These two tasks are from Tools for NC Teachers. Students consider a house and the volume of specific rooms. This is remixable.

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There are four office buildings on Pickney Street. The blue building has 22 rooms on each of the 14 floors. Compared to the blue building, the white building has half as many rooms on each floor and half as many floors. Compared to the white building, the red building has double the number of floors and the same number of rooms on each floor. Compared to the blue building, the gray building has twice as many floors and half as many rooms on each floor.

Part 1:

Write an expression for each building. Do not worry about solving the expressions.

Part 2:

Write mathematical comparisons that compare each of the following:

a)     The blue building has _____ as many rooms as the white building.

b)    The red building has ____ as many rooms as the blue building.

c)     The red building has ____ as many rooms as the white building.

d)    The gray building has ___ as many rooms as the blue building.

e)     The white building has ___ as many rooms as the gray building.

f)     The red building has ____ as many rooms as the gray building.

Part 3:

For each comparison above, explain your reasoning and how you know you are correct.