Table of COntents Introduction – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 3 Format of Books – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 4 Suggestions for Use – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 7 Annotated Answer Key and Extension Activities – – – – – – – – – – – 9 Reproducible Tool Set – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 176 ISBN 978-0-8454-8718-1 Copyright © 2015 The Continental Press, Inc. Excepting the designated reproducible blackline masters, no part of this publication may be reproduced in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. All rights reserved. Printed in the United States of America. FLM NJ ATE CC G3_FM.indd 2 3/13/15 10:42 AM 17 One-Step Word Problems with Multiplication and Division Pages 139 and 140 Objective To solve multiplication and division word problems PAR T 1 Introduction Introduction Review words that are clues for the operations of multiplication and division. Students should recognize that into equal groups is a signal to divide. Then guide the students in writing a representative number sentence for a word problem, using a variable to represent the unknown. Relate this to the array on the page. Repeat with the example of a multiplication situation. Emphasize that in a number sentence, one expression, such as 2 3 b, is equal to another, i.e., the expressions name the same number in different ways. Think About It Students should recognize the length of the classroom in feet as the dividend and the number of steps as the divisor, and write a sentence such as 24 4 12 5 s. Common Core State Standard 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 36 4 and the number of rows 4 3 r 5 36 the dividend Vocabulary equation: a number sentence that says two expressions are equal expression: a grouping of numbers and operations that shows the value of something 80 UNIT 4 FLM Nat ATE G3 3rd Ed_U4.indd 80 36 4 4 5 r 9 © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. 2/24/15 9:48 AM PAGES LESSON 141 AND 142 17 O ne-Step Word Problems with Multiplication and Division PAR T the hours it takes to get to the beach Answers will vary. 2 3 times as long multiplication 3325h 6 45 4 9 5 n or equivalent 2 Focused Instruction Focused Instruction Students change a word problem into a representative division sentence and then solve it. The questions help students to identify what the numbers represent and to write the sentence. They should recognize that to solve the division problem, they can use the inverse operation of multiplication. In a second example, students decipher the clue words in a problem to determine a multiplication situation, write appropriate expressions, and finally write and solve a multiplication sentence with a variable for the unknown. Conclude the Focused Instruction section by having students answer the two word problems. 8 3 3 5 t or equivalent PAR T 2 3 w 5 14 Practice Guided Practice 3 Guided Students should complete the Guided Practice section on their own. Offer assistance as needed, pointing out the reminder and hint boxes along the right side of the page. 14 4 2 5 w 7 5 3 a 5 30 6 •••••• •••••• •••••• •••••• 4 © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. FLM Nat ATE G3 3rd Ed_U4.indd 81 Connections to Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. UNIT 4 81 2/24/15 9:48 AM LESSON 17 O ne-Step Word Problems with Multiplication and Division PAGES 143 AND 144 PAR T Practice I ndependent Practice 4 Independent Answer Rationales 1 In choice A, the student likely misinterpreted the word twice as the answer 2. In choice C, the student added 2 instead of dividing by 2. In choice D, the student multiplied the ears of corn by 2 instead of dividing. Choice B is correct. There are twice as many ears of corn as pumpkins, so there are half as many pumpkins as ears of corn. Divide: 48 4 2 5 24. 2 Think of the question, “How many times can groups of 8 be taken out of 56?” So the equation should show the number of pieces of gum divided by the number of pieces per pack, which equals the number of packs: 56 4 8 5 g, so g 5 7. DOK 2 3.OA.3 DOK 2 3.OA.3 56 4 8 5 g or equivalent; g 5 7 DOK 2 3.OA.3 She is not correct. She should have written 3 3 n 5 15. 3 Andrea’s number of tickets is 3 times as many as Bill’s, which means you must multiply by 3. Her number of tickets is equal to 15, so 3 times some number equals 15. That means Bill has taken 5 tickets because 3 3 5 5 15. 4 Part A There are a total of 54 swimmers. Each team is made up of 9 swimmers. Use division to find the number of teams by dividing the total number of swimmers by the number on each team: 54 4 9 5 s. Use multiplication by multiplying the number of teams and the number of swimmers on each team to get the total number of swimmers: 9 3 s 5 54. In both equations, s 5 6, so there are 6 teams. Part B The words twice as many mean “multiply by 2.” The number of girls is unknown, g. So g multiplied by 2 equals the number of boys, 36: 2 3 g 5 36. So there were 18 girls because 2 3 18 5 36. 5 Parts A and B If the worker makes 3 rows of cans, there will be 8 cans in each row because 3 3 8 5 24. The array will show 3 rows of 8. The worker could also make 8 rows with 3 cans in each row. If the worker makes 4 rows of cans, there will be 6 cans in each row because 4 3 6 5 24. He could also make 6 rows with 4 cans in each row. Arrays can show the number of rows and the number of cans in each row. 82 UNIT 4 FLM Nat ATE G3 3rd Ed_U4.indd 82 DOK 3 3.OA.3 9 3 s 5 54 or 54 4 9 5 s; s 5 6 18 DOK 3 3.OA.3 Answers may vary: •••••• •••••• •••••• •••••• •••••••• •••••••• •••••••• 4 3 6 5 24 and 3 3 8 5 24 © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. 2/24/15 9:48 AM PAGE LESSON 145 DOK 3 3.OA.3 32 4 4 5 8 17 O ne-Step Word Problems with Multiplication and Division 6 Part A Each frame needs 4 10-inch pieces of wood. To find the number of frames Jared can make with 32 pieces of wood, divide the total number of pieces by the number needed for each frame. The quotient is the number of frames he can make: 32 4 4 5 8. Part B Since each frame is $9, divide the total amount Jared wants to make by the cost of each frame. The quotient is the number of frames he needs to sell: $72 4 $9 5 8 frames. He needs to sell 8 frames because 72 4 9 5 8. Extension Activity Select a topic that students are likely to have had firsthand experience with—a fair or festival, a class trip to a museum or other venue, a yard sale. Tell the class that they are going to write one-step word problems about this topic, and brainstorm some ideas for problems, noting them on the board. Give each student four 4-3-6-inch index cards. Direct the students to write one problem for each operation: addition, subtraction, multiplication, and division. Encourage creativity and the use of as many basic facts as they can. On the back of each card, the student should note the operation and the correct number sentence with answer. Collect the problems to share with the class and store them in a labeled folder. © The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. FLM Nat ATE G3 3rd Ed_U4.indd 83 UNIT 4 83 2/24/15 9:48 AM
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