7th Grade Math

GLE 0706.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,

and reasonableness of the solution. Also addresses GLE 0706.4.2, GLE 0706.4.4.

650 Measurement and Proportional Reasoning

Problem-Solving Investigation

Similar Solids

PART A BC

Main Idea Solve problems by making a model.

AYITA: I am decorating the school’s gymnasium for

the spring dance with cubes that will hang from

the ceiling. I have 100 square feet of cardboard.

YOUR MISSION: Make a model to find how much

cardboard will be needed for each cube if the edge

of one cube measures 12 inches.

Understand You know that each cube is 12 inches long. She has 100 square feet of cardboard.

Plan Make a cardboard model of a cube with sides 12 inches long. You will also need

to determine where to put tabs so that all of the edges are glued together.

Solve Start with a cube, then unfold it to show the pattern. Five of the edges do not

need tabs because they are the fold lines.

The remaining 7 edges need a tab. Use _^12 -inch tabs.

7 × 12 in. × _^12 in. 42 in^2 7 tabs

6 × 12 in. × 12 in. + __________864 in^2 6 faces

906 in^2 total area

12 in.

(^12) in.
Convert 906 square inches to square feet.
Then divide the total material by the amount
of material needed for one cube.
906 in^2 × 1 ft
2
_
144 in^2
= 6.3 ft^2 100 ft^2 ÷ 6.3 ft^2 = 15.9
So, Ayita has enough cardboard to make 15 cubes.
Check Make another cube to determine whether all the edges can be glued together
using your model.

1. How can making a model be useful when solving a real-world problem?

Multi-Part

Lesson 2

650_651_C11_PSI_895130.indd 650 12/30/09 4:36 PM