectangle is 63 Square feet. Therefore the correct option is a.

Find Unknown Measures

Find the unknown measure of the rectangle.

Answer: 12 meters

Explanation: Given Perimeter = 42 meters width = 9 m To find Length (l) of the rectangle P = (2 × l) + (2 × w) 42 = (2 × l ) + (2 × 9) 42 = 2l + 18 2l = 42 – 18 2l = 24 l = 24/2 l = 12 m Thus the length of the above rectangle is 12 m

Answer: 7 centimeters

Explanation: Given Area = 28 square centimeters length  = 4 cm To find Height (w) of the rectangle A = l × w 28 = 4 cm × w w = 28/4 w = 7 cm Thus the height of the above rectangle is 7 cm

Answer: 8 inches

Explanation: Given Area = 200 square inches width  = 25 in. To find Base (b) of the rectangle A = w × b 200 = 25 in. × b b = 200/25 b = 8 inches Thus the base of the above rectangle is 8 inches

Question 5. Susie is an organic vegetable grower. The perimeter of her rectangular vegetable garden is 72 yards. The width of the vegetable garden is 9 yards. How long is the vegetable garden? length = _____ yards

Answer: 27 yards

Explanation: Given, The perimeter (P) of her rectangular vegetable garden is 72 yards. The width (w) of the vegetable garden is 9 yards. to find length (l) P = (2 × l) + (2 × w) 72 yards  = (2 × l ) + (2 × 9 yards) 72 = 2l + 18 2l = 72 – 18 2l = 54 l = 54/2 l = 27 yards Therefore length = 27 yards

Question 6. An artist is creating a rectangular mural for the Northfield Community Center. The mural is 7 feet tall and has an area of 84 square feet. What is the length of the mural? length = _____ feet

Answer: 12 feet

Explanation: Given, The mural is 7 feet (w) tall and has an area of 84 square feet(A). To find the length (l) A = l × w 84 = l × 7 l = 84 /7 l= 12 feets Therefore the length is 12 feets

Question 1. The area of a rectangular photograph is 35 square inches. If the width of the photo is 5 inches, how tall is the photo? Options: a. 5 inches b. 7 inches c. 25 inches d. 30 inches

Answer: 7 inches

Explanation: Given, The area of a rectangular photograph is 35 square inches (A) The width of the photo is 5 inches (w) To find how tall is the photo (l) A= l × b 35 square in. = l × 5 in. l = 35/5 l = 7 inches Therefore the photo height is 7 inches. Thus the correct answer is option b.

Question 2. Natalie used 112 inches of blue yarn as a border around her rectangular bulletin board. If the bulletin board is 36 inches wide, how long is it? Options: a. 20 inches b. 38 inches c. 40 inches d. 76 inches

Answer: 20 inches

Explanation: Given width is 36 in and the total inches used was 112. To find length Perimeter of Rectangle = 2(L + W) Your equation is, 2(L + 36) = 112 Solving for L: 2(L + 36) = 112 L + 36 = 112 / 2 L + 36 = 56 L = 56 – 36 L = 20 Therefore the correct option is a.

Question 3. A professional basketball court is in the shape of a rectangle. It is 50 feet wide and 94 feet long. A player ran one time around the edge of the court. How far did the player run? Options: a. 144 feet b. 194 feet c. 238 feet d. 288 feet

Answer: 288 feet

Explanation: Given, the basketball court is 50 feet wide and 94 feet long The perimeter of the rectangle(P) is given by: P = 2(length + width) 50 + 94 = 144 144 x 2 = 288 The player ran 288 feet Therefore the correct option is d.

Question 4. On a compass, due east is a \(\frac{1}{4}\) turn clockwise from due north. How many degrees are in a \(\frac{1}{4}\) turn? Options: a. 45° b. 60° c. 90° d. 180°

Explanation: We have been given that on a compass, due east is a 1/4 turn clockwise from due north. Since we know that a compass is in form of a circle and the measure of degrees in a circle is 360 degrees. To find the number of degrees in a one-fourth turn, we will divide 360° by 4. Number of degrees in a 1/4 turn of compass = 360°/4 Number of degrees in a 1/4 turn of compass = 90° Therefore, there are 90 degrees in a 1/4 turn of the compass. The correct option is c.

