Kylie has an idea for how to calculate 23 times 23. She says, Twenty times 20 is

Question

Kylie has an idea for how to calculate 23 times 23. She says, Twenty times 20 is 400, and 3 times 3 is 9; so 23 times 23 should be 400 plus 9, which is 409. Is Kylie's method valid? If not, how could you modify her work to make it correct? Don't just start over in a different way; work with Kylie's idea. Use the large square below, which consists of 23 rows with 23 small squares in each row, to help you explain your answer. Annie is working on the multiplication problem 19 times 21. She says that 19 times 21 should equal 20 times 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 times 21. She says that 19 times 21 less than 20 times 21, and 20 times 21 is 20 more than 20 times 20, which she knows is 400. Mary thinks this ought to help her calculate 19 times 21, but she can't quite figure it out. Discuss Mary's idea in detail. Can you make her explanation work?

Explanation / Answer

1) 23 * 23

She is using 20 * 20 + 3*3

instead she should use:

(20+3) (20+3)

Here, distributive property can be used to calculate this:

This will give:

20 * (20+3) + 3 * (20+3)

400 + 60 + 60 + 9

which gives 529

To calculate the number of squares here,

we need to multiply number of rows * number of columns

23 * 23 = 529

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