1. 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 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

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

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

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

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

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

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

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

9. (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 8 Fluency Multiply Mentally Say the multiplication sentence. 34 x 2 = 68. 34 x 2 = ____ 24 x 3 = ____ 31 x 3 = ____ Say the multiplication sentence. 31 x 3 = 93. 22 x 4 = ____ Say the multiplication sentence. 22 x 4 = 88 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.

10. Lesson 8 Fluency Multiply Using Disks On your boards, draw number disks to show this multiplication sentence. HundredsTensones 32 x1 2 +30 32 1 x ____ ones 1 x ____ tens 1 x 32 Fill in the blanks and write the problem vertically. 2 3

11. Lesson 8 Fluency Multiply Using Disks On your boards, draw number disks to show this multiplication sentence. HundredsTensones 32 x2 4 +60 64 2 x ____ ones 2 x ____ tens 2 x 32 Fill in the blanks and write the problem vertically. 2 3

12. Lesson 8 Fluency Multiply Using Disks On your boards, draw number disks to show this multiplication sentence. HundredsTensones 32 x3 6 +90 96 3 x ____ ones 3 x ____ tens 3 x 32 Fill in the blanks and write the problem vertically. 2 3

13. Lesson 8 Fluency Multiply Using Disks On your boards, draw number disks to show this multiplication sentence. HundredsTensones 32 x4 8 +120 128 4 x ____ ones 4 x ____ tens 4 x 32 Fill in the blanks and write the problem vertically. 2 3

14. Lesson 8 Fluency Multiply Using Disks On your boards, draw number disks to show this multiplication sentence. HundredsTensones 28 x2 16 +40 56 2 x ____ ones 2 x ____ tens 2 x 28 Fill in the blanks and write the problem vertically. 8 2

15. Lesson 8 Fluency Multiply Using Disks On your boards, draw number disks to show this multiplication sentence. HundredsTensones 51 x3 3 +150 153 3 x ____ one 3 x ____ tens 3 x 51 Fill in the blanks and write the problem vertically. 1 5

16. Lesson 8 Application Problem 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?

17. Lesson 8 Concept Development 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. HundredsTensones What is the value in the ones? 2 x 4 ones = 8 ones = 8 2 x 4 ones 8 ones What is the value in the tens? 2 x 2 tens = 4 tens = 40 2 x 2 tens 4 tens What is the value in the hundreds? 2 x 3 hundreds = 6 hundreds = 600 2 x 3 hundreds 6 hundreds

18. Lesson 8 Concept Development 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. HundredsTensones 2 x 4 ones 8 ones 2 x 2 tens 4 tens 2 x 3 hundreds 6 hundreds + + 324 x2 8 40 +600 648 <-2x4 ones <-2x2 tens <-2x3 hundreds Write 2 x 324 vertically on your board. Record the partial products for the ones, tens, and hundreds.

19. Lesson 8 Concept Development Problem 1: Represent 2 x 324 with disks, writing a matching equation, and recording the partial products vertically. HundredsTensones 2 x 4 ones 8 ones 2 x 2 tens 4 tens 2 x 3 hundreds 6 hundreds + + 324 x2 8 40 +600 648 <-2x4 ones <-2x2 tens <-2x3 hundreds 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!

20. 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. HundredsTensones 3 x 1 ones 3 ones 3 x 3 tens 9 tens 3 x 2 hundreds 6 hundreds 231 x3 3 90 +600 693 <-3x1 ones <-3x3 tens <-3x2 hundreds Does your work look like this?

21. Lesson 8 Concept Development 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. 4 x 5 ones 20 ones 4 x 6 hundreds 24 hundreds 605 x4 20 2,400 2,420 <-4x5 ones <-4x6 hundreds ThousandsHundredsTensOnes Tell your partner the value of the digit in each place. Do we need to regroup?

22. Lesson 8 Concept Development Problem 2: Model and solve 4 x 605 modeling the repeated addition on the place value chart. We can change 10 ones for 1 ten twice and 10 hundreds for 1 thousand twice. Show me, please! Does yours look like this? 4 x 5 ones 20 ones 4 x 6 hundreds 24 hundreds 605 x4 20 2,400 2,420 <-4x5 ones <-4x6 hundreds ThousandsHundredsTensOnes

23. Lesson 8 Concept Development Problem 2: Model and solve 4 x 605 modeling the repeated addition on the place value chart. 4 x 5 ones 20 ones 4 x 6 hundreds 24 hundreds 605 x4 20 2,400 2,420 <-4x5 ones <-4x6 hundreds ThousandsHundredsTensOnes What value is represented on the place value chart? 2 thousands + 4 hundreds + 2 tens = 2,420 Add the numbers that we wrote in the equation. What is the sum? Your turn! Repeat with 5 x 464.

24. Lesson 8 Concept Development 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.

25. Lesson 8 Concept Development 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.

26. Lesson 8 Concept Development 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.

27. Lesson 8 Concept Development 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 the 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

28. Lesson 8 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?

29. Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart.. 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. ThousandsHundredsTensOnes  5 x 464

30. Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart.. ThousandsHundredsTensOnes   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. 5 x 464

31. Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart.. ThousandsHundredsTensOnes    5 x 464 5 times 4 hundreds? Record 20 hundreds in your place value chart as 2 thousands.

32. Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart.. ThousandsHundredsTensOnes    5 x 464 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 the three partial products? Just looking at the place value chart for now, what are the products from smallest to greatest in unit form? 2 tens 3 hundreds 2 thousands

33. Lesson 8 Concept Development Problem 3: Solve 3 x 851 using a partial products drawing on the place value chart.. ThousandsHundredsTensOnes    5 x 464 2 tens 3 hundreds 2 thousands What is the total product recorded both in your equation and in your place value chart? 464 X5 20 300 +2,000 2,320 2, 3 2 0

34. Lesson 8 Concept Development Problem 4: Solve 4 x 6,379 using a partial products drawing on the place value chart. 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. 4 x 6,379 Ten thousandsThousandsHundredsTensOnes  

35. Lesson 8 Concept Development Problem 4: Solve 4 x 6,379 using a partial products drawing on the place value chart. 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. 4 x 6,379 Ten thousandsThousandsHundredsTensOnes    

36. Lesson 8 Concept Development Problem 4: Solve 4 x 6,379 using a partial products drawing on the place value chart. What is 4 times 3 hundreds? Record 12 hundreds as 1 thousand 2 hundreds a bit lower than the 2 hundreds 8 tens. 4 x 6,379 Ten thousandsThousandsHundredsTensOnes     

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

38. Lesson 8 Concept Development Problem 4: Solve 4 x 6,379 using a partial products drawing on the place value chart. 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. 4 x 6,379 Ten thousandsThousandsHundredsTensOnes       6,379 x4 36 280 1,200 +24,000 25,516 3 tens 6 ones 2 hundreds 8 tens 1 thousand 2 hundreds 2 ten thousands 4 thousands

39. Lesson 8 Concept Development Problem 4: Solve 4 x 6,379 using a partial products drawing on the place value chart. Now let’s regroup then find the total of the partial products. 4 x 6,379 Ten thousandsThousandsHundredsTensOnes       6,379 x4 36 280 1,200 +24,000 25,516 2 5,5 1 6 What is the total? Work with a partner to solve 3 x 2,567.

40. Problem Set 10 Minutes

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

43. 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?

47. 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?

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

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

51. Exit Ticket Lesson 1