7.4. Distributive Property. Activity Materials square tiles Make an array with tiles to show 6 rows of 7. Unlock the Problem

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1 ? Name 7.4 ALGEBRA Essential Question Distributive Property How can you use the Distributive Property to find products? Number and Operations 3.4.E, 3.4.K Algebraic Reasoning 3.5.B Also 3.4.D, 3.5.D MATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E Unlock the Problem Mark bought 6 new fish for his aquarium. He paid $7 for each fish. How much did he spend in all? Find 6 $7. You can use the Distributive Property to solve the problem. The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Activity Materials square tiles Make an array with tiles to show 6 rows of 7. Describe the groups in this problem. Circle the numbers you will use to solve the problem. Remember sum the answer to an addition problem addends the numbers being added Hands On Break apart the array to make two smaller arrays for facts you know. 6 7 = = 6 7 = 6 (5 + 2) 6 7 = (6 5) + (6 2) 6 7 = _ + _ 6 7 = _ So, Mark spent $ _ for his new fish. Think: 7 = Multiply each addend by 6. Add the products. Math Talk Mathematical Processes What other ways could you break apart the 6 7 array? Module 7 229

2 Share and Show 1. Draw a line to show how you could break apart this 6 8 array into two smaller arrays for facts you know. What numbers do you multiply? _ and and _ What numbers do you add? _ + _ 6 8 = 6 (_ + _) 6 8 = (_ _) + (_ _) 6 8 = _ + _ 6 8 = _ Math Talk Mathematical Processes Why do you have to add to find the total product when you use the Distributive Property? Write one way to break apart the array. Then find the product Problem Solving 4. Shade tiles to make an array that shows a fact with 7, 8, or 9 as a factor. Write the fact. Explain how you found the product. 230

3 Name Problem Solving 5. Sense or Nonsense? Robin says, I can find 8 7 by multiplying 3 7 and doubling it. Does her statement make sense? Justify your answer. 6. Multi-Step Brandon needs 8 boxes of spinners for his fishing club. The cost of each box is $9. How much will Brandon pay? 8 $9 = Look at how Brandon solved the problem. Find and describe his error. 8 9 = (4 9) + (5 9) 8 9 = = 81 Use the array to help solve the problem and correct Brandon s error. 8 9 = (4 + 4) = (_ _) + (_ _) 8 9 = _ + _ 8 9 = _ So, Brandon will pay $ _ for the spinners. Module 7 Lesson 4 231

4 Daily Assessment Task Mathematical Processes Fill in the bubble for the correct answer choice. You may use models or strategies to solve. 7. Use Diagrams Maurice planted 8 rows of popcorn plants. There are 6 plants in each row. The array shows Maurice s garden. How many popcorn plants does Maurice have? A 36 C 48 B 42 D At a grocery store, the cans of nuts are arranged in 9 rows. There are 6 cans in each row. Which shows one way to find the total number of cans of nuts? A (5 + 4) 6 B (3 + 3) 6 C (5 + 5) 6 D (5 + 3) 6 9. Multi-Step Jillian bought 6 books for $7 each. She paid with $50. How much change should Jillian receive? A $37 C $43 B $18 D $8 TEXAS Test Prep 10. Representation Which number sentence below is an example of the Distributive Property? 232 A 6 8 = B (8 2) 3 = 8 (2 3) C 6 8 = 8 6 D 6 8 = (6 2) + (6 6)

5 Homework and Practice Name Number and Operations 3.4.E, 3.4.K Algebraic Reasoning 3.5.B Also 3.4.D, 3.5.D MATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E 7.4 ALGEBRA Distributive Property Write one way to break apart the array. Then find the product Shade tiles to make an array that shows a fact with 5, 6, or 7 as a factor. Explain how you found the product. Problem Solving 4. Shawn makes a tile design by using 7 rows of 8 tiles. Explain how Shawn can break apart his design to find how many tiles he used. Module 7 Lesson 4 233

6 Lesson Check TEXAS Test Prep Fill in the bubble completely to show your answer. 5. There are 8 tables in the art class. Five students sit at each table. How many students are in the art class? A 13 B 40 C 45 D Seven large trucks are in a parking lot. Each truck has 6 wheels. How many wheels are there in all? A 67 B 40 C 42 D Jonas buys 6 packages of corn. Each package has 8 ears of corn. Which way can Jonas use to show how many ears of corn he buys? A (4 + 2) 8 B (3 + 2) 8 C (6 + 6) 8 D (4 + 4) 6 8. A store sells bags of 9 apples. Mr. Hyon buys 5 bags of apples to make pies. Which way can Mr. Hyon use to show how many apples he buys? A (4 9) + (5 9) B (3 5) + (6 5) C (4 5) + (5 9) D (3 5) + (9 5) 9. Multi-Step Minka buys 8 CDs for $6 each. She pays with three $20 bills. How much change should Minka receive? 234 A $48 B $12 C $34 D $ Multi-Step Kent buys 5 bags of potatoes that cost $7 each. He gives the clerk $40. How much change should Kent receive? A $35 B $12 C $5 D $52

7 Name Module 7 Assessment Vocabulary Choose the best term from the box to complete the sentence. 1. A of 4 is any product that has 4 as one of its factors. (p. 217) 2. This is an example of the Property. 3 8 = (3 6) + (3 2) This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. (p. 229) Vocabulary Commutative Property of Multiplication Distributive Property multiple Concepts and Skills Write one way to break apart the array. Then find the product. q TEKS 3.4.E, 3.4.K Find the product. q TEKS 3.4.E, 3.4.K = _ = _ = _ = _ _ _ _ _ _ Module 7 235

8 Fill in the bubble for the correct answer choice. You may use models to solve. TEXAS Test Prep 14. Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all? q TEKS 3.4.E, 3.4.K A 36 B 6 C 12 D Zach gave his dog 1 dog biscuit each day, for 5 days. Then he gave his dog 2 dog biscuits a day for the next 5 days. How many biscuits did Zach give to his dog? q TEKS 3.4.E, 3.4.K A 5 C 15 B 30 D Annette bought 4 boxes of pencils. If there are 8 pencils in each box, how many pencils did she buy? q TEKS 3.4.E, 3.4.K A 32 B 12 C 16 D Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days? q TEKS 3.4.E, 3.4.K 236 Record your answer and fill in the bubbles on the grid. Be sure to use the correct place value