Investigating Inequalities:
Choose roles: Record each group member’s name next to their role:
•
Announcer: ________________________________
•
Recorder: _________________________________
•
Walker A: _________________________________
•
Walker B: _________________________________
Set-up: use the number cards to construct a number line on the floor.
Conduct the investigation:
• Walkers stand at starting numbers (see table below).
• Recorder confers with group to determine appropriate inequality
symbol comparing Walker positions, and records symbol in the table.
• Announcer calls out operation and both walkers calculate their new
numbers and walk to their new locations on the number line.
• Recorder records their new positions and again confers with group to
determine appropriate inequality symbol. Be sure to write a true
inequality statement.
• Repeat until table is complete, then answer the questions that follow.
Operation
Walker A’s
Position
Starting number
2
Inequality
Symbol
Walker B’s
Position
Add 2
Subtract 3
Add −2
Subtract −4
Multiply by 2
Subtract 7
Multiply by −3
Add 5
Divide by −4
Subtract 2
Multiply by −1
Use your completed table to answer
the questions on the next page.
4
1. What happens to the walkers’ relative positions on the number line
when the operation adds or subtracts a positive number? A negative
number? Does anything happen to the direction of the inequality
symbol?
2. What happens to the walkers’ relative positions on the number line
when the operation multiplies or divides by a positive number? Does
anything happen to the inequality symbol?
3. What happens to the walkers’ relative positions on the number line
when the operation multiplies or divides by a negative number? Does
the inequality symbol change directions?
4. Which operations on an inequality reverse the inequality symbol? Does
it make any difference which numbers you use? Consider fractions and
decimals as well as integers.
5. Check your findings about the effects of adding, subtracting,
multiplying, and dividing by the same number on both sides of an
inequality by creating your own table of operations and walkers’
positions:
Engaging Mathematics:
Algebra I TEKS-Based Activities
Student Name: ________________________________________ Date: ________________
True or Not?
Substitute each value in the table into the inequality at the top. If the resulting inequality is true,
shade the box with T. If resulting inequality is false, shade the box with F.
5m  10
a20
m  5
T
F
a  5
T
F
m  4
T
F
a  4
T
F
m  3
T
F
a  3
T
F
m  2
T
F
a  2
T
F
m  1
T
F
a  1
T
F
m0
T
F
a0
T
F
m 1
T
F
a 1
T
F
m2
T
F
a2
T
F
m3
T
F
a3
T
F
m4
T
F
a4
T
F
m5
T
F
a5
T
F
On each number line below, place dots on the values that made the inequality true.
5m  10
a20
Communicating About Mathematics
In the first table, how would values of m between 2 and 3 be shaded? Why?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
© Region 4 Education Service Center
All rights reserved.
211
Engaging Mathematics:
Algebra I TEKS-Based Activities
Student Name: ________________________________________ Date: ________________
True or False?
Substitute each value in the table into the inequality at the top. If the resulting inequality is true,
shade the box with T. If resulting inequality is false, shade the box with F.
3 x  9
2y   6
x  5
T
F
y  5
T
F
x  4
T
F
y  4
T
F
x  3
T
F
y  3
T
F
x  2
T
F
y  2
T
F
x  1
T
F
y  1
T
F
x 0
T
F
y 0
T
F
x 1
T
F
y 1
T
F
x2
T
F
y 2
T
F
x 3
T
F
y 3
T
F
x4
T
F
y 4
T
F
x 5
T
F
y 5
T
F
Transfer your answer to the number line below by placing dots on the values that made the
inequality true.
–3x  9
–2y  –6
Communicating About Mathematics
Write a sentence describing the values that make each inequality true.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
© Region 4 Education Service Center
All rights reserved.
213
Engaging Mathematics:
Algebra I TEKS-Based Activities
Student Name: ________________________________________ Date: ________________
Mr. Willett’s Purchase
Mr. Willett decided to buy a suit and a pair of shoes. He wants to spend less than $350. The
price of the suit is 3 times the price of the shoes.
Use the table below to find 3 possible purchases Mr. Willett could buy. In addition, find at least
1 purchase that Mr. Willett would not buy.
Cost of Shoes
Cost of Suit
Total Cost
Less than $350?
yes
no
yes
no
yes
no
yes
no
Communicating About Mathematics
How could you determine the purchase he would not make?
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
© Region 4 Education Service Center
All rights reserved
209