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Associative Property of Multiplication to find Products? 8.2 Associative Property ALGEBRA of Multiplication ? Essential Question How can you use the Associative Property of Multiplication to find products? Texas Essential Knowledge and Skills Number and Operations—3.4.F Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts; 3.4.K Solve one-step and two-step problems involving multiplication and division within 100 How can you use the Associative Property of Algebraic Reasoning—3.5.B Represent and solve one- Multiplication to find and two-step multiplication and division problems within 100 products? Also 3.4.D, 3.4.G, 3.5.D MATHEMATICAL PROCESSES 3.1.E Create and use representations 3.1.G Display, explain, and justify mathematical ideas and arguments Are You Ready? Access Prior Knowledge Use the Are You Ready? 8.2 in the Assessment Guide to assess students’ Lesson Opener understanding of the prerequisite skills Making Connections for this lesson. Invite students to tell you what they know about different modes of transportation. Explain to students that the Mole Mountain Express described in the problem is like a Vocabulary taxi, shuttle, or bus. Associative Property of Multiplication Have you ever taken a taxi, a shuttle, or a bus? What was it like? Have you ever taken Go to Multimedia eGlossary at bags with you on a trip? How many? thinkcentral.com Using the Digital Lesson You may wish to model the stated problem with students using pictures or manipulatives, such as counters. Learning Task What is the problem the students are trying to solve? Connect the story to the problem. Resources • How many passengers go each time? (4 passengers each trip) • How many bags does each passenger take? (2 bags per passenger) For the student For the teacher • How could you find the number of bags delivered on one trip? (Multiply the Interactive Digital Management Student Edition Center organizes program number of passengers, 4, by the number of bags per passenger, 2. Or, add the provides students resources by TEKS! number of bags per passenger, 2, 4 times.) with an interactive learning • What expression could you use to find the number of bags delivered on one trip? environment! eTeacher (4 × 2 or 2 + 2 + 2 + 2) Edition Math on the Spot Video Tutor Online Assessment Literacy and Mathematics System • Have students look for clue words in the problem that indicate that multiplication iTools Virtual might be used to solve it. Manipulatives • Have students write a short story about one of the travelers. Encourage them to Soar to Success Math include details such as what the traveler has in his/her bag and what he/she is doing Online Intervention at Mole Mountain. Lesson 8.2 243A Name Number and Operations—3.4.F, 3.4.K Associative Property Algebraic Reasoning— 8.2 3.5.B Also 3.4.D, 3.5.D of Multiplication MATHEMATICAL PROCESSES ALGEBRA 3.1.E Connect Essential Question Students relate the Associative Property of Addition ? How can you use the Associative Property of to the Associative Property of Multiplication. Multiplication to find products? Connect You have learned the Associative Unlock the Problem Property of Addition. When the grouping of the Math Idea addends is changed, the sum stays the same. Have students draw a quick picture of the roller Always multiply the numbers inside the parentheses first. coaster train to check their understanding of the (2 + 3) + 4 = 2 + (3 + 4) problem. The Associative Property of Multiplication states The example uses arrays to represent the problem. that when the grouping of the factors is changed, • What does each separate array show? Possible the product is the same. It is also called the Grouping Property of Multiplication. answer: 2 rows of 2 seats each; 2 × 2 Use the Math Idea to remind students to complete UnlockUnlock the Problem the operation inside the parentheses first. Each car on the roller coaster • Underline what you need to find. After students complete the problem with the new has 2 rows of seats. Each row has grouping, ask the following questions: 2 seats. There are 3 cars in each • Describe the grouping of the seats. • Does it matter which factors you multiply first? train. How many seats are on 3 cars with 2 rows of 2 seats each roller coaster train? No; whichever way I multiply the factors, the product will still be the same. Use an array. • Was one grouping easier than the other for You can use an array You can change the grouping with × × parentheses and the product is the same. finding the final answer? Explain. Possible to show 3 (2 2). × × = ■ explanation: yes; multiplying by 2 is easier for me, 3 × (2 × 2) = ■ (3 2) 2 ( × ) × so 3 2 2 was easier because I multiplied by _6 × 2 = _12 3 × _4 = _12 2 both times. Math Talk So, there are 3 cars with 4 seats in Mathematical Processes each car. Explain why the products Mathematical Processes 3 × (2 × 2) and (3 × 2) × 2 Math Talk There are _12 seats on each roller are the same. coaster train. Use Math Talk to focus on students’ understanding Possible explanation: it does not matter how the factors that changing the grouping of the factors does not are grouped. The products will be the same. change the product. Module 8 243 © Houghton Mifflin Harcourt Publishing Company Kinesthetic / Verbal English Language Learners ELL Language Support Small Group Leveled Activities ELPS ELPS 1.A.2, 2.D.2, 2.I.4 Beginning: Activity 8 2.I.4, 3.G.1, 3.H.3 Intermediate: Activity 3 2.D.2, 2.E.3, 3.F.2 Strategy: Creative Grouping Materials: square tiles Advanced: Activity 41 4.F.3, 4.F.8 • Partner advanced English learners with beginning English learners. Advanced High: Activity 43 4.F.8, 4.G.2, 4.G.4 • Have beginning English learners use tiles to show (2 + 3) + 4; then thinkcentral.com Go to for the ELL Activity show 2 + (3 + 4). Guide containing these leveled activities. • Have the advanced English learner help explain each model and how each shows the Associative Property of Addition. (2 1 3) 1 4 • Beginning English learners should ask for clarification if they do not 243 Module 8 understand a word or phrase. Example Use the Commutative and Associative Properties. You can also change the order of the factors. The product is the same. Example This example shows that you can change the order of × × = ■ × × = ■ (4 3) 2 4 (3 2) the factors and the product will be the same. × × = ■ × × = ■ 4 (3 2) Associative Property 4 (2 3) Commutative Property • How could the Commutative and Associative 4 × _6 = _24 (4 × 2) × 3 = ■ Associative Property Properties be used to make (3 × 8) × 2 easier to solve? Possible answer: change the order and the _8 × 3 = _24 grouping to 8 × (3 × 2) so that you can use a basic fact, 8 × 6, instead of 24 × 2 or 16 × 3. ShareShare and ShowShow • How can multiplication properties help you find products? Possible answer: you can change the grouping 1. Find the product of 5, 2, and 3. Write another way to group the factors. Is the product the same? Why? or the order of the factors to find products of facts you know. (5 × 2) × 3 = 30; Possible answer: I can regroup the factors as 5 × (2 × 3) = 30; the product is the same because the grouping does not change the product. Share and Show Write another way to group the factors. Then find The first problem connects to the learning model. the product. Possible groupings are given for 2–5. Have students use the MathBoard to explain their 2. (2 × 1) × 7 3. 3 × (3 × 4) thinking. 2 × (1 × 7) (3 × 3) × 4 Use the checked exercises for Quick Check. Students 14 36 should show their answers for the Quick Check on the MathBoard. 4. 5 × (2 × 5) 5. 3 × (2 × 6) (5 × 2) × 5 (3 × 2) × 6 3 2 1 Quick Check 50 36 IF a student misses the checked exercises Algebra Find the unknown factor. 6. 7 × (2 × _4 ) = 56 7. 60 = (2 × _5 ) × 6 8. _8 × (2 × 2) = 32 Differentiate Instruction with THEN RtI Tier 1 Lesson 37 9. 42 = 7 × (2 × _3 ) 10. 8 × (5 × _1 ) = 40 11. 0 = _0 × (25 × 1) 244 © Houghton Mifflin Harcourt Publishing Company Problems Exercises 6–11 require students to extend their thinking to find an unknown factor when 2 factors and a product are given. Remind students to apply the Associative Property to help solve these problems. Visual Enrich Individual • Challenge students to fill in the unknown numbers so that the product of the numbers in each row and each column equal 24. 2 62 342 416 • Have students create their own grids in which the numbers in each row and each column have the same product. Go to Go to thinkcentral.com for additional enrichment activities in the Enrich Activity Guide. Lesson 8.2 244 Name Problem Solving Problem SolvingSolving Use the graph for 12–13. Have students read problem 12 and discuss what they Roller Coasters need to find. Students have to read a graph and draw 12. Multi-Step Each car on the Steel 7 a picture to help solve a multiplication problem with Force train has 3 rows with 2 seats 6 in each row. How many seats are 5 three factors. 4 on the train? Draw a quick picture. 3 2 36 seats; Check students’ drawings. Problems Train per Cars 1 0 Problem 13 requires students to interpret a graph to 13. Multi-Step A Kingda Ka train has 4 seats per car, but the last car solve this multistep problem involving subtraction, Kingda Ka has only 2 seats.
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