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Multiple Towers

Multiple Towers. 3.2. Jeremy has a collection of 84 baseball cards. He wants to put them into a card holder which has 14 sections. How many cards can fit into each section? Will any cards be left-over?.

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Multiple Towers

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  1. Multiple Towers 3.2

  2. Jeremy has a collection of 84 baseball cards. He wants to put them into a card holder which has 14 sections. How many cards can fit into each section? Will any cards be left-over?

  3. A school bus can carry 55 students. There are 143 students attending a field trip and they will need to arrange for buses to carry them. How many buses will need to be ordered? • 5 • 2 • 8 • 3

  4. Guiding Questions • How can multiples help you find solutions to a division problem?

  5. Multiples can help you solve division problems! • When we skip count by a certain number, we are finding multiples of that number. What are the first few multiples of 21? Multiples of 21 1 x 21 = 21 2 x 21 = 42 3 x 21 = 63 4 x 21 = 84 5 x 21 = 105 6 x 21 = 126 Work with your partner to list some more multiples of 21 in order. As you work, consider the following: Do you see any patterns? How can counting by 20 help you find multiples of 21? Think Ahead: What would 10 x 21 be? How can you use the 10th multiple to make sure your answers are correct?

  6. Multiple Towers • We’re going to count again by 21s, but now when you say a number, I will write it on this strip of paper, which we’re going to call a multiple tower. Later, we will use this list of multiples to help solve multiplication and division problems. . .

  7. ___ x 21 = 210 210 : 10 = ____ • After 210, what’s the next multiple of 21 that ends in zero? How do you know that? How many multiples are in that number? • How can we write a division problem using that answer? A multiplication problem?

  8. 21 420 20 x 21 = 420 20 Why is the 2 over the 2 and not the 4? 10 multiples of 21 is 210. So, we know that it takes 20 multiples of 21 to get to 420. See the 21 in 210 and the 42 in 420? Remember from last week that the “0” on the end simply means we have multiplied that number by 10. 210 is ten times more than 21. And, 420 is ten times more than 42. So, if we are counting 21, 42, 63…then we can multiply each by 10 to get 210, 420, 630, and so on. The pattern doesn’t change! Quick Check: Why is the answer to the above problem 20 and not just 2?

  9. Multiple Tower continued… • We need to circle all the numbers that are 21 multiplied by a multiple of 10. Tell me when we reach one of those “landmark” numbers! If we continue listing multiples until the tower is as tall as I am, what number do you predict we will end up on? Is your prediction a multiple of 21?

  10. 1,029 1,008 987 966 945 924 903 882 861 840 819 798 777 756 735 714 693 672 651 630 609 588 567 546 525 504 483 462 441 420 399 378 357 336 315 294 273 252 231 210 189 168 147 126 105 84 63 42 21 Here, I counted 21s and stopped at 1,029. Without counting from the bottom, figure out how many numbers are in the tower. (How many 21s are in the number 1,029. Can the numbers 210, 420, 630, and 840 help you figure that?

  11. Equations • 49 x 21 = 1,029 • 1,029 : 21 = 49 There are 49 multiples of 21 in the number 1,029. The amount 1,029 can be divided up into 49 groups of 21.

  12. Guiding Questions • How can multiples help you find solutions to a division problem? Answer this in your journal. Then, complete page 49-50 and turn it in.

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