A PROBLEM SOLVING PLAN USING MODELS
VERBAL
MODEL
Ask yourself what you need to know to solve the problem. Then
write a verbal model that will give you what you need to know.
LABELS
Assign labels to each part of your verbal model.
Use the labels to write an algebraic model based on your verbal
model.
ALGEBRAIC
MODEL
SOLVE
Solve the algebraic model and answer the original question.
CHECK
Check that your answer is reasonable.
EXAMPLE
2
Write an Algebraic Model
A football field is about 53 yards wide and 120 yards long. A soccer field has
the same area, but is 60 yards wide. How long is the soccer field?
STUDY TIP
Sometimes a diagram
can help you see what
you know and what
you need to find to
solve the problem.
Solution
Write a verbal model showing that the area (width length) of the soccer field
equals the area (width length) of the football field.
10 20 30 40 50 40 30 20 10
Student Help
53 yd
60 yd
10 20 30 40 50 40 30 20 10
120 yd
x yd
VERBAL
MODEL
Width of p Length of Width of p Length of
soccer field soccer field
football field football field
LABELS
Width of soccer field 60
(yards)
Length of soccer field x
(yards)
Width of football field 53
(yards)
Length of football field 120
(yards)
ALGEBRAIC
MODEL
60 x 53 120
60 x 6360
x 106
ANSWER 䊳
Write algebraic model.
Simplify.
Solve with mental math. (60 p 106 6360)
The soccer field is 106 yards long.
Write an Algebraic Model
1. You want two rectangular gardens to have equal areas. The first garden is
5 meters by 16 meters. The second garden is 8 meters wide. How long should
the second garden be? Apply the problem solving plan to find the answer.
1.6
A Problem Solving Plan Using Models
37