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Using Multiple
Representations
to Introduce
Integers
Sample Pages
Susan Mercer
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
-5
-3
-3
-8
0
moved negative
3 then negative 5
and end at
negative 8
8 negative tiles
–3 + –5
Problem
If you owe 3 dollars
and borrow 5 dollars
you will end up owing
8 dollars
Sea
Level
-3
-5
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
ZERO
-3
ZERO
ZERO
3 pairs and they equal
0 that leaves 3
positive tiles
-3
0
3
moved negative
3 then positive 6
and end at
positive 3
–3 + 6
Problem
If you owe 3 dollars
and get 6 dollars you
will end with 3 dollars
3 above
sea level
+6
–3
Represent Using Money
Sea
Level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 1
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
-4
-3
+5
0
-2
ZERO
Only 2 negative tiles
are left
+5
moved positive 5 then
negative 3 then
negative 4 and end at
negative 2
5 + –3 + –4
Problem
If you have 5 dollars
and spend 3 dollars
then spend another 4
dollars you will end
up owing 2 dollars
-3
+5
-4
Sea
2 below Level
sea level
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
-4
+2
-8
0
-10 -8
10 negative tiles
are left
–8 + 2 + –4
Problem
If you owe 8 dollars
and make 2 dollars
but then borrow 4
more dollars you will
end up owing 10
dollars
Represent Using Money
-4
+2
-8
Sea
Level
10 below
sea level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 2
Word Problems
1)
At 6:00am the temperature was 4˚ below zero. By 3:00pm the
temperature had risen 15˚. What was the temperature at 3:00pm?
Represent the problem using a picture
11 ˚
+ 15˚
0˚
- 4˚
6:00 am
Write a math expression of the problem
- 4 + 15 = 11
-4˚
3:00 pm
Answer the question in a complete sentence.
At 3:00 pm the temperature will be 11˚ above zero.
2)
Sabrina went scuba diving. She descended 20 meters below the surface
and then ascended 7 meters. How far below the surface was she?
Represent the problem using a picture
Write a math expression of the problem
surface
-20 + 7 = -13
-20
+7
-13
-20
Answer the question in a complete sentence.
After ascending 7 meter she was at 13 meters below the surface.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 3
Subtraction of Integers
1-2-3-4 Method
3)
-4
1) Copy the
same
number
8
2) Change
subtraction to
addition
-4
3) Write the
opposite
-12
-8
4) Add the integers
4)
-7
1) Copy the
same
number
-1
2) Change
subtraction to
addition
-7
3) Write the
opposite
-6
1
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 4
Multiplication of Integers
Discover the Rules!
Rule #1
–3 • 4 = – 12
5 • –2 = – 10
–6 • 3 = – 18
2 • –3 = – 6
Study the problems.
What patterns do you notice?
These are multiplication problems.
All answers are negative.
One number is positive and one is negative.
1 • –3 = – 3
–10 • 4 = – 40
Describe the rule and give two examples.
A positive number multiplied by a negative number always
equal a negative answer. So the answer is negative 12 if
negative 3 is multiplied by positive 4 or if positive 3 is
multiplied by negative 4.
Rule #2
–3 • –4 = 12
5 • 2 = 10
–6 • –3 = 18
–2 • –3 = 6
1•3= 3
Study the problems.
What patterns do you notice?
These are multiplication problems.
All answers are positive.
both numbers are positive or both are
negative.
–10 • –4 = 40
Describe the rule and give two examples.
If two positive or two negative numbers are multiplied the
answer is positive. So the answer is positive 12 if positive 3 is
multiplied by positive 4 or if negative 3 is multiplied be negative 4.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 5