Question 5. Hakeem’s frog made three quick jumps. The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters. What was the total length of the frog’s three jumps? Options: a. 189 centimeters b. 225 centimeters c. 486 centimeters d. 585 millimeters

Answer: 225 centimeters

Explanation: Given: distance of first jump = d1= 1 meter distance of second jump = d2 = 85 centimeters distance of third jump = d3 = 400 millimeters This problem is about the conversion unit of length. We have to recall that : 1 m = 100 cm 1 m = 1000 mm Total distance = d = d1 + d2 + d3 d = 1 m + 85 m + 400 mm d = 1 m + 85/100 m + 400/1000 m d = 2.25  × 100 cm d = 225 centimeters Therefore the correct option is b.

Question 6. Karen colors in squares on a grid. She colored \(\frac{1}{8}\) of the squares blue and \(\frac{5}{8}\) of the squares red. What fraction of the squares are not colored in? Options: a. \(\frac{1}{8}\) b. \(\frac{1}{4}\) c. \(\frac{1}{2}\) d. \(\frac{3}{4}\)

Answer: \(\frac{1}{4}\)

Explanation: since karen colored in 1/8 and 5/8 you add the numerators to get 6/8 you subtract the 8/8 the whole grid from 6/8 to get 2/8 ⇒ 1/8 + 5/8 = 6/8 ⇒ 8/8 – 6/8 = 2/8 = 1/4 There fore the correct option is b.

Problem Solving Find the Area

Solve each problem.

Answer: 96 square feet

Explanation: The area of the square window is 4 ft × 4 ft = 16 square feet. Area of the rectangle = 14 ft × 8 ft = 112 square feet Now we have to find the area of the wall NOT including the window 112 square feet – 16 square feet = 96 square feet Thus the area of the wall NOT including the window is 96 square feet.

Answer: 235 square yards

Explanation: The area of the non-shaded rectangle is 5 yd × 9 yd = 45 square yards. The area of the rectangle is 20 yd × 14 yd = 280 square yard The area covered with new sod is 280 square yard – 45 square yard = 235 square yards.

Question 4. A rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting? The area of the frame = _____ square inches

Answer: 192 square inches

Explanation: area of painting without frame A1 = l × b = 24 x 20 = 480 square inches area of painting with frame A2 = l × b =28×24 =672 square inches area of the frame not covered by paint =area with frame(A1) – area without frame(A2) =672 – 480 =192 Therefore the area of the frame is 192 square inches

Question 5. One wall in Jeanne’s bedroom is 13 feet long and 8 feet tall. There is a door 3 feet wide and 6 feet tall. She has a poster on the wall that is 2 feet wide and 3 feet tall. How much of the wall is visible? The area of the wall visible = _____ square feet

Explanation: One wall in Jeanne’s bedroom is 13 feet long and 8 feet tall. There is a door 3 feet wide and 6 feet tall. She has a poster on the wall that is 2 feet wide and 3 feet tall. 13 × 8 is 104. 104 – (3×6) and -(2 × 3) is 80 Thus the area of the wall visible is 80 square feet.

Question 1. One wall in Zoe’s bedroom is 5 feet wide and 8 feet tall. Zoe puts up a poster of her favorite athlete. The poster is 2 feet wide and 3 feet tall. How much of the wall is not covered by the poster? Options: a. 16 square feet b. 34 square feet c. 35 square feet d. 46 square feet

Answer: 34 square feet

Explanation: One wall in Zoe’s bedroom is 5 feet wide and 8 feet tall. Area of the rectangle = l × w A = 5 feet × 8 feet A = 40 square feet Zoe puts up a poster of her favorite athlete. The poster is 2 feet wide and 3 feet tall. Area of the rectangle = l × w A = 2 feet × 3 feet S = 6 square feet To find: How much of the wall is not covered by the poster, we need to subtract 6 square feet from 40 square feet 40 square feet – 6 square feet = 34 square feet Thus the are of the wall is not covered by the poster is 34 square feet. The correct answer is option b.

