4.4 The Distributive Property CA-77 Class Activity 41 Critique Multiplication St

Question

4.4 The Distributive Property CA-77 Class Activity 41 Critique Multiplication Strategies CCSS CCSS SMP3 1. Kylie has an idea for how to calculate 23-23. She says Twenty times 20 is 400, and 3 times 3 is 9, so 23.23 should be 400 plus 9, which is 409. Is Kylie's method valid? If not, how could just start over in a different way: work with Kvlies idea. Use the large square below consists of 23 rows with 23 small squares in each row, to help you explain your answer. you modify her work to make it correct? Don' 2. Annie is working on the multiplication problem 19-21. She says that 19-21 should equal 20 20 because 19 is one less than 20 and 21 is one more than 20. This is a wonderful idea, but is Annie correct? If not, use the diagram below to help you explain to Annie why not. There are 20 rows of dots with 21 dots in each row. Mary is working on the multiplication problem 19.21. She says that 19-21 is 21 less than 20-21, and 20-21 is 20 more than 20-20, which she knows is 400. Mary thinks this ought to help her calculate 19.21, but she can't quite figure it out. Discuss Mary's idea in detail. Can you make her idea work? 3.

Explanation / Answer

1) no, Kylie method is not valid.

in 20.20, 20 is added to itself 20 times i.e 20+20+20+..............twenty times

in block form it will be shown as fig -1 below. when you count all boxes it will be 400

in 3.3, 3 is added to itself 3 times i.e 3+3+3

in boxes form it can be seen as figure-2 as below.when you counted all the boxes it will be 9

so,similarly in 23.23 , 23 is added to itself 23 times i.e 23+23+23+.................twenty three times

in boxes form it can be shown as figure - 3 given below.when you will count all the boxes it will be 529

now it is clear by adding figure - 1 & figure - 2 we will never get figure - 3.

so, for get 23.23 we have to add 23 to itself 23 times which will give us the answer 529.

2) no Annie work is not right

19.21 means 21 is added to itself 19 times. i.e 21+21+21.........nineteen times

while 20.20 means 20 is added to itself 20 times.i.e 20+20+20........twenty times

we can see that both figure is not same so Annie logarithm is wrong.

3) Mary is right.

1st case

because 19.21 = 21 is added to itself 19 times i.e 21+21+21........nineteen times

20.21 = 21+21+21......twenty times.

so, diffrence in both is 21

2nd case

20.21 = 20+20+20........twenty one times

20.20 = 20+20+20......... twenty times

so,diffrence between both is 20.

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