# Math Module 3 Multi-Digit Multiplication and Division Topic C: Multiplication of up to Four Digits by Single-Digit Numbers Lesson 10: Multiply three- and.

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Math Module 3 Multi-Digit Multiplication and Division Topic C: Multiplication of up to Four Digits by Single-Digit Numbers Lesson 10: Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm 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 www.engageny.orgwww.engageny.org

Lesson 10 Target You will multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm We can do this!

Lesson 10 Fluency Expanded Form 532 Say the number. 500 + 30 + 2 Write the number in expanded form.

Lesson 10 Fluency Expanded Form 415 Say the number. 400 + 10 + 5 Write the number in expanded form.

Lesson 10 Fluency Expanded Form 204 Say the number. 200 + 4 Write the number in expanded form.

Lesson 10 Fluency Expanded Form 3,241 Say the number. 3,000 +200 + 40 + 1 Write the number in expanded form.

Lesson 10 Fluency Expanded Form 2,053 Say the number. 2,000 + 50 + 3 Write the number in expanded form.

(Write 3 × 2 =.) Say the multiplication sentence in unit form. S: 3 ones × 2 = 6 ones. T: Write the answer in standard form. S: (Write 6.) T: (Write 30 × 2 =.) Say the multiplication sentence in unit form. S: 3 tens × 2 = 6 tens. T: Write the answer in standard form. S: (Write 60.) Lesson 10 Fluency Multiply Mentally Say the multiplication sentence. 342 x 2 = 684. 342 x 2 = ____ 124 x 3 = ____ 132 x 3 = ____ Say the multiplication sentence. 132 x 3 = 396. 221 x 4 = ____ Say the multiplication sentence. 221 x 4 = 884 Say the multiplication sentence. 124 x 3 = 372. 201 x 4 = ____ Say the multiplication sentence. 201 x 4 = 804. 213 x 4 = ____ Say the multiplication sentence. 213 x 4 = 852.

322 x 7 = _____ Say the sentence. Say it as a three-product addition sentence in unit form. 3 hundreds x 7 + 2 tens x 7 + 2 ones x 7 Solve using the partial product strategy. 322 x 7 14 140 2,100 2,254 Multiply using Partial Products Lesson 10

7 thousands, 1 hundred, 3 tens, 5 ones x 5 = _____ Say the sentence. Say it as a four-product addition sentence in unit form. 7 thousands x 5 + 1 hundred x 5 + 3 tens x 5 + 5 ones x 5 Solve using the partial product strategy. 7,135 x 5 25 150 500 35,000 35,675 Multiply using Partial Products Lesson 10

3 x 7,413= _____ Say the sentence. Say it as a four-product addition sentence in unit form. 7 thousands x 3 + 4 hundreds x 3 + 1 ten x 3 + 3 ones x 3 Solve using the partial product strategy. 7,413 x 3 9 30 1,200 21,000 22,239 Multiply using Partial Products Lesson 10

Application Problem 5 minutes The principal wants to buy 8 pencils for every student at her school. If there are 859 students, how many pencils does the principal need to buy?

Lesson 10 Concept Development Problem 1: Solve 5 × 2,374 using partial products, then connect to the algorithm. 5 × 2,374 With your partner, solve for 5 × 2,374 using the partial products method. You will have two minutes.

Lesson 10 Concept Development Problem 1: Solve 5 × 2,374 using partial products, then connect to the algorithm. Now let’s solve using the algorithm. Say a multiplication sentence for the ones column. 2,374 x 5 4 ones times 5 is 20 ones or 2 tens. Tell your partner how to record 20 ones or 2 tens. I am going to record 2 tens on the line in the tens column and the 0 in the ones column. Do you have 20 ones recorded in your answer from the partial products? 2 0

Lesson 10 Concept Development Problem 1: Solve 5 × 2,374 using partial products, then connect to the algorithm. What is multiplied in the tens column? 7 tens times 5 is 35 tens. 2,374 x 5 2 0 I noticed when I look back at the partial products, I also have 35 tens or 3 hundreds 5 tens. Tell your partner what to do with 3 hundreds 5 tens and the 2 tens we recorded on the line. We have to add the 2 tens to get 37 tens or 3 hundreds 7 tens. Why do the partial products only show 350 though?

Lesson 10 Concept Development Problem 1: Solve 5 × 2,374 using partial products, then connect to the algorithm. 2,374 x 5 2 7 3/ 0 In the partial products method, we add the 2 tens to 35 tens later after multiplying each place value separately. In the algorithm, you add as you go. Let’s record 3 hundreds 7 tens or 37 tens. Cross off the 2 tens on the line because they’ve been added in. What is our multiplication sentence for the hundreds column? 3 hundreds times 5 is 15 hundreds or 1 thousand 5 hundreds.

Lesson 10 Concept Development Problem 1: Solve 5 × 2,374 using partial products, then connect to the algorithm. 2,374 x 5 2 7 1 3/ / / 0 8 11, I noticed the 1,500 in the partial products strategy came next. The algorithm is multiplying in the same order starting with the ones column and moving left. We add the 3 hundreds that were changed from tens. Now we have 18 hundreds. I cross out the 3 on the line because I’ve added it. Last, we have the thousands column. 2 thousands times 5 plus 1 thousand is 11 thousands. Notice that our answer is the same when we used the algorithm and the partial products strategy.

Lesson 10 Concept Development Problem 1b: Solve 9 x 3,082 using partial products, then connect to the algorithm. 3,082 x 9 Now let’s try another problem! Solve using partial products then the standard algorithm. 3,082 x 9

Lesson 10 Concept Development Problem 2: Solve 6 x 3,817 using the algorithm. With your partner, solve for 6 × 3,817 using the algorithm. You have two minutes. 6 x 3,817

Lesson 10 Concept Development Problem 2b: Solve 3 x 7,109 using the algorithm. With your partner, solve for 3 × 7,109 using the algorithm. You have two minutes. 3 x 7,109 7,109 x 3

Lesson 10 Concept Development Problem 3: Solve a word problem that requires four-digit by one-digit multiplication using the algorithm. There are 5,280 feet in a mile. If Bryan ran 4 miles, how many feet did he run? Discuss with your partner how you would solve this problem On your own, use the algorithm to solve for how many feet Bryan ran. You have 2 minutes. 5,280 x 4 is 21,120. Bryan ran 21,120 feet.

Problem Set 10 Minutes

What pattern did you notice while solving Problems 1(a) and 1(b)? What happens to the product if one factor is doubled? Halved?

What other patterns did you notice while working on Problem 1?

Problem 3 only gave one factor. How did you find the other factor?

If one of your classmates was absent for the past week, how would you explain how you solved Problem 4? Describe any visuals you could use to help you with your explanation.

How did Lesson 9 help you to understand today’s lesson? Debrief Lesson Objective: Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm.

Exit Ticket Lesson 1

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