Math Module 3 Multi-Digit Multiplication and Division Topic C: Multiplication of up to Four Digits by Single-Digit Numbers Lesson 7: Use place value disks to represent two-digit by one-digit multiplication 4.OA.2 4.NBT.5 4.NBT.1 PowerPoint designed by Beth Wagenaar Material on which this PowerPoint is based is the Intellectual Property of Engage NY and can be found free of charge at

Lesson 7 Target You will use place value disks to represent two- digit by one-digit multiplication We can do this!

Fluenc y Practic e – Sprint A Think! Take your mark! Get set!

Fluenc y Practic e – Sprint B Think! Take your mark! Get set!

Lesson 7 Fluency Multiply Mentally Say the multiplication sentence. 1 x 4 = 4. 1 x 4 = ____ 4 x 4 = ____ 20 x 4 = ____ Say the multiplication sentence. 20 x 4 = x 4 = ____ Say the multiplication sentence. 21 x 4 = 84. Say the multiplication sentence. 4 x 4 = x 4 = ____ Say the multiplication sentence. 20 x 4 = x 4 = ____ Say the multiplication sentence. 24 x 4 = 96.

Lesson 7 Fluency Multiply Mentally Say the multiplication sentence. 3 x 2 = 6. 3 x 2 = ____ 2 x 3 = ____ 40 x 2 = ____ Say the multiplication sentence. 40 x 2 = x 2 = ____ Say the multiplication sentence. 43 x 2 = 86. Say the multiplication sentence. 2 x 3 = x 3 = ____ Say the multiplication sentence. 30 x 3 = x 3 = ____ Say the multiplication sentence. 32 x 3 = 96.

Lesson 7 Application Problem Lesson 7 The basketball team is selling t- shirts for $9 each. On Monday, they sell 4 t-shirts. On Tuesday, they sell 5 times as many t- shirts as on Monday. How much money did the team earn altogether on Monday and Tuesday?

Lesson 7 Concept Development Problem 1: Represent 2 × 23 with disks, writing a matching equation and recording the partial products vertically. Use your place value chart and draw disks to represent 23. Draw disks on your place value chart to show 1 more group of 23. What is the total value in the ones? 2 × 3 ones = 6 ones = 6. Write 2 × 3 ones under the ones column. Let’s record 2 × 23 vertically. We record the total number for the ones below, just like in addition.   2 x 3 ones 6 ones 23 x x 3 ones

Lesson 7 Concept Development Problem 1: Represent 2 × 23 with disks, writing a matching equation and recording the partial products vertically.   2 x 3 ones 23 x ones Let’s look at the tens. What is the total value in the tens? 2 × 2 tens = 4 tens = 40 Write 2 × 2 tens under the tens column. 2 x 2 tens Let’s represent our answer in the equation. We write 40 to represent the value of the tens. 4 tens 2 x 3 ones 2 x 2 tens What is the total value represented by the disks? + = 46 Notice that when we add the values that we wrote below the line that they add to 46, the product!

Lesson 7 Use your place value chart and draw disks to represent 23. Draw disks on your place value chart to show 2 more groups of 23. What is the total value in the ones? 3 × 3 ones = 9 ones = 9. Write 3 × 3 ones under the ones column. Let’s record 3 × 23 vertically. We record the total number for the ones below, just like in addition.   3 x 3 ones 9 ones 23 x x 3 ones Concept Development Problem 1: Represent 3 × 23 with disks, writing a matching equation and recording the partial products vertically.

Lesson 7   3 x 3 ones 23 x ones Let’s look at the tens. What is the total value in the tens? 3 × 2 tens = 6 tens = 60 Write 3 × 2 tens under the tens column. 3 x 2 tens Let’s represent our answer in the equation. We write 60 to represent the value of the tens. 6 tens 3 x 3 ones 3 x 2 tens What is the total value represented by the disks? + = 69 Concept Development Problem 1: Represent 3 × 23 with disks, writing a matching equation and recording the partial products vertically.

Lesson 7 Concept Development Problem 2: Model and solve 4 × 54. Draw disks to represent 54 on your place value chart. HundredsTensones What is 54 in unit form? 5 tens 4 ones. Draw 3 more groups of 54 on your chart and then write the expression 4 × 54 vertically on your board. What is the value of the ones now? 4 × 4 ones = 16 ones. Record the value of the ones. 54 x4 16 ones

Lesson 7 Concept Development Problem 2: Model and solve 4 × 54. HundredsTensones What is the value of the tens? 4 × 5 tens = 20 tens. Record the value of the tens. 16 ones 20 tens Add up the partial products you recorded. What is the sum? 20 tens + 16 ones = 216 Let’s confirm that on our place value chart. 54 x4

Lesson 7 Concept Development Problem 2: Model and solve 4 × 54. Can we change to larger units? We can change 10 ones for 1 ten and 10 tens for 1 hundred twice. Show me on your board. HundredsTensones 16 ones 20 tens What value is represented on the place value chart? 2 hundreds + 1 ten + 6 ones = x4

Lesson 7 Concept Development Problem 2: Model and solve 5 × 52. Draw disks to represent 52 on your place value chart. HundredsTensones What is 52 in unit form? 5 tens 2 ones. Draw 4 more groups of 52 on your chart and then write the expression 5 × 52 vertically on your board. What is the value of the ones now? 5 × 2 ones = 10 ones. Record the value of the ones. 52 x5 10 ones

Lesson 7 Concept Development Problem 2: Model and solve 5 × 52. HundredsTensones What is the value of the tens? 5 × 5 tens = 25 tens. Record the value of the tens. 10 ones 25 tens Add up the partial products you recorded. What is the sum? 25 tens + 10 ones = 260 Let’s confirm that on our place value chart. 52 x5

Lesson 7 Concept Development Problem 2: Model and solve 5 × 52. HundredsTensones 10 ones 25 tens Can we change to larger units? We can change 10 ones for 1 ten and 10 tens for 1 hundred twice. Show me on your board. What value is represented on the place value chart? 2 hundreds + 6 tens + 0 ones = x5

Problem Set 10 Minutes

Problem Set 10 Minutes

What pattern do you notice in the answers to Problems 1(a), 1(b), 1(c), and 1(d)?

Describe the renaming you had to do when solving Problem 2(a). How is it different from the renaming you had to do when solving Problem 2(b)?

Why did some of the problems require you to use a hundreds column in the place value chart, but others did not? When you start solving one of these problems, is there a way to tell if you are going to need to change 10 tens to 1 hundred or 10 ones to 1 ten? How did the Application Problem connect to today’s lesson? If we found the total number of shirts sold first (24) and then multiplied to find the total amount of money, what would our multiplication problem have been? (24 × 9.) What do the partial products for 24 × 9 represent in the context of the word problem? Talk to your partner about which method you prefer: writing the partial products or using a place value chart with disks? Is one of these methods easier for you to understand? Does one of them help you solve the problem faster? Debrief Lesson Objective: Use place value disks to represent two-digit by one- digit multiplication

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