Question 2. A garage door is 15 feet wide and 6 feet high. It is painted white, except for a rectangular panel 1 foot high and 9 feet wide that is brown. How much of the garage door is white? Options: a. 22 square feet b. 70 square feet c. 80 square feet d. 81 square feet

Answer: 81 square feet

Explanation: Given that the garage door is 15 feet wide and 6 feet high. W = 15 feet H = 6 feet Area of the rectangle = l × w A = 6 feet × 15 feet A = 90 square feet It is painted white, except for a rectangular panel 1 foot high and 9 feet wide that is brown. H = 1 foot W = 9 feet Area of the rectangle = l × w A = 1 feet × 9 feet A = 9 feet To find: How much of the garage door is white, we need to subtract 9 feet from 90 feet. 90 feet – 9 feet = 81 feet. Thus the area of the garage door is white is 81 square feet. The correct answer is option d.

Question 3. Kate baked a rectangular cake for a party. She used 42 inches of frosting around the edges of the cake. If the cake was 9 inches wide, how long was the cake? Options: a. 5 inches b. 12 inches c. 24 inches d. 33 inches

Explanation: Given, Kate baked a rectangular cake for a party. She used 42 inches of frosting around the edges of the cake. The width of the cake is 9 inches. 9 + 9 = 18 42 – 18 = 24 24 / 2 = 12 the length is 12 inches Thus the correct answer is option b.

Question 4. Larry, Mary, and Terry each had a full glass of juice. Larry drank \(\frac{3}{4}\) of his. Mary drank \(\frac{3}{8}\) of hers. Terry drank \(\frac{7}{10}\) of his. Who drank less than \(\frac{1}{2}\) of their juice? Options: a. Larry b. Mary c. Mary and Terry d. Larry and Terry

Answer: Mary Mary drank the least because when half of 8 is \(\frac{4}{8}\). The correct answer is option b.

Question 5. Which of the following statements is NOT true about the numbers 7 and 9? Options: a. 7 is a prime number. b. 9 is a composite number. c. 7 and 9 have no common factors other than 1. d. 27 is a common multiple of 7 and 9.

Answer: 27 is a common multiple of 7 and 9.

Explanation: Statement 27 is a common multiple of 7 and 9 is false because 27 is not the multiple of 7. Thus the correct answer is option d.

Question 6. Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M. How long did the movie last? Options: a. 1 hour 35 minutes b. 1 hour 45 minutes c. 1 hour 55 minutes d. 2 hours 15 minutes

Answer: 1 hour 45 minutes

Explanation: Given, Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M. Subtract ending time and starting time. 4 hr 15 min -2 hr 30 min 1 hr 45 min Thus the correct answer is option B.

Lesson 13.1

Explanation: Given, Length (L) = 16 ft Width (W) = 9 ft we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 16 ft + 16 ft + 9 ft + 9 ft P = 50 ft Therefore the perimeter of the above Rectangle is 50 ft

Explanation: Given, sides = 13 in. we know that the perimeter of a square is 4×s P = 4 × 13 in. P = 4 × 13 in. P = 52 in. Therefore the perimeter of the above square is 52 in.

Answer: 130

Explanation: Given, Length (L) = 40 cm Width (W) = 25 cm we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 40 cm + 40 cm + 25 cm + 25 cm P = 130 cm Therefore the perimeter of the above Rectangle is 130 cm.

Explanation: Given, Length (L) = 16 m Width (W) = 18 m we know that the perimeter of a Rectangle is L + L+ W + W P = L + L+ W + W P = 16 m+ 16 m+ 18 m+ 18 m P = 68 m Therefore the perimeter of the above Rectangle is 68 m.

