standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
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.


aligns: no