Download Integers - Super Math Units

Using Multiple
Representations
to Introduce
Integers
Answer Key
Susan Mercer
Opposites
Find the pair of opposites:
up
right
empty
white
have
backwards
hot
cold
no
full
left
negative
loss
down
black
south
forwards
owe
north
gain
positive
yes
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 1
Integers - Money
During this unit you are going to use integers to represent situations
that and problems include opposites.
For example:
having $5
is represented by +5
owing $5
is represented by –5
going up 4 steps
is represented by +4
going down 4 steps
is represented by –4
gain $12
is represented by +12
loss $12
is represented by –12
Use integers to represent the following situations:
have $10
_+10_
owe $23
_–23_
up 5 steps
_+5_
down 13 steps
_–13_
loss $23
_–23_
gained $27
_+27_
loss $43
_–43_
have $1
_+1_
forward 10 steps
_+10_
backwards 4 steps
_– 4_
positive 7
__+7_
negative 16
_–16_
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 2
Integers - Tiles
The numbers .... –3, –2, –1 , 0, +1, +2, +3,.... are integers.
The numbers +1, +2, +3 are positive integers.
The numbers –3, –2, –1 are negative integers.
When working with integers we are going to use the tile model.
a white tile will represent
+1
a black tile will represent a –1
a white tile and a black tile represent the number 0.
Therefore
represents the number –3.
represents the number +5
represents the number +2
( this is the same as 2 + 0 )
Using tiles, represent the following numbers:
+4
–6
–3
+1
10
–10
0
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 3
Integers - Number Lines
During this unit you are going to use number lines. Label each number
line and place the integer in its appropriate place.
4
0
0
-6
4
–6
2
0
-9
0
–2
–9
0
-7
0
0
7
7 and –7
+7 and –7 are opposites
Place the number and its opposite.
-5
0
-2
5
0
–5
-8
0
2
+2
0
8
–8
S. Mercer - Using Multiple Representations to Introduce Integers
0
ANSWER KEY
page - 4
Integers - Sea Level
During this unit you are going represent above and below sea level
using integers. Represent each number. Remember to start at Sea Level.
0
+6
Sea
Level
Sea
Level
0 (Sea Level)
+6 (going up 6 steps)
+4
Sea
Level
+4
-2
Sea
Level
–2 (going down two steps)
+5
Sea
Level
Sea
Level
-5
–5
+5
+7
Sea
Level
+7
S. Mercer - Using Multiple Representations to Introduce Integers
-2
Sea
Level
–2
ANSWER KEY
page - 5
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
+5
+4
9
4
0
moved positive 4
then positive 5
and end at
positive 9
9 positive tiles
4+5
Problem
If you have 4 dollars
and get 5 dollars you
will end with 9 dollars
+5
9 above
sea level
+4
Sea
Level
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
+1
+6
01
7
7 positive tiles
moved positive 1
then positive 6
and end at
positive 7
1+6
Problem
+6
If you have 1 dollars
and get 6 dollars you
will end with 7 dollars
Represent Using Money
+1
7 above
sea level
Sea
Level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 6
Addition of Integers
Represent Using
Tiles
Represent Using a Number
Line
-3
-2
--5
-3
0
moved negative 3 then
negative 2 and end at
negative 5
5 negative tiles
–3 + –2
Problem
If you owe 3 dollars
and borrow 2 dollars
you will end up
owing 5 dollars
Sea
Level
–
3
Represent Using
Money
–2
Represent
Vertically
5 below
sea level
Represent Using
Tiles
Represent Using a Number
Line
-7
-1
--8
-1 0
moved negative 1
then negative 7 and
end at negative 8
8 negative tiles
–1 + –7
Problem
If you owe 1 dollar
and borrow 7 dollars
you will end up
owing 8 dollars
–7
Represent Using
Money
–
1
8 below
sea level
Sea
Level
Represent
Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 7
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 - 8
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
-5
+5
5
0
Each line equals Zero.
0+0+0+0+0=0
moved positive 5
then negative 5
and end at 0
5 + –5
Problem
at sea
level
-5
If you have 5 dollars
and spend 5 dollars
you will end with 0
dollars.
+5
Sea
Level
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
-6
-10
-4
0
10 negative tiles
–4 + –6
Problem
If you owe 4 dollars
and borrow 6 dollars
you will end up owing
10 dollars
-4
-6
Represent Using Money
Sea
Level
10 below
level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 9
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
-5
0
-5
move negative 5
and end at
negative 5
5 negative tiles
0 + –5
If you have no money
and borrow 5 dollars
you will end up owing
5 dollars
Problem
Sea
Level
-5
5 below
sea level
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
-7
-5
0
-12
move negative 7
then negative 5
and end at
negative 12
12 negative tiles
–7 + –5
Problem
If you owe 7 dollars
and borrow 5 dollars
you will end up owing
12 dollars
-7
-5
Represent Using Money
12 below
sea level
Sea
Level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 10
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 - 11
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
+2
-4
-4
2 negative tiles
are left
0
-2
0 + –4 + 2
Problem
If you have no money
and spend 4 dollars
but then make 2
dollars you will end
up owing 2 dollars
+2
Sea
2 below Level
sea level
-4
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
-2
-6
+10
0
2 positive tiles
are left
2
10
10 + –2 + –6
Problem
-6
If you have 10 dollars
and spend 2 dollars
then spend another 6
dollars you will end
with 2 dollars
Represent Using Money
-2
+10
2 above
sea level
Sea
Level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 12
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 - 13
Word Problems
3)
At midnight the temperature was 48˚F. By midday the temperature
had risen 36˚. What was the temperature at midday?
