Math Module 3 MultiDigit Multiplication and Division Topic

Math Module 3 Multi-Digit Multiplication and Division Topic C: Multiplication of up to Four Digits by Single-Digit Numbers Lesson 8: Extend the use of place value disks to represent three- and four- digit by one-digit multiplication 4. OA. 2 4. NBT. 5 4. NBT. 1 Power. Point designed by Beth Wagenaar Material on which this Power. Point is based is the Intellectual Property of Engage NY and can be found free of charge at www. engageny. org

I LOVE MATH! Lesson 8 Target You will extend the use of place value disks to represent three- and fourdigit by one-digit multiplication

Lesson 8 Fluency Expanded Form • Say the addition sentence with the answer in standard form. 200 + 30 + 4 = ____ 234

Lesson 8 Fluency Expanded Form • Say the addition sentence with the answer in standard form. 3, 000+ 500 + 60 + 8 = 3, 568 _____

Lesson 8 Fluency Expanded Form • Say the addition sentence with the answer in standard form. 497 400 + 7 + 90 = ____

Lesson 8 Fluency Expanded Form 572 • Say the number. • Write the number in expanded form. 500 + 70 + 2

Lesson 8 Fluency Expanded Form 8, 463 • Say the number. • Write the number in expanded form. 8, 000 + 400 + 60 + 3

Lesson 8 Fluency Expanded Form 9, 075 • Say the number. • Write the number in expanded form. 9, 000 + 70 + 5

Fluency Lesson 8 Multiply Mentally 34 x 2 = ____ • Say the multiplication (Write 3 × 2 =. ) Say the multiplication sentence in unit form. sentence. S: 3 ones × 2 = • 6 ones. 34 x 2 = 68. T: Write the answer in standard form. S: (Write 6. ) T: (Write 30 × 2 • =. )Say Saythe themultiplication sentence in unit form. S: 3 tens × 2 = 6 tens. sentence. T: Write the answer • 31 inx 3 standard = 93. form. S: (Write 60. ) 31 x 3 = ____ 22 x 4 = ____ • Say the multiplication sentence. • 22 x 4 = 88 24 x 3 = ____ • Say the multiplication sentence. • 24 x 3 = 72. 20 x 4 = ____ • Say the multiplication sentence. • 20 x 4 = 80. 24 x 4 = ____ • Say the multiplication sentence. • 24 x 4 = 96.

Fluency Lesson 8 Multiply Using Disks 1 x 32 On your boards, draw number disks to show this multiplication sentence. Fill in the blanks and write the problem vertically. Hundreds Tens ones 32 x 1 2 +30 32 3 1 x ____ tens 2 1 x ____ ones

Fluency Lesson 8 Multiply Using Disks 2 x 32 On your boards, draw number disks to show this multiplication sentence. Fill in the blanks and write the problem vertically. Hundreds Tens ones 32 x 2 4 +60 64 3 2 x ____ tens 2 2 x ____ ones

Fluency Lesson 8 Multiply Using Disks 3 x 32 On your boards, draw number disks to show this multiplication sentence. Fill in the blanks and write the problem vertically. Hundreds Tens ones 32 x 3 6 +90 96 3 3 x ____ tens 2 3 x ____ ones

Fluency Lesson 8 Multiply Using Disks 4 x 32 On your boards, draw number disks to show this multiplication sentence. Fill in the blanks and write the problem vertically. Hundreds Tens ones 32 x 4 8 +120 128 3 4 x ____ tens 2 4 x ____ ones

Fluency Lesson 8 Multiply Using Disks 2 x 28 On your boards, draw number disks to show this multiplication sentence. Fill in the blanks and write the problem vertically. Hundreds Tens 2 2 x ____ tens ones 8 2 x ____ ones 28 x 2 16 +40 56

Fluency Lesson 8 Multiply Using Disks 3 x 51 On your boards, draw number disks to show this multiplication sentence. Fill in the blanks and write the problem vertically. Hundreds Tens ones 51 x 3 5 3 x ____ tens 1 3 x ____ one 3 +150 153

Application Problem Lesson 8 8 minutes Andre bought a stamp to mail a letter that cost 46 cents. He also mailed a package that cost 5 times as much as a stamp. How much did it cost to mail the package and the letter?

