The document provides an explanation and examples of the partial products algorithm for multiplication. It explains that each factor is thought of as a sum of ones, tens, hundreds, etc. and each part is multiplied by each part of the other factor before adding the results. It includes step-by-step worked examples of multiplying numbers using the partial products method. It also includes a "Who Wants To Be A Millionaire" style math game testing skills with place value, algorithms, and multiplication.

1. Everyday Math and Algorithms A Fun Review!

2. Partial Products Algorithm for Multiplication

3. In the partial-product multiplication algorithm, each factor is thought of as a sum of ones, tens, hundreds, and so on. For example, in 67 x 53, think of 67 as 60 + 7, and 53 as 50 + 3. Then each part of one factor is multiplied by each part of the other factor, and all of the resulting partial products are added together. What is partial-product multiplication?

4. Calculate 50 X 60 6 7 X 5 3 Calculate 50 X 7 3,000 350 180 21 Calculate 3 X 60 Calculate 3 X 7 Add the results 3,551 To find 67 x 53, think of 67 as 60 + 7 and 53 as 50 + 3. Then multiply each part of one sum by each part of the other, and add the results. +

5. Calculate 10 X 20 1 4 X 2 3 Calculate 20 X 4 200 80 30 12 Calculate 3 X 10 Calculate 3 X 4 Add the results 322 Let’s try another one. +

6. Calculate 30 X 70 3 8 X 7 9 Calculate 70 X 8 2,100 560 270 72 Calculate 9 X 30 Calculate 9 X 8 Add the results Do this one on your own. 3,002 Let’s see if you’re right. +

7. Now for some fun...

8. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Welcome to Who Wants to be a Millionaire

9. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

10. A: Ones C: Hundreds B: Tens D: Thousands 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Our number system is based on a simple pattern of tens. Each place has ten times the value of the place to its right. Place value tells you how much each digit stands for. In the number 546,872, the 8 is in the ______ place.

11. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

12. A: 200 + 400 + 30 + 7 C: 2,000 x 400 x 30 x 7 B: 2,000 + 403 + 7 D: 2,000 + 400 + 30 + 7 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 There are many ways to write the same whole number. How is 2,437 written in expanded form?

13. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

14. A: Partial-product multiplication C: Area model B: Traditional multiplication D: Complete number strategy 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 In this multiplication algorithm, each factor is thought of as a sum of ones, tens, hundreds, and so on. Then each part of one factor is multiplied by each part of the other factor, and all of the resulting partial products are added together.

15. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

16. A: An even number C: A method for solving a problem B: A fraction D: A pet pig 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 What is an “algorithm”?

17. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

18. A: 2,000 C: 200 B: 20 D: 2 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 How much is the 2 worth in 29?

19. Congratulations! You’ve Reached the $1,000 Milestone! Congratulations! Congratulations!

20. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

21. A: 160 C: 210 B: 250 D: 137 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Using the partial-products method of multiplication, what is 32 x 5? Hint: Add 30 x 5 and 2 x 5.

22. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

23. A: 150 C: 1,800 B: 800 D: 1,500 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 To be able to use the partial-products method, you must be able to multiply by tens. What is 30 x 50? Hint: Multiply 3 x 5 and add the zeros.

24. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

25. A: 400 C: 407 B: 40 D: 4 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 How much is the 4 worth in 471?

26. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

27. A: 920 C: 720 B: 942 D: 845 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Using the partial-products method of multiplication, what is 471 x 2? Hint: Add 400 x 2, 70 x 2, and 1 x 2.

28. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

29. A: 4,000 x 500 x 10 x 0 C: 400 + 500 + 10 + 0 B: 4,000 + 500 + 10 + 0 D: 1,000 + 500 + 40 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 How would you write 4,510 in expanded notation??

30. Congratulations! You’ve Reached the $32,000 Milestone! Congratulations! Congratulations!

31. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

32. A: 5,355 C: 9,600 B: 4,972 D: 1,068 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Using the partial-products method of multiplication, what is 89 x 12? Hint: Add 80 x 10, 80 x 2, 9 x 10, and 9 x 2.

33. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

34. A: 50 C: 13 B: 40 D: 200 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 48 x 56 (40 x 50) 2,000 (40 x 6) 240 ( __ x 8) 400 (6 x 8) + 48 2,688

35. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

36. A: 5,672,390 C: 1 B: 0 D: 100 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 5,672,390 x 0 = ?

37. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

38. A: I don’t like candy C: I like candy a lot B: I like candy a little D: I LOVE CANDY 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 How much do you like candy?

39. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100

40. A: Mrs. Agee C: Mrs. Agee B: Mrs. Agee D: Mrs. Agee 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Who is your favorite teacher?

41. YOU WIN $1 MILLION DOLLARS!