Page 52 - Algebra 1

Exploration Using Unit Analysis
If a measure of length changes, then the unit analysis occurs in one dimension. If a measure of area changes, the units for the dimensions of both length and width must change.
Draw two congruent squares with side lengths of 3 inches on a sheet of paper. Label the sides of the first square 1 yard. Divide both the length and width of the second square into 3 equal sections. This will divide the square into 9 congruent smaller squares. Label the sides of the second square 3 feet.
1 yd 3 ft
1 yd
3 ft
a. What is the area of the first square? Show your calculation.
b. What is the area of the second square? Show your calculation.
c. Write two unit ratios for converting between feet and yards.
d. Which unit ratio should be used for converting yards to feet? Explain your choice.
e. Justify Use a unit ratio to convert the area of the first square into square feet. Show your calculation.
f. Write Why is it necessary to multiply by the unit ratio twice to convert square yards to square feet?
Extend the example of the area of squares to the volume of cubes. Draw two cubes, one with dimensions of 1 yard and one with dimensions of 3 feet.
1 yd
3 ft
1 yd
3 ft
Math Reasoning
Write How could a single unit ratio be used to perform the area conversion?
g. What is the volume of the first cube? Show your calculation.
h. What is the volume of the second cube? Show your calculation.
i. Justify Use a unit ratio to convert the volume of the first cube into cubic feet. Show your calculation.
j. Write Why is it necessary to multiply by the unit ratio three times to convert cubic yards to cubic feet?
Lesson 8 37