Lesson 6: I can connect area diagrams and the distributive property to partial products of the standard algorithm without renaming. 5th Grade Module 2 – Lesson 5

Get Ready to Multiply Mentally! You will need the Pattern Sheet (2.B.49) You will have 2 minutes to do as many problems as you can! Remember to use mental math strategies! 5th Grade Module 2 – Lesson 5

Get Your White Board Ready! Multiply by Multiples of 100 5th Grade Module 2 – Lesson 5 21 x 100 = ____ Say the multiplication sentence. 2,100 2,100 x 4 = ____ Say the multiplication sentence. 8, x 400 = ____ Say 21 x 400 as a three- step multiplication sentence, taking out the hundred. 21 x 100 x 4 = 8, x 400 = 8, x 400 = 8,400

Get Your White Board Ready! Multiply by Multiples of 100 5th Grade Module 2 – Lesson x 100 = _____ Say the multiplication sentence. 31,200 31,200 x 3 = ____ Say the multiplication sentence. 93, x 300 = ____ Say 312 x 300 as a three-step multiplication sentence, taking out the hundred. Say 312 x 300 as a three-step multiplication sentence, taking out the hundred. 312 x 100 x 3 = 93, x 300 = 93, x 300 = 93,600

Get Your White Board Ready! Multiply by Multiples of 100 5th Grade Module 2 – Lesson 5 2,314 x 100 = _____ Say the multiplication sentence. 231,400 2,314 x 2 = ____ Say the multiplication sentence. 4,628 2,314 x 200 = ____ Say 2,314 x 200 as a three-step multiplication sentence, taking out the hundred. Say 2,314 x 200 as a three-step multiplication sentence, taking out the hundred. 2,314 x 100 x 2 = 462,800 2,314 x 200 = 462,800 2,314 x 200 = 462,800

Let’s Review Multiplying Using the Area Model & Algorithm (solve in your notebook) 43 x 12 = _____ 243 x 12 = _____ 312 x 23= _____ 1.Solve each using an area model 2.Solve each using the standard algorithm Solutions on next slide.

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Application Problem Scientists are creating a material that may replace damaged cartilage in human joints. This hydrogel can stretch to 21 times its original length. If a strip of hydrogel measures 3.2 cm, what would its length be when stretched to capacity? To watch a video of a hydrogel in action click here

Use ink to share solution or Click to Reveal Answer to Application Problem

Concept Development Divide your white board into two sections. On one side we’ll solve with an area model, and on the other side, we will connect it to the standard algorithm. Area ModelStandard Algorithm 64 x 73 Let’s represent 64 groups of However, how can we decompose 73 to make finding these partial products easier to solve? Yes! We can split it into Let’s re- create our area model Let’s fill in each partial product. Then add them up! = 4,672 Solve using the standard algorithm. Check with your partner that you solved it correctly! 73 x Let’s compare the two models. What do you notice?

Let’s Just Practice Creating an Area Model Draw an area model for 56 x 34 Draw an area model for 326 x 27 *Draw using ink tools.

814 x 39 Partner A Solve using the Standard Algorithm Partner B Solve using the Area Model Compare your Solutions ,746

624 x 82 Partner B Solve using the Standard Algorithm Partner A Solve using the Area Model Compare your Solutions ,168

Get Ready to Complete the Problem Set on Your Own! Complete Pages 2.B.50 & 2.B.51 You will have minutes to work. Try your Best! 5th Grade Module 1 – Lesson 5

What pattern did you notice between Parts (a) and (b) of Problem 1? How did this slight difference in factors impact your final product? Explain to your partner how you recorded the regrouping in Problem 2(a). What were you thinking and what did you write as you multiplied 9 tens times 5 tens? Let’s think about a problem like 23 × 45 and solving it with the algorithm. What is the first partial product that we would find? (3 × 45) The second? (20 × 45) Would this be the only order in which we could find the partial products? What else could we do? What information did you need before you could find the cost of the carpet in Problem 3? How did you find that information? Why is area measured in square units?

5th Grade Module 1 – Lesson 5 EXIT TICKET Page 2.B.52