Hands-On Standards, Common Core Edition Grade 4
Hands-On Standards, Common Core Edition Grade 4 hand2mind 78868 ISBN 978-0-7406-9433-2 ISBN 978-0-7406-9429-5 Vernon Hills, IL 60061-1862 800-445-5985 www.hand2mind.com 2012 by ETA hand2mind All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Permission is granted for limited reproduction of those pages from this book with a copyright line in the inner margin for classroom use and not for resale. Printed in the United States of America. 12 13 14 15 16 17 18 19 20 21 10 9 8 7 6 5 4 3 2 1
Contents Introduction....1 A Walk Through a Lesson....2 A Walk Through a Student Page...4 Operations and Algebraic Thinking 6 Lesson 1 Mathematical Reasoning...8 4.OA.3 Lesson 2 Finding Factor Pairs...12 4.OA.4 Lesson 3 Prime and Composite Numbers...16 4.OA.4 Lesson 4 Identifying Multiples...20 4.OA.4 Lesson 5 Extend Patterns...24 4.OA.5 Lesson 6 Identify the Rule...28 4.OA.5 Lesson 7 Input/Output Tables...32 4.OA.5 Number and Operations in Base Ten 36 Lesson 1 Divide by Multiples of 10...38 4.NBT.1 Lesson 2 Writing Numbers in Different Forms..................42 4.NBT.2 Lesson 3 Comparing and Ordering Numbers...46 4.NBT.2 Lesson 5 Multiply With a Two-Digit Number...54 4.NBT.5 Lesson 6 Divide With a One-Digit Divisor...58 4.NBT.6 Number and Operations Fractions 62 Lesson 1 Finding Equivalent Fractions...64 4.NF.1 Lesson 2 Comparing and Ordering Fractions...68 4.NF.2 Lesson 3 Reason with Fractions...72 4.NF.2 Lesson 4 Add and Subtract Fractions...76 4.NF.3a, 4.NF.3d Lesson 5 Breaking Apart Fractions...80 4.NF.3b Lesson 6 Add and Subtract Mixed Numbers..84 4.NF.3c Lesson 7 Multiples of Unit Fractions...88 4.NF.4a Lesson 8 Multiplying Fractions by Whole Numbers...92 4.NF.4b Lesson 9 Composing Decimal Fractions...96 4.NF.5 Lesson 10 Fractions and Decimals...100 4.NF.6 Lesson 11 Comparing Decimals...104 4.NF.7 Lesson 4 Multiply With a One-Digit Multiplier...50 4.NBT.5
Measurement and Data 108 Lesson 1 Perimeter and Area...110 4.MD.3 Lesson 2 Understanding Angles...114 4.MD.5a, 4.MD.5b Lesson 3 Measure and Classify Angles...118 4.MD.6 Lesson 4 Tessellation Angles...122 4.MD.6, 4.MD.7 BLM 10 Plane Shapes Recording Sheet...157 BLM 11 Hundred Chart...158 BLM 12 Centimeter Grid...159 BLM 13 2 9 Number Spinner...160 Glossary of Manipulatives...161 Index...163 Geometry 126 Lesson 1 Parallel and Perpendicular Lines...128 4.G.1 Lesson 2 Plane Shapes...132 4.G.2 Lesson 3 Identify and Classify Triangles...136 4.G.2 Lesson 4 Line Symmetry...140 4.G.3 Lesson 5 Symmetrical Figures...144 4.G.3 Blackline Masters BLM 1 Factor Pairs Worksheet...148 BLM 2 Tile Arrays...149 BLM 3 Input/Output Table...150 BLM 4 Number Forms Recording Sheet...151 BLM 5 Place-Value Chart...152 BLM 6 4-Column Recording Chart...153 BLM 7 Fraction Towers...154 BLM 8 Double Fraction Tower Number Lines...155 BLM 9 Circle/Clock...156
Introduction How do we help students find meaning in mathematics? That is, how do we give students more than a rote script for reciting facts and churning out computations? How do we help students develop understanding? Hands-On Standards, Common Core Edition Grade 4 is an easy-to-use reference manual for teachers who want to help students discover meaning in mathematics. Each of the manual s 33 lessons demonstrates a hands-on exploration using manipulatives. The goal is to help students get a physical sense of a problem to help students get their hands on the concepts they need to know and to help them see the meaning. Each lesson in Hands-On Standards targets a clearly stated objective. The main part of a lesson offers a story problem that students can relate to and has the students work on the problem using a hands-on approach. Full-color photographs demonstrate the suggested steps. In addition to the main activity, each lesson includes suggested points of discussion, ideas for more exploration, a formative assessment item, and practice pages to help students solidify their understanding. The instructional model is a progression from concrete to abstract. This book is divided into five sections Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations Fractions, Measurement and Data, and Geometry. These correspond to the five content domains for Grade 4 as cited in the Common Core State Standards for Mathematics. Each lesson in this book uses one of the following manipulatives: AngLegs Attribute Blocks Base Ten Blocks Centimeter Cubes Color Tiles Cuisenaire Rods Deluxe Rainbow Fraction Circles Fraction Tower Equivalency Cubes Geoboard GeoReflector Mirror Pattern Blocks Three Bear Family Counters Read on to find out how Hands-On Standards, Common Core Edition Grade 4 can help the students in your class find meaning in math and build a foundation for future math success! 1
