Children’s Thinking Activity Part 1

1. Children’s Thinking Activity Part 1 • 1A. Do you see 5 boxes each with 7 turtles?

2. Children’s Thinking Activity 1 • 1B. Do you see 5, 10, 15, 20, 25, and then 10 more?

3. Children’s Thinking Activity 1 • 1C. • Can you see 5 • 5 + 2 • 5?

4. Children’s Thinking Activity Part 1 • 2A. Do you see 12 bags with 6 candies in each?

5. Children’s Thinking Activity Part 1 • 2B. Do you see 10 bags, with 60, and then 2 more bags 2 • 6 = 12?

6. Children’s Thinking Activity Part 1 • 2C Can you see 10 • 6 + 2 • 6?

7. What skills and concepts did these students know? • BASIC MULTIPLICATION FACTS! • And… (give examples for each)

8. Link the pictorial models • Suppose I want to multiply 3 • 4.

9. Link the pictorial models • Suppose I want to multiply 3 • 40. • This is much harder to draw, but it can be done.

10. 40 3 Link the pictorial models • As the numbers get bigger, it is harder to draw in all the little dots. But the area model will work well: 3 • 40:

11. 15 7 Rectangular Area Model • Let’s look a little closer: Let this be a unit square--that is, a square that measures 1 unit on each side. Then, this is a representation for 7 • 15.

12. 10 + 5 7 70 + 35 Rectangular Area Model • Look at this more closely: • This is the same as 7 • 10 + 7 • 5

13. 10 + 10 + 10 + 2 10 + 4 Rectangular Area Model • This idea works for more: 32 • 14

14. 10 + 10 + 10 + 2 10 + 4 32 • 14 Do you see 4 • 2? 4 • 30? 10 • 2? 10 • 30?

15. Rectangular Model • You try: 46 • 23 Use the base 10 blocks or draw a picture. • Now, can you explain where these products are in the diagram? 46 • 23 = (46 • 20) + (46 • 3) or = (23 • 40) + (23 • 6)

16. The area model and the standard multiplication algorithm

17. 34 X 56

18. 34 X 56

19. 34 X 56

20. Compare models • Can you explain how this is related to the lattice multiplication model you did for Exploration 3.13? • Can you explain how this rectangular model is related to the standard multiplication algorithm? • Can you explain how this rectangular model is related to the four students’ models?

21. 25 • 4 + 4 • 4 Ryshawn and Nicholas 20 • 4 + 9 • 4

22. Multiplication-the area model • How could Jemea’s strategy be represented using the rectangular area model?

23. Jemea 30 • 12 - 12

24. Thomas 17 • 36 = ((17 • 10) • 3)+ (6 • 10) + (6 • 7)

25. Understanding FOIL

26. Explain why… • Can you show, using pictures or base-10 blocks, why 3 • 14 = 14 • 3? • Can you show or explain why? Give a reason? Draw a picture? • 2 • (3 • 14) = (2 • 3) • 14? • 2 • (3 • 14) = (3 • 2) • 14? • 2 • (3 • 14) = 3 • (2 • 14) • 2 • (3 • 14) = 14 • (2 • 3) • 2 • (3 • 14) = 3 • 14 + 3 • 14 • 2 • (3 • 14) ≠ 2 • 3 + 2 • 14

27. Ellen begins the following problem. 46X 37 42 Is Ellen correct or incorrect? Explain why.

28. 46 46X 37X 37 42 42 280 46X 37 2842 What is 280? Is it 7 • 4 or 7 • 40? What does the placeholder mean?

29. Where is the error? 46 46X 37X 37 42 42 280 46X 37 2842 What is 280? Is it 7 • 4 or 7 • 40? What does the placeholder mean?