standard_description: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Problem 1
The three shapes below represent the bases of three different prisms. Each grid is 1 unit
$$\times$$
1 unit, and each prism has a height of 10 units.
[IMG]
What is the volume of each prism?
Problem 2
A triangular prism has the measurements shown below.
[IMG]
If the volume of the prism is 270 cubic inches, what is the height of the prism?
Problem 3
Investigate the relationship between the volume of a prism and a pyramid with the same base.
a.   Watch the YouTube video
Volume of Three Square Pyramids Fitting into a Cube
.
b.   What is the relationship between the volume of the prism and the volume of the pyramid?
c.   What formula can you use to find the volume of a pyramid?
d.   Find the volume of a rectangular pyramid with height 5 cm and base measuring 8 cm × 6 cm.


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