Lesson 13.2

Answer: 180

Explanation: Given, Height (h) = 15 in. Breath (b) = 12 in. Area of the rectangle =  A = b×h A = 12 in. × 15 in. A = 180 square inches Therefore the Area of the rectangle is 180 square inches.

Answer: 300

Explanation: Given, Height (h) = 15 yd Breath (b) = 20 yd Area of the rectangle =  A = b×h A = 15 yd. × 20 yd A = 300 square yard Therefore the Area of the rectangle is 300 square yards.

Explanation: Given, Sides (s) = 5 km Area of the square. A = s×s A = 5 km × 5 km A = 25 Square km Therefore the Area of the square is 25 square km.

Explanation: Given, Height (h) = 14 ft Breath (b) = 7 ft Area of the rectangle =  A = b×h A = 14 ft. × 7 ft A = 98 square ft Therefore the Area of the rectangle is 98 square ft.

Page No: 258

Lesson 13.3

Answer: 116 square cm

Explanation: Divide the figure into two parts Figure 1: L = 6 cm Area of the square = s × s A = 6 cm × 6 cm = 36 sq. cm. Figure 2: L = 10 cm W = 8 cm Area of the rectangle = l × w A = 10 cm × 8 cm = 80 sq. cm Area of the combined rectangles = 36 sq. cm + 80 sq. cm = 116 square centimeters

Answer: 112 square in.

Explanation: Divide the figure into two parts Figure 1: L = 8 in. W = 4 in. Area of the rectangle = l × w A = 8 in. × 4 in. = 32 sq. in. Figure 2: L = 4 in. W = 12 in. Area of the rectangle = l × w A = 4 in. × 12 in. = 48 sq. in. Figure 3: L = 8 in. W = 4 in. Area of the rectangle = l × w A = 8 in. × 4 in. = 32 sq. in. Area of the combined rectangles = 32 sq. in + 48 sq. in + 32 sq. in. = 112 square inches.

Lesson 13.4

Answer: 25 feet

Explanation: A = 375 sq. ft h = 15 ft Area of the rectangle =  A = b×h 375 sq. ft = b × 15 ft b = 375/15 = 25 ft Thus the base of the figure is 25 ft.

Answer: 8 mi

Explanation: A = 56 sq. mi b = 7 mi Area of the rectangle =  A = b×h 56 sq. mi = 7 mi × h h = 56/7= 8 mi Thus the height of the figure is 8 mi.

Lesson 13.5

Question 5. Jeanette is painting a rectangular wall that is 10 feet long and 8 feet tall. There is a window that is 5 feet wide and 3 feet tall on the wall. What is the area of the wall that Jeannette will paint? ____ square feet

Answer: 65 square feet

Explanation: Given, Jeanette is painting a rectangular wall that is 10 feet long and 8 feet tall. There is a window that is 5 feet wide and 3 feet tall on the wall. 8 times 10 is eighty, then you need to subtract 3 times 5 (which is 15), and that makes it 65 feet squared. 80 sq. ft – 15 sq. ft = 65 square feet

Question 6. Rob has a combined flower and vegetable garden that is 9 meters long and 11 meters wide. The flower garden is in the center and is a square with sides of 3 meters. How many square meters of the garden is used for vegetables? ____ square meters

Answer: 90 square meters

Explanation: First, you would need to find the area of both the FULL veggie garden and flower garden. Veggie Garden = 9×11 = 99 Flower Garden = 3×3 = 9 Then you would subtract the area of the veggie garden by the area of the flower garden. 99 – 9 = 90 meters squared

Conclusion:

Just solve all exercise questions and cross-check your solutions from Go Math Grade 4 Solution Key Chapter 13  Algebra Perimeter and Area . Like this, you can easily examine your strengths and weaknesses and focus on the areas you are faltering. Step-by-step Solutions presented here in the 4th Grade Go Math Answer Key Chapter Algebra Perimeter and Area useful for homework help and gain subject knowledge perfectly.

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