Concept Development Lesson 8 Problem 1: Represent 2 x 324 with disks, writing a matching equation, and recording the partial products vertically. • • • Use your place value chart to represent the number 2 times 324. What is the value in the ones? 2 x 4 ones = 8 • What is the value in the hundreds? What is the value in the tens? • 2 x 3 hundreds = 600 2 x 2 tens = 40 Hundreds 2 x 3 hundreds 6 hundreds Tens 2 x 2 tens 4 tens ones 2 x 4 ones 8 ones

Concept Development Lesson 8 Problem 1: Represent 2 x 324 with disks, writing a matching equation, and recording the partial products vertically. • Beneath your place value chart, as we did in yesterday’s lesson, write an expression that shows the total value expressed in the chart. • Write 2 x 324 vertically on your board. Record the partial products for the ones, tens, and hundreds. Hundreds Tens ones 324 x 2 8 2 x 3 hundreds 6 hundreds + 2 x 2 tens 4 tens + 2 x 4 ones 8 ones <-2 x 4 ones <-2 x 2 tens <-2 x 3 hundreds 40 +600 648

Concept Development Lesson 8 Problem 1: Represent 2 x 324 with disks, writing a matching equation, and recording the partial products vertically. • What is the value of the disks represented on the chart? • Add the values that you wrote in the equation. What is their sum? • 648 is another way to represent the answer! Hundreds Tens ones 324 x 2 8 2 x 3 hundreds 6 hundreds + 2 x 2 tens 4 tens + 2 x 4 ones 8 ones <-2 x 4 ones <-2 x 2 tens <-2 x 3 hundreds 40 +600 648

Lesson 8 Concept Development Problem 1: Represent 2 x 324 with disks, writing a matching equation, and recording the partial products vertically. • Now with your partner, work to solve 3 x 231. • Does your work look like this? Hundreds Tens ones 231 x 3 <-3 x 1 ones <-3 x 3 tens 3 <-3 x 2 hundreds 3 x 2 hundreds 6 hundreds 3 x 3 tens 9 tens 3 x 1 ones 3 ones 90 +600 693

Concept Development Lesson 8 Problem 2: Model and solve 4 x 605 modeling the repeated addition on the place value chart. • Draw disks to represent 4 x 605 on your place value chart. Write 4 x 605 vertically on your board. • Tell your partner the value of the digit in each place. • Do we need to regroup? Thousands Hundreds Tens Ones 605 x 4 x 6 hundreds 24 hundreds 4 x 5 ones 20 ones 4 <-4 x 5 ones <-4 x 6 2 hundreds 0 2, 400 2, 420

Concept Development Problem 2: Model and solve 4 x 605 modeling the repeated addition on the place value chart. Lesson 8 • We can change 10 ones for 1 ten twice and 10 hundreds for 1 thousand twice. • Show me, please! • Does yours look like this? Thousands Hundreds Tens Ones 605 x 4 4 x 6 hundreds 24 hundreds 4 x 5 ones 20 ones <-4 x 5 ones 2 <-4 x 6 hundreds 0 2, 400 2, 420

Lesson 8 Concept Development Problem 2: Model and solve 4 x 605 modeling the repeated addition on the place value chart. • What value is represented on the place value chart? Your turn! Repeat with 5 x 464 • Add the numbers that we wrote in the equation. What is the sum? Thousands Hundreds Tens Ones . 4 x 5 ones 20 ones 4 x 6 hundreds 24 hundreds 2 thousands + 4 hundreds + 2 tens = 2, 420 605 x 4 <-4 x 5 ones <-4 x 6 2 hundreds 0 2, 400 2, 420

Concept Development Lesson 8 Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . • Write the equation 3 × 851. This time, rather than recording 3 groups of 851 to begin, let’s record the partial products as we multiply each unit. • 3 × 1 one is? • Record 3 ones in your place value chart at the top of the ones place.

Concept Development Lesson 8 Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . • 3 times 5 tens? • Record 15 tens in your place value chart as 1 hundred 5 tens a bit lower than the ones so you can see the separate partial product.

Concept Development Lesson 8 Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . • 3 times 8 hundreds? • Record 24 hundreds in your place value chart as 2 thousands 4 hundreds.

