Lesson 6.8. Activity Materials square tiles
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1 Name Write Related Facts Essential Question How can you write a set of related multiplication and division facts? Unlock the Problem ALGEBRA Lesson 6.8 Operations and Algebraic Thinking 3.OA.C.7 Also 3.OA.A.2, 3.OA.A.3 MATHEMATICAL PRACTICES MP2, MP6, MP7, MP8 Related facts are a set of related multiplication and division equations. What related facts can you write for 2, 4, and 8? Activity Materials square tiles Hands On What model can you use to show how multiplication and division are related? STEP 1 Use 8 tiles to make an array with 2 equal rows. Draw the rest of the tiles. How many tiles are in each row? Write a division equation for the array using the total number of tiles as the dividend and the number of rows as the divisor. _ _ = _ Write a multiplication equation for the array. _ _ = _ STEP 2 Now, use 8 tiles to make an array with 4 equal rows. Draw the rest of the tiles. How many tiles are in each row? Write a division equation for the array using the total number of tiles as the dividend and the number of rows as the divisor. _ _ = _ So, 8 2 = _, 2 4 = _, 8 4 = _, and 4 2 = _ are related facts. Write a multiplication equation for the array. _ _ = _ Chapter 6 345
2 Try This! Draw an array with 4 rows of 4 tiles. Your array shows the related facts for 4, 4, and = _ 16 4 = _ Since both factors are the same, there are only two equations in this set of related facts. MATHEMATICAL PRACTICE 6 Attend to Precision Write another set of related facts that has only two equations. Share and Show MATH BOARD 1. Complete the related facts for this array. 2 8 = = 8 Math Talk 4 4 = 16 factor factor product MATHEMATICAL PRACTICES 7 Identify Relationships Look at the multiplication and division equations in a set of related facts. What do you notice about the products and dividends? Write the related facts for the array Why do the related facts for the array in Exercise 2 have only two equations? 346
3 Name On Your Own Write the related facts for the array Write the related facts for the set of numbers. 9. 2, 5, , 8, , 6, 36 Complete the related facts = _ 7 _ = _ = = _ _ = 30 6 _ = = _ 30 5 = _ 14. _ 9 = 27 _ 3 = 27 _ 9 = 3 27 _ = Write a set of related facts that has only two equations. Draw an array to show the facts. 16. DEEPER Maria makes an array of 4 rows of 5 tiles. She wants to make an array to show the fact 5 5. What can she do to change the array to show 5 5 as a related fact? Chapter 6 Lesson 8 347
4 MATHEMATICAL PRACTICES COMMUNICA E CONSTRUCT ARGUMENTS Use the table for MATHEMATICAL PRACTICE 3 Verify the Reasoning of Others Ty has a package of glitter dough. He says he can give 9 friends 5 equal sections. Describe his error. What is the correct answer? Clay Supplies Item Number in Package Clay 12 sections Clay tool set 11 tools Glitter dough 36 sections Math WRITE Show Your Work 18. SMARTER Mr. Lee divides 1 package of clay and 1 package of glitter dough equally among 4 students. How many more glitter dough sections than clay sections does each student get? 19. DEEPER Ms. Cohn divides 21 markers equally among 7 students. Write an equation to show how many markers each student gets. Then write a related fact. 20. SMARTER Select the equations that represent the array. Mark all that apply. A 2 10 = 20 D 20 2 = 10 B 20 4 = 5 E 4 5 = 20 C 5 4 = 20 F 20 5 = 4 348
5 Name Write Related Facts Write the related facts for the array Practice and Homework 3. Lesson 6.8 COMMON CORE STANDARD 3.OA.C.7 Multiply and divide within = = = = 2 Write the related facts for the set of numbers. 4. 3, 7, , 9, , 8, 32 Problem Solving 7. CDs are on sale for $5 each. Jennifer has $45 and wants to buy as many as she can. How many CDs can Jennifer buy? 8. Mr. Moore has 21 feet of wallpaper. He cuts it into sections that are each 3 feet long. How many sections does Mr. Moore have? 9. WRITE Math Write a division fact. Write the rest of the related facts. Chapter 6 349
6 Lesson Check (3.OA.C.7) 1. What number completes the set of related facts? 5 = = 5 5 = = 2. Write the related facts for the set of numbers. 4, 7, 28 Spiral Review (3.OA.A.1, 3.OA.B.5, 3.OA.C.7, 3.NBT.A.3) 3. Beth runs 20 miles each week for 8 weeks. How many miles does Beth run in 8 weeks? 4. Find the product Uri s bookcase has 5 shelves. There are 9 books on each shelf. How many books are in Uri s bookcase? There are 6 batteries in one package. How many batteries will 6 packages have? FOR MORE PRACTICE GO TO THE Personal Math Trainer
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