GPS
Guided Problem Solving
Guided Problem Solving
Understanding
Word Problems
FOR USE WITH PAGE 548, EXERCISE 23
Understanding Word Problems Read the problem below. Let Jake’s thinking
guide you through the solution. Check your understanding with the exercises at the
bottom of the page.
Guided Instruction
Students are shown the thinking
process alongside the
computations for solving a
word problem.
Satellites One of the smallest space satellites ever developed has the shape of
a pyramid. Each of the four faces of the pyramid is an equilateral triangle with
sides about 13 cm long. What is the area of one equilateral triangular face of
the satellite? Round your answer to the nearest whole number.
English Language Learners ELL
Students may not be familiar with
the terms pyramid and face. A
pyramid is a three-dimensional
solid whose flat surfaces, called
faces, are triangles. One face,
called the base, can be any
polygon. In this case, all faces are
congruent equilateral triangles.
Students study three-dimensional
figures in Chapter 11.
What Jake Thinks
What Jake Writes
I’ll make a sketch.
First, the pyramid. Then a face.
Each equilateral-triangle face has 13-cm sides.
I have to find the area. I’ll use red for an altitude.
Special Needs
L1
That gives me half of an equilateral triangle, or a
30°-60°-90° triangle.
Ask: Why is the shorter leg 6.5 cm?
The shorter leg is half of 13.
6.5 !3
The short leg of the triangle is 6.5 cm.
Math Tip
The altitude is !3 times the short leg.
A pyramid with four faces that
are equilateral triangles is called a
tetrahedron. It is one of the five
Platonic solids and Plato
associated it the element of fire.
13 cm
6.5
The area is 12 base times height.
A≠
1
bh
2
Have students model the foursided pyramid of equilateral
triangles using modeling clay.
I’ll use a calculator.
A≠
1
⭈ 13 ⭈ 6.5"3
2
Error Prevention!
I have to round to the nearest whole number.
Tactile Learners
In Exercise 5, some students will
replace 13 with 13k, but fail to
replace 6.5 with 6.5k. Ask: If each
side is 13k, how does the short
leg of the 30°-60°-90° triangle
change. it becomes 6.5k
A N 73.18 cm2
A N 73 cm2
EXERCISES
What would be the area of a face of the satellite for each side length given?
1. 6.5 cm
2. 26 cm
3. 1.3 m
4. 2.6 m
292.7 cm2
7318 m2
29,272 m2
18.3 cm2
5. If you change the length of each side of the satellite by a factor k to 13k cm,
how does the area of a face change? changes by a factor k2
552
552
Guided Problem Solving
Understanding Word Problems