Preserve or Reverse?
Each table group will visit four stations to explore what happens to an inequality when
different operations are applied to both numbers. Last week, we wrote a generalization that
said inequalities and equations are solved the same way, it’s just that equations have one
answer and inequalities have many.
When solving an equation, we think of the equal sign as the middle of a scale, and that both
sides have the same exact value. So as long as we do the same thing to both sides, the
equation stays “balanced” or equal.
Ex)
10 + 1 + 4 = 2 + 13
10 + 1 + 4 -3 = 2 + 13 -3
12 = 12 
15 = 3(5)
15 ÷ 3 = 3(5) ÷ 3
5=5
Let’s test our theory about solving inequalities today!
At each station:




Roll both dice and record in your table.
Choose an inequality that describes the two numbers your rolled (> or <?)
Apply the operation given to both numbers and record your work.
Decide whether the operation preserved (stayed true) your inequality, or
reversed (switched) your inequality.
You will have 7 minutes to explore as a group, individually recording your work.
When the timer goes off, you will write down any patterns you noticed and the
evidence to justify it.
Station 1
Die 1 Inequality Die 2 Operation
New Inequality
Inequality symbol
preserved or reverse?
Ex)
-3
<
5
Add 2
Add -3
Subtract 2
Subtract -1
Add 1
Subtract -4
-3 + 2 < 5 + 2
-1 < 7
Preserved
Station 2
Die 1 Inequality Die 2 Operation
Ex)
-3
<
4
Multiply
by -1
Multiply
by -1
Multiply
by -1
Multiply
by -1
Multiply
by -1
Multiply
by -1
New Inequality
Inequality symbol
preserved or reverse?
(-1)(-3) < (-1)(4)
3 < -4? (no!)
3>4
Reversed
Station 3
Die 1 Inequality Die 2 Operation
𝟏
Ex)
-2
New Inequality
>
-4
𝟐
Multiply
by 2
Divide by 2
Divide by
Multiply
by 3
Multiply
by -1
𝟏
(𝟐)(-2) < (𝟐)(-4)
-1 < -2? (yes!)
3>4
Multiply
𝟏
by
𝟏
𝟐
Inequality symbol
preserved or reverse?
Preserved