A Walk Through a Lesson Each lesson in Hands-On Standards includes many features, including background information, objectives, pacing and grouping suggestions, discussion questions, and ideas for further activities, all in addition to the step-by-step, hands-on activity instruction. Take a walk through a lesson to see an explanation of each feature. Lesson Introduction A brief introduction explores the background of the concepts and skills covered in each lesson. It shows how they fit into the larger context of students mathematical development. Try It! Arrow In order to provide a transition from the introduction to the activity, an arrow draws attention to the Try It! activity on the next page. When the activity has been completed, return to the first page to complete the lesson. 2 Objective The Objective summarizes the skill or concept students will learn through the hands-on lesson. Common Core State Standards Each lesson has been created to align with one or more of the Common Core State Standards for Mathematics. Talk About It The Talk About It section provides post-activity discussion topics and questions. Discussion reinforces activity concepts and provides the opportunity to make sure students have learned and understood the concepts and skills. Solve It Solve It gives students a chance to show what they ve learned. Students are asked to return to and solve the original word problem. They might summarize the lesson concept through drawing or writing, or extend the skill through a new variation on the problem. 12 2 Objective Common Core State Standards 4.OA.4 Operations and Algebraic Thinking Finding Factor Pairs Finding factor pairs allows students to deepen their understanding of division as they learn about factors and divisibility rules. To find all the factor pairs of a number, students should be encouraged to proceed in an organized fashion by finding the factor pair of 1, then 2, then 3, then 4, and so on. This will help them avoid skipping any factor pairs, which is a common mistake if students try to haphazardly identify factor pairs. Factor pairs also allow students to understand the difference between prime and composite numbers. Talk About It Discuss the Try It! activity. Ask: Why do we call the sets of numbers we found the factor pairs of 10? What do all the pairs have in common? Ask: How many factor pairs are there for 9? How many are there for 7? Explain that 7 is a prime number whose only factors are 1 and itself. Ask: Will all prime numbers have only one factor pair? Why? Ask: What if you put two orange Cuisenaire Rods together? What number would you have then? Have students use Rods to find the new number. Ask: What factor pair of 20 does the train of two orange Rods show? Solve It With students, reread the problem. Have students use Rods to model the factor pairs for 10. They should then write a sentence telling who was correct, Lisa or Adrienne, and how they used Rods to find the answer. More Ideas For other ways to teach about identifying the factors of a number Have students use a complete set of Cuisenaire Rods, or two sets combined, to model factor pairs of larger numbers. For example, ask students to use Rods to model the number 18 showing two different factor pairs. Write the following numbers on the board: 25, 36, 50, and 63. Ask groups of students to work together to make arrays for each number using Color Tiles. Students should discover that the number of rows and the number of columns in the array represent a factor pair for the product shown. Formative Assessment More Ideas More Ideas provides additional activities and suggestions for teaching about the lesson concept using a variety of manipulatives. These ideas might be suggestions for additional practice with the skill or an extension of the lesson. Have students try the following problem. Which of the following are factors of 40? A. 3 and 15 B. 4 and 10 C. 8 and 6 D. 7 and 7 Formative Assessment Formative assessments allow for on-going feedback on students understanding of the concept.
