5th Grade Module 2 – Lesson 5 Lesson 5: I can connect visual models and the distributive property to partial products of the standard algorithm without renaming. 5th Grade Module 2 – Lesson 5

Get Ready to Estimate Products by Rounding! You will need the Pattern Sheet (2.B.37) Directions: Estimate and then Multiply! You will have 4 minutes to do your best! 5th Grade Module 2 – Lesson 5

Let’s Practice Multiplying Mentally! Get your White Board Ready! Say the multiplication Sentence with the product. 90 On your white board, write the number sentence & fill-in the blank. 9 x 10 = What’s 9 x 9 ? 9 9 x 9 = 90 - __ 9 x 9 = 81 5th Grade Module 2 – Lesson 5

Let’s Practice Multiplying Mentally! Get your White Board Ready! Say the multiplication Sentence with the product. 900 On your white board, write the number sentence & fill-in the blank. 9 x 100 = What’s 9 x 99 ? 9 9 x 99 = 900 - __ 9 x 99 = 891 5th Grade Module 2 – Lesson 5

Let’s Practice Multiplying Mentally! Get your White Board Ready! Say the multiplication Sentence with the product. 150 On your white board, write the number sentence & fill-in the blank. 15 x 10 = ____ What’s 15 x 9 ? 15 15 x 9 = 150 - __ 15 x 9 = 135 5th Grade Module 2 – Lesson 5

Let’s Practice Multiplying Mentally! Get your White Board Ready! Say the multiplication Sentence with the product. 2900 On your white board, write the number sentence & fill-in the blank. 29 x 100 = ____ What’s 29 x 99 ? 29 29 x 99 = 2900 - __ 29 x 99 = 2871 5th Grade Module 2 – Lesson 5

Get Your White Board Ready! Multiply by Multiples of 100 31 x 100 = ____ 3,100 Say the multiplication sentence. Say the multiplication sentence. 3,100 x 2 = ____ 6,200 Say 31 x 200 as a three-step multiplication sentence, taking out the hundred. 31 x 200 = ____ 31 x 100 x 2 = 6,200 31 x 200 = 6,200 5th Grade Module 2 – Lesson 5

Get Your White Board Ready! Multiply by Multiples of 100 24 x 100 = ____ 2,400 Say the multiplication sentence. Say the multiplication sentence. 2,400 x 3 = ____ 7,200 Say 24 x 300 as a three-step multiplication sentence, taking out the hundred. 24 x 300 = ____ 24 x 100 x 3 = 7,200 24 x 300 = 7,200 5th Grade Module 2 – Lesson 5

Get Your White Board Ready! Multiply by Multiples of 100 34 x 100 = ____ 3,400 Say the multiplication sentence. Say the multiplication sentence. 3,400 x 2 = ____ 6,800 Say 34 x 200 as a three-step multiplication sentence, taking out the hundred. 34 x 200 = ____ 34 x 100 x 2 = 6,800 24 x 200 = 6,800 5th Grade Module 2 – Lesson 5

5th Grade Module 2 – Lesson 5 Application Problem Aneisha is setting up a play space for her new puppy. She will be building a fence around part of her yard that measures 29 feet by 12 feet. How many square feet of play space will her new puppy have? If you have time, solve it in more than one way. 5th Grade Module 2 – Lesson 5

5th Grade Module 2 – Lesson 5 Display Solutions 5th Grade Module 2 – Lesson 5

We can think (20 x 5) plus 5 more Concept Development 21 x 5 Can you solve this mentally using the unit form strategy? We can think (20 x 5) plus 5 more Twenty 5’s and 1 more 5. Twenty 5’s = 100 1 more 5 = 105 Let’s try to represent our thinking with a tape diagram. Draw on your white board your thinking. Let’s draw it though without so many units. Like we built area models in 4th grade and in Module 1. One way is with 5 as the factor and we can stack it vertically (21 groups of 5): 1 20 5 Area Model 5th Grade Module 2 – Lesson 5

What if we turn the area model so that we count 5 groups of 21? What values can we put in the area model? 21 x 5 1 20 5 21 groups of 5 1 x 5 1 five and 20 fives. 5 and 100 105 21 x 5 = 105 20 x 5 This area model helps us show all the units without having to draw every single one. It made it easier to see (20 x 5) + (1 x 5). What if we turn the area model so that we count 5 groups of 21? 21 Will the product change? 5 5th Grade Module 2 – Lesson 5

Let’s connect the area model to the standard algorithm. 23 x 31 First, we need to think which factor we want to name as our unit. Is it easer to count, 31 twenty-threes or 23 thirty-ones? Turn & Talk We could use either but let’s use 31 groups of 23. Draw the area model with me on your white board. 1 group of 23 is on top 23 1 Does it matter how we split the rectangle? 23 x 1 = 23 The 30 group is on the bottom. 30 Solve with your partner. 23 x 30 = 690 Add up the partial products: 23 + 690 = 713 5th Grade Module 2 – Lesson 5

Using the Standard Algorithm Let’s Solve 23 x 31 Using the Standard Algorithm Work with your partner to solve using the standard algorithm on your white board. 2 3 x 3 1 + 6 9 0 7 1 3 30 1 23 690 Let’s compare the area model and the standard algorithm. What do you notice? 5th Grade Module 2 – Lesson 5

5th Grade Module 2 – Lesson 5 Let’s try some three-digit by two-digit problems. Record these in your notebook. 343 x 21 What should we designate as the unit (top number)? 343 3 4 3 x 2 1 1 343 6860 3 4 3 + 6 8 6 0 7 2 0 3 20 Let’s find the value of 21 groups of 343. Draw an area model and solve. Then solve with the standard algorithm. Let’s discuss the connections between the two models. 5th Grade Module 2 – Lesson 5

Let’s try another problem. Record in your notebook. What should we designate as the unit (top number)? Remember…using the larger digit as the unit will be more efficient. 231 x 32 231 2 3 1 x 3 2 2 462 6930 4 6 2 + 6 9 3 0 7 3 9 2 30 Let’s find the value of 32 groups of 231. Draw an area model and solve. Then solve with the standard algorithm. Let’s discuss the connections between the two models. 5th Grade Module 2 – Lesson 5

Get Ready to Complete the Problem Set on Your Own! Complete Pages 2.B.38 & 2.B.39 You will have 10-15 minutes to work. Try your Best! 5th Grade Module 1 – Lesson 5

5th Grade Module 1 – Lesson 5 LET’S Debrief Look back at the area models in Problems 1 and 2. What is the same about these two problems? How could you use Problem 1 to help you solve Problem 2? How is multiplying three digits by two digits different than multiplying two digits by two digits? How is it the same? What is different about Problem 4? Does using a decimal value like 12.1 as the unit being counted change the way you must think about the partial products? 5th Grade Module 1 – Lesson 5

5th Grade Module 1 – Lesson 5 EXIT TICKET 2.B.40 5th Grade Module 1 – Lesson 5