Division. Reverse Box Method

Transcription

1 Division Reverse Box Method

2 Why do we use the reverse box method? The box method of multiplication is used because it develops a strong conceptual understanding of multiplication! If you have not read about this strategy, please take a moment to do so. It directly relates to this method of division. These methods build conceptual understanding; the traditional method does not build conceptual understanding. The box method is based on the distributive property of multiplication, which is a very important concept. Research supports teaching students conceptually before teaching the algorithm. Students will learn the traditional algorithm for both multiplication and division in fifth grade.

3 In the last few days, we have looked at arrays, and you have found the division equation. What if we did not have the array? How much of the equation would you need? What strategies do you suggest? Talk with your group, and be prepared to share your ideas with the class.

4 Consider this problem: = Can you build this array only knowing the dividend and divisor? Why or why not? How would you find the quotient using an array? Where would each part of the equation be represented in your model? With your group, build the array.

5 N: First, we took out 115 blocks. J: We know we have to have 5 rows. (That is like 5 groups.) N: After we put 2 tens in each row, we had one ten left. We exchanged it for 10 ones. R: Then we put 3 ones in each row. N: There were no blocks left, so there is no remainder

6 115 5 = 23 (no remainder)

7 Consider this problem: = Can you build this array only knowing the dividend and divisor? Why or why not? How would you find the quotient using an array? Where would each part of the equation be represented in your model? With your group, build the array.

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9 What if we did not have the base 10 blocks? Can you draw an array without having blocks? When you have done this in the past?

10 Can we use the box method of multiplication to divide? How would this work? What parts of the picture would we know? What parts would we have to find?

11 Let s use this with the equations we just solved = 5 Where does the 115 need to be? How can we do this?

12 Let s use this with the equations we just solved = 5 As much of the dividend as possible should be in the array. Are there times when the dividend will not all be in the array? If so, when?

13 Let s use this with the equations we just solved = How can we determine how much more is needed in the array?

14 Let s use this with the equations we just solved = Can we add 10 more to each row?

15 Let s use this with the equations we just solved = There are 15 left. How many more can we add to each row if we have 5 rows?

16 Let s use this with the equations we just solved = Is the entire dividend part of the array? What does this mean? What is the quotient?

17 Let s use this with the equations we just solved = 23 r

18 Let s use this with the equations we just solved = 4 Where does the 212 need to be? How can we do this?

19 To find the quotient, we will model this using 3 as the number of groups. (We do not want to model groups of 3!) What will the other side represent?? This side will represent the number. 3 This side will represent the number of groups. The numbers inside the box represent the total amount placed in groups. This should be if there is not a remainder.

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48 1,226 r 1

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