Question

A. Determine whether the descriptions of the figure in Step 4 and Step 15 are true or false.

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Step 1 Step 2
Step 3
Step 4 is a 5-by-5 array of squares with the lower left corner square moved to the upper right corner. Select Choice
Step 15 is a 15-by-15 array of squares with the lower left corner square moved to the upper right corner. Select Choice
b. How many small squares will there be in each of these steps?
Step 4: Select Choice
Step 15: Select Choice
c. Does the equation y = n²-1 represent the relationship between the step number, and the number of small squares, y, in each step? Select Choice
d. Complete the following to explain how the equation that represents the relationship between n and y relates to the pattern.
If you move the small square in the upper right corner to the lower left comer, it makes an Select Choice
array of small squares, which gives ².

Answer 1

Explanation:

a)

with step 1 to 3 we see that the numbers of squares serving the length of the sidelines is following the step number 1:1.

so, step 1 has a side length of 1 square.

step 2 has a side length of 2 squares.

step 3 has a side length of 3 squares.

so, we expect step 4 to have a side length of 4 squares.

but the first statement says "5-by-5", so, the side length is 5.

therefore, this statement is false.

and yes, we expect step 15 to have a side length of 15.

and the shift of the single square from the bottom left to the top right is also correct.

therefore, the statement is true.

b)

step 4 = 4×4 = 16 squares

step 15 = 15×15 = 225 squares

c)

no.

just look at step 1.

y = 1² - 1 = 1 - 1 = 0.

but I can clearly see that there is 1 square.

d)

it makes an n×n array. which is the same as n².