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Week 7

*Don’t forget to sign in!*. Week 7. What does the distribution property of multiplication mean? That is, what does 19 • 73 = (16 + 2 + 1) • 73 = 16 • 73 + 2 • 73 + 1 • 73

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Week 7

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  1. *Don’t forget to sign in!* Week 7 What does the distribution property of multiplication mean? That is, what does 19 • 73 = (16 + 2 + 1) • 73 = 16 • 73 + 2 • 73 + 1 • 73 Tell us about multiplication? Write a sentence or two explanation of what distribution means (mathematically) for this example.

  2. Agenda • D2L Comment • Finish Exploration 3.13 • Class Notes • Videos • Area models • Assign homework

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

  4. Link the pictorial models • Suppose I want to multiply 3 • 40. • This is much harder to draw, but it can be done. Do you see 3 • 40 = ?

  5. 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:

  6. 15 7 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.

  7. 10 + 5 7 70 + 35 Area Model • Look at this more closely: • This is the same as 7 • 10 + 7 • 5 • 7 • 10 and 7 • 5 are partial products.

  8. 10 + 10 + 10 + 2 10 + 4 Area Model • This idea works for more: 32 • 14 • Identify the partial products:

  9. 10 + 10 + 10 + 2 10 + 4 32 • 14 • Do you see 4 • 2? 4 • 30? 10 • 2? 10 • 30?Add the partial products.

  10. Area 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)

  11. 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 area model is related to the standard multiplication algorithm? • Can you explain how this area model is related to the four students’ models from the video on Friday?

  12. 25 • 4 + 4 • 4 Ryshawn and Nicholas 20 • 4 + 9 • 4

  13. Jemea 30 • 12 - 12

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

  15. Homework • See course webpage for homework. • For Wednesday, print off division worksheet and bring to class.

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