Topic 14: Algebraic Expressions
for use after Bits and Pieces III
Investigation 5
Ben spends 30 minutes on homework daily for each subject. The minutes
he spends doing homework is the number of subjects he has multiplied by
30. The variable s stands for the number of subjects.
Subjects
with
homework
0
Minutes
doing
homework
0 30
Total
homework
time
0
1
1 30
30
2
2 30
60
s
s 30
30s
The expression 30s is an algebraic expression. An algebraic expression can
include numbers, variables, and operation symbols. In this expression, 30 is
constant because the number of minutes per subject does not change. The
variable is s because it changes.
You can evaluate the algebraic expression 30s by substituting a given
number for the variable s.
Problem 14.1
A. 1. Ben’s older sister, Emma, spends 40 minutes on homework daily for
each subject. Write an algebraic expression to represent the time
that Emma spends on homework.
2. Evaluate your expression for 3 subjects.
3. On Monday, Ben has homework in 4 subjects, and Emma has
homework in 3 subjects. Who spends more time doing homework
that afternoon? Explain.
B. On Tuesday, Ben has homework in 5 of his subjects.
1. How much time will Ben need to spend on homework?
2. Ben spends an unknown number of minutes before dinner working
on his homework. Use an algebraic expression to represent the
number of minutes Ben will need to spend after dinner to complete
his homework.
3. What does your variable in question 2 represent?
4. Are you able to evaluate the expression? Explain.
An expression may have more than one variable.To evaluate an expression
with more than one variable, replace each variable with its value.Then simplify.
Problem 14.2
A. 1. A fruit bowl contains apples and bananas. Write a variable
expression for the number of pieces of fruit in the bowl. Use a to
represent the number of apples and b to represent the number of
bananas.
2. Evaluate your expression for a = 2 and b = 3.
3. Evaluate your expression for a = 5 and b = 4.
B. 1. Write a word description that could describe 4w + 3d.
2. Evaluate the expression for w = 5 and d = 3.
1
3. Evaluate the expression for w = 2 and d = 5.
EXERCISES
Write an algebraic expression for each situation.
1. the cost of x apples at $0.49 each
2. the number of hits a 0.306 batter gets in b times at bat
3. the number of minutes it takes to read p pages at 10 minutes per page
4. the money left on a $20 gift card after spending y dollars
5. the distance d traveled over h hours
Evaluate each algebraic expression for a = 12 and b = 3.
6. a - 2
7. 5a
3a
8. a + b
3
9. 2b
4
1
Evaluate each algebraic expression for d = 4, e = 9, and f 2.
10. d + f
11. de
12. f - e
13. 4d + 2f
Write a word description that could describe each algebraic expression.
14. a + 24
15. 365 - d
16. 7w
m
17. 55
18. At a craft store, each package of beads costs $3.95.
a. Write an algebraic expression for the cost for p packages
of beads.
b. Amy gives the sales clerk $20 for p packages of beads. Write an
algebraic expression to represent Amy’s change.
c. What is the greatest number of packages that Amy can buy
with $20.00?
At a Glance
Topic 14: Algebraic Expressions
PACING 1 days
Mathematical Goals
• Substitute values for variables and evaluate algebraic expressions.
• Describe, define and provide examples of variables and expressions with a
missing value based on real-world and mathematical problems.
Guided Instruction
Read aloud with the students, the introductory paragraph. Call attention to
the table and the introduction of the variable s. Ensure that students
understand that a variable represents a number. The variable s represents
the number of subjects. The variable s does not represent subjects. This is a
common misconception for students.
Before Problem 14.1 A, ask:
• Why would you want to write an expression with a variable? (A variable
can help you express an idea or situation that can change.)
• Suppose you wanted to represent 3 telephone calls per day. What
expression would you write to represent the number of calls in d days?
(3d)
• Evaluate your expression for 5 days. (15)
• Evaluate your expression for 30 days. (90)
For Problem 14.1 A, have students set up a table of values for Emma like
the table provided for Ben. Ask:
• When you compare the table for Ben to the table for Emma, how often
did they spend the same amount of total time doing homework? (every
multiple of 120 minutes; 120 minutes, 240 minutes, 360 minutes, etc.)
After Problem 14.1 B, ask:
• Why are you unable to evaluate this expression? (Because we do not
know how long Ben spent on his homework before dinner; We do not
know what the value of the variable is.)
You will find additional work on algebraic expressions in the grade 7 unit
Variables and Patterns.
Vocabulary
•
•
•
•
algebraic expression
constant
variable
evaluate
ACE Assignment Guide
for Topic 14
Core 1-18
Answers to Topic 14
Problem 14.1
A. 1. 40s
Exercises
1. 0.49x
2. 120 minutes
2. 0.306b
3. They spend the same amount of time on
3. 10p
their homework.
30(4) = 40(3).
B. 1. 30(5) = 150. He will spend 150 minutes
doing homework.
2. 150 - x
3. x represents the number of minutes Ben
spends doing his homework before dinner.
4. You cannot evaluate this expression
because you do not know the value of the
variable.
Problem 14.2
A. 1. a + b
2. 5
4. dh
5. 20 – y
6. 10
7. 60
8. 15
9. 6
10. 1 1
4
1
11.
3
12. 1
18
13. 4
14. Answers may vary. Sample: The number of
bottles of water you have when you have a
individual bottles and one unopened case.
3. 9
B. 1. Answers may vary. Sample: Abigail earns
$4 for each window that she washes and $3
for each room that she dusts.
2. 4(5) + 3(3) = $29
3. 4a 1 b + 3(5) = $17
2
15. Answers may vary. Sample: The number of
days left in a year after d days have passed.
16. Answers may vary. Sample: The number of
days in w weeks.
17. Answers may vary. Sample: The time it takes
to travel m miles at 55 mi/hr.
18. a. 3.95p
b. 20 – 3.95p
c. 5 packages; 20 – 3.95(5)
= 19.75.