Try It! The Try It! activity opens with Pacing and Grouping guides. The Pacing guide indicates about how much time it will take for students to complete the activity, including the post-activity discussion. The Grouping guide recommends whether students should work independently, in pairs, or in small groups. Next, the Try It! activity is introduced with a real-world story problem. Students will solve the problem by performing the hands-on activity. The word problem provides a context for the hands-on work and the lesson skill. The Materials box lists the type and quantity of materials that students will use to complete the activity, including manipulatives such as Color Tiles and Pattern Blocks. This section of the page also includes any instruction that students may benefit from before starting the activity, such as a review of foundational mathematical concepts or an introduction to new ones. Try It! 30 minutes Groups of 6 Here is a problem about identifying factor pairs. Mr. Robinson s fourth-grade class is using Cuisenaire Rods to show the factors of different numbers. Lisa says that the number 10 has one pair of factors. Adrienne says that the number 10 has two pairs of factors. Who is correct? Introduce the problem. Then have students do the activity to solve the problem. Distribute Cuisenaire Rods and Factor Pairs Worksheets (BLM 1) to students. Tell students that each Rod corresponds to a number from 1 to 10 and they can find the number a Rod represents by counting how many white Rods make up the larger Rod. Materials Cuisenaire Rods (1 set per group) Factor Pairs Worksheet (BLM 1; 1 per group) crayons or pencils (several per group) Operations and Algebraic Thinking 1. Instruct students to find the orange Rod. Ask: What number does the orange Rod show? Students should use white Rods to measure, if necessary. Then have students make a train the same size using Rods of only one color. 2. Ask: What size Rod did you use? How many Rods did you use? Tell students that these two numbers represent a factor pair for the number 10. Students should transfer their trains to the worksheet. 3. Ask students to find another factor pair for 10 and model it two different ways using Rods. Students should write the factor pairs and draw the Rod trains on the Factor Pairs Worksheet. Repeat with other values. Some students may make trains out of different colors of Rods. Emphasize that trains of Rods must be made of only one color to show multiplication. If trains are made up of more than one color, they show addition, not multiplication. Reinforce that two factors must be multiplied to equal the target product. 13 Look Out! Look Out! describes common errors or misconceptions likely to be exhibited by students at this age dealing with each skill or concept and offers troubleshooting suggestions. Step-by-Step Activity Procedure The hands-on activity itself is the core of each lesson. It is presented in three or sometimes four steps, each of which includes instruction in how students should use manipulatives and other materials to address the introductory word problem and master the lesson s skill or concept. An accompanying photograph illustrates each step. 3
A Walk Through a Student Page Each lesson is followed by a corresponding set of student pages. These pages take the student from the concrete to the abstract, completing the instructional cycle. Students begin by using manipulatives, move to creating visual representations, and then complete the cycle by working with abstract mathematical symbols. Lesson 2 Operations and Algebraic Thinking Name Answer Key Exercise Concrete and Representational exercises (pictorial representations of the featured manipulative) help students bridge conceptual learning to symbolic mathematics. Use Cuisenaire Rods to build each number and factor pairs shown. Complete the trains. Write each multiplication sentence. 1. (Check students work.) 12 2 6 = 12 4 3 = 12 3 4 = 12 2 6 = 12 2. 18 2 6 3 3 6 2 9 9 = 18 = 18 = 18 = 18 Build each number and its factor pairs using Cuisenaire Rods. Sketch your models. Write each multiplication sentence. Standards-Based Math Practice Abstract exercises provide standards-based math practice to allow students to deepen their understanding of the featured skill. 3. 20 4. 16 5 4; 4 5; 2 10; 10 2 2 8; 8 2; 4 4 Find factor pairs for each number. Write each multiplication sentence. 5. 14 6. 25 7. 21 2 7; 7 2 5 5 3 7; 7 3 ETA hand2mind 14 Hands-On Standards, Common Core Edition Download student pages at hand2mind.com/hosstudent. 4
Extended Response Extended Response exercises feature an open-ended constructed response question to help teachers gauge student understanding. Answer Name Key Challenge! Why does Question 4 have an odd number of factor pairs? Are there other problems on the previous page that have an odd number of factor pairs? Explain. Challenge: (Sample) in Question 4, one of the factor pairs is 4 4. Because both factors are the same, another multiplication sentence cannot be written for 16 using these factors. Question 7; One of the factor pairs for 36 is 6 6. Question 9; The factor pair for 25 is 5 5. Answers for the Teacher Answers are provided for teachers on the included student pages. Student Pages Download Download clean copies of the student pages by visiting the URL listed. ETA hand2mind Download student pages at hand2mind.com/hosstudent. Hands-On Standards, Common Core Edition 15 5