Concept Development Lesson 8 Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . • Just as we record the partial products numerically, we draw them. This does not show the connection to addition well, but it does show the partial products well. Can you see three partial products? • Just looking at the place value chart for now, what are the products from smallest to greatest in unit form? 3 ones 1 hundred 5 tens 2 thousands 4 hundreds

Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . • What is the total product recorded both in your equation and in your place value chart? Lesson 8

Concept Development Lesson 8 Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . 5 x 464 • Let’s try another example. Write the equation 5 × 464. Again, let’s record the partial products as we multiply each unit. • 5 x 4 ones is? • Record 20 ones in your place value chart as 2 tens in the tens place. Thousands Hundreds Tens == Ones

Concept Development Lesson 8 Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . 5 x 464 • 5 times 6 tens? • Record 30 tens in your place value chart as 3 hundreds a bit lower than the ones so you can see the separate partial product. Thousands Hundreds Tens == === Ones

Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . 5 x 464 • 5 times 4 hundreds? • Record 20 hundreds in your place value chart as 2 thousands. Thousands Hundreds Tens == == Ones

Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . 5 x 464 Lesson 8 • Just as we record the partial products numerically, we draw them. This does not show the connection to addition well, but it does show the partial products well. Can you see three partial products? • Just looking at the place value chart for now, what are the products from smallest to greatest in unit form? Thousands Hundreds Tens Ones == == 2 thousands 3 hundreds 2 tens

Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart. . 5 x 464 • What is the total product recorded both in your equation and in your place value chart? Thousands Hundreds Tens Ones == 2 tens === == 2, 3 3 hundreds 2 thousands 2 0 464 X 5 20 300 +2, 000 2, 320

Concept Development Lesson 8 Problem 4: Solve 4 x 6, 379 using a partial products drawing on the place value chart. 4 x 6, 379 • Write the equation 4 x 6, 379. Let’s record the partial products as we multiply each unit. • 4 x 9 ones is? • Record 36 ones as 3 tens 6 ones in your place value chart at the top. Ten thousands Thousands Hundreds Tens Ones ===== =

Lesson 8 Concept Development Problem 4: Solve 4 x 6, 379 using a partial products drawing on the place value chart. 4 x 6, 379 • 4 times 7 tens? • Record 28 tens as 2 hundreds 8 tens a bit lower than the 3 tens 6 ones so you can see the separate partial product. Ten thousands Thousands Hundreds == Tens Ones ===== = =====

Concept Development Lesson 8 Problem 4: Solve 4 x 6, 379 using a partial products drawing on the place value chart. 4 x 6, 379 • What is 4 times 3 hundreds? • Record 12 hundreds as 1 thousand 2 hundreds a bit lower than the 2 hundreds 8 tens. Ten thousands Thousands Hundreds Tens Ones === == ===== =

Concept Development Problem 4: Solve 4 x 6, 379 using a partial products drawing on the place value chart. 4 x 6, 379 Lesson 8 • What is 4 times 6 thousands? • Record 24 thousands as 2 ten thousands 4 thousands a bit lower than the 1 thousand 2 hundreds. Ten thousands Thousands Hundreds Tens Ones === == === == ===== =

Concept Development Problem 4: Solve 4 x 6, 379 using a partial products drawing on the place value chart. 4 x 6, 379 Lesson 8 • Can you see four partial products? • Find the total partial products both in your equation and in your place value chart. Notice that you will need to regroup when you find the total of the partial products. Ten thousands Thousands = == ==== 6, 379 Hundreds Tens Ones x 4 = ===== = 3 tens 6 ones 36 == ===== 2 hundreds 8 tens 280 === 1, 200 1 thousand 2 hundreds == 2 ten thousands 4 thousands +24, 000 25, 516

Concept Development Problem 4: Solve 4 x 6, 379 using a partial products drawing on the place value chart. 4 x 6, 379 Lesson 8 • Now let’s regroup then find the total of the partial products. • What is the total? Ten thousands Thousands Work with a = === partner to solve == ===== 3 x 2, 567. === Hundreds Tens = == == ==== 2 5, 5 1 6, 379 Ones x 4 ===== = 36 280 1, 200 +24, 000 6 25, 516

Problem Set 10 Minutes

What pattern did you notice in the answers to Problems 1(a) and 1(b)?

If you needed an estimate for Problem 1(c), how could you round one of the numbers? How close would your estimate be to the exact answer?

Explain to your partner how to solve Problem 2(c). How did you make sure you didn’t make any mistakes when there were so many steps to this problem?

Can you think of a word problem that could be modeled by Problem 2(d)?

Debrief Lesson Objective: Extend the use of place value disks to represent three- and four-digit by one-digit multiplication. • How did the Application Problem connect to today’s lesson? • Compare the two methods of drawing the multiplication on the place value chart.

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