 # Lesson 7: I can connect area diagrams and the distributive property to partial products of the standard algorithm with renaming. 5th Grade Module 1 –

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Lesson 7: I can connect area diagrams and the distributive property to partial products of the standard algorithm with renaming. 5th Grade Module 1 – Lesson 7

Time to Sprint! Your teacher will give you today’s sprint. 5th Grade Module 1 – Lesson 7

Let’s Review Multiplying Using the Area Model & Algorithm (solve in your notebook) 24 x 15 = _____ 824 x 15 = _____ 1.Solve each using an area model 2.Solve each using the standard algorithm Solutions on next slide. 5th Grade Module 1 – Lesson 7

20 4 5 10 100 200 2 4 x 1 5 1 2 0 + 2 4 0 3 6 0 800 20 4 5 10 4,000 8,000 8 2 4 x 1 5 4 1 2 0 + 8 2 4 0 1 2 3 6 0 20 40 100 200 20 40 5th Grade Module 1 – Lesson 7

Application Problem The length of a school bus is 12.6 meters. If 9 school buses park end to end with 2 meters between each one, what’s the total length from the front of the first bus to the end of the last bus? 5th Grade Module 1 – Lesson 7

Solution to Application Problem 5th Grade Module 1 – Lesson 7

524 x 136 What do you notice about this problem compared to the problems we did yesterday? Turn & Talk Which factor should we use as our unit? 524 or 136? Think which way would be easier to count. Let’s name 524 as our unit. Let’s name 524 as our unit. How will our area model be different than the ones we made in yesterday’s lesson? Let’s work together to solve using the area model & standard algorithm We will have 3 columns & 3 rows We will have 3 columns & 3 rows 5th Grade Module 1 – Lesson 7

524 x 136 Let’s build the area model. Record in your notebook with me. Draw a rectangle with 3 columns & 3 rows Let’s label the top unit (524) 500 20 4 Let’s label the rows using the other factor 6 30 100 Work with your partner to to solve the partial products. Then solve for the final product. Work with your partner to to solve the partial products. Then solve for the final product. Solution on next slide… Problem 1 5th Grade Module 1 – Lesson 7

500 20 4 300012024 15000600120 500002000400 6 30 100 3,144 15,720 52,400 = 71,264 + + Solution Using Area Model Now try to solve this problem using the standard algorithm. Remember that you are multiplying with 3 different place values so you will have 3 addends! Notice how the partial products match up to the partial products in the standard algorithm. Compare the solutions 5th Grade Module 1 – Lesson 7

4,519 x 326 What is different about this problem? Which factor will be our unit? Is one more efficient to use? Turn & Talk Which factor will be our unit? Is one more efficient to use? Turn & Talk Will the fourth digit change anything about how we multiply? Why or why not? Will the fourth digit change anything about how we multiply? Why or why not? Before we solve, let’s ESTIMATE our product. Round the factors & make an estimate. Before we solve, let’s ESTIMATE our product. Round the factors & make an estimate. 5,000 x 300 = 1,500,000 Partner A Solve using the Area Model Partner B Solve using the Standard Algorithm Let’s Solve the Actual Product Volunteers will share their solutions! Is your actual product reasonable given the estimate? Volunteers will share their solutions! Is your actual product reasonable given the estimate? Problem 2 5th Grade Module 1 – Lesson 7

4,509 x 326 Let’s estimate the product first. Round each factor to multiply. 5,000 x 300 = 1,500,000 The first factor has a zero in the tens place. Let’s write 4,509 in expanded form. 4,000 + 500 + 9 The first factor has a zero in the tens place. Let’s write 4,509 in expanded form. 4,000 + 500 + 9 How many columns will we need to represent the top length of our area model? We need 3 columns! Why only three columns if we have a 4-digit number? We need 3 columns! Why only three columns if we have a 4-digit number? 4,000 500 9 6 20 300 Work with your partner to solve in your notebook. Partner B solve using the area model. Partner A solve using the standard algorithm. Compare your solutions! Work with your partner to solve in your notebook. Partner B solve using the area model. Partner A solve using the standard algorithm. Compare your solutions! Problem 3 5th Grade Module 1 – Lesson 7

Solution 4,509 x 326 Is our product reasonable compared to our estimate of 1,500,000? 5th Grade Module 1 – Lesson 7

Problem 4 4,509 x 306 Estimate the Product 5,000 x 300 = 1,500,000 How is the problem different from 4,509 x 326? Thinking about the expanded forms of the factors, imagine the area model. How will you decompose the length & width? Thinking about the expanded forms of the factors, imagine the area model. How will you decompose the length & width? 4,000 500 9 6 300 Why don’t we need three rows this time? 5th Grade Module 1 – Lesson 7

Problem 4 4,509 x 306 4,000 500 9 6 300 Solve the area model in your notebook. Record the partial products for each row. Solve the area model in your notebook. Record the partial products for each row. 1,200,000 24,000 150,000 3,000 2,700 54 27,054 1,352,700 Let’s record what we drew with the algorithm. 4 5 0 9 x 3 0 6 2 7 0 5 4 Begin with the first partial product 6 x 4,509 Now let’s record 300 x 4,509 When we multiply a number by 100, what happens to the value and position of each digit? Now let’s record 300 x 4,509 When we multiply a number by 100, what happens to the value and position of each digit? So, if we multiply 4,509 x 300 what needs to be recorded in the ones and tens place after the digit shift? + 1 3 5 2 7 0 0 1, 3 7 9, 7 5 4 5th Grade Module 1 – Lesson 7

Get Ready to Complete the Problem Set on Your Own! Complete Pages 2.B.63 - 2.B.65 You will have 10-15 minutes to work. Try your Best! 5th Grade Module 1 – Lesson 7

Explain why a multiplication problem with a three-digit multiplier will not always have three partial products. Use Problem 1 (a) and (b) as examples. How are the area models for Problem 2 (a) and (b) alike and how are they different? What pattern did you notice in Problem 3? Does it matter which factor goes on the top of the model or the algorithm? Why or why not? What are you thinking about as you make these decisions on how to split the area into parts?

5th Grade Module 1 – Lesson 7 EXIT TICKET Page 2.B.66

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