Represent the problem using a picture
+84 ˚
Write a math expression of the problem
+ 36˚
+48 ˚
48 + 36 = 84
48 ˚
12:00am
0˚
12:00 pm
Answer the question in a complete sentence.
At 12:00 pm the temperature will be 84˚ above zero.
3)
Sabrina owes $5 to her mother and $16 to a friend, how much money
does Sabrina have?
Represent the problem using a picture
Write a math expression of the problem
0 dollars
-5
-5
-5 + -16 = -11
-16
-21
Answer the question in a complete sentence.
Sabrina owes 21 dollars in total.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 14
Word Problems
Comparing addition and subtraction
1)
Sabrina earned $15 babysitting. She spent $6 in candy. How much
money did she have left?
Represent the problem using a picture
Write a math expression using subtraction
$15
-6
+15
1)
$9
15
6
Write a math expression using integers
no
money
Solve the problem.
1)
2)
2)
15
6
9
15
-6
9
2)
15
-6
Answer the question in a complete sentence.
Sabrina has 9 dollars after buying
the candy.
Duncan invested in the stock market. The first year he gained $150.
The second year he lost $80. What was his net gain?
Represent the problem using a picture
Write a math expression using subtraction
$150
-80
+150
$80
1)
150
80
Write a math expression using integers
no
money
Solve the problem.
1)
2)
150
80
70
150
-80
70
2)
150
-80
Answer the question in a complete sentence.
After the second year has a net gain of
70 dollars.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 15
Word Problems
Comparing addition and subtraction
1)
Duncan has $30. He spends $12 on a CD. How much money does he
have left?
Represent the problem using a picture
Write a math expression using subtraction
$30
-12
+30
$18
1)
30
12
Write a math expression using integers
no
money
Solve the problem.
1)
2)
2)
2)
30
-12
Answer the question in a complete sentence.
30
12
18
30
-12
18
Duncan has $18 left.
Sabrina’s mom gained 15 pounds during the summer vacation. During
fall she lost 12 pounds. What was her net weight loss or gain?
Represent the problem using a picture
Write a math expression using subtraction
15
-12
+15
1)
3
no
weight
gain
Solve the problem.
1)
2)
15
12
Write a math expression using integers
2)
15
-12
Answer the question in a complete sentence.
15
12
3
15
-12
3
Sabrina’s mom net weight gain was 3
pounds.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 16
Subtraction of Integers
1-2-3-4 Method
1)
10
1) Copy the
same
number
5
2) Change
subtraction to
addition
3) Write the
opposite
5
-5
10
4) Add the integers
2)
5
1) Copy the
same
number
-2
2) Change
subtraction to
addition
5
3) Write the
opposite
7
2
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 17
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 - 18
Subtraction of Integers
1-2-3-4 Method
5)
0
-5
2) Change
subtraction to
addition
1) Copy the
same
number
0
3) Write the
opposite
5
5
4) Add the integers
6)
0
1) Copy the
same
number
8
2) Change
subtraction to
addition
0
3) Write the
opposite
-8
-8
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 19
Subtraction of Integers
1-2-3-4 Method
7)
15
10
2) Change
subtraction to
addition
1) Copy the
same
number
10
3) Write the
opposite
-15
-5
4) Add the integers
8)
3
-8
2) Change
subtraction to
addition
1) Copy the
same
number
3) Write the
opposite
8
3
11
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 20
Subtraction of Integers
1-2-3-4 Method
9)
-4
4
2) Change
subtraction to
addition
1) Copy the
same
number
3) Write the
opposite
-4
-4
-8
4) Add the integers
10)
6
-6
2) Change
subtraction to
addition
1) Copy the
same
number
6
3) Write the
opposite
6
12
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 21
Review
Addition and Subtraction of Integers
Based on what you have learned so far, solve the following problems:
1)
10 + –8 = 2
2)
–7 + –3 = –10
3)
4 + –9 = –5
4)
–10 + 15 = 5
5)
–3 + – 5 + – 9 = –17
6)
10 + –9 + – 4 = –3
7)
10 – 15 = –5
8)
10 – (–3) = 13
9)
–5 – 10 = –15
10) –5 – (–3) = –2
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 22
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 - 23
Multiplication of Integers
Discover the Rules!
Rule #3
–3 • 4 • – 2= 24
4 • –5 • –2 = 40
–2 • – 2 • 3 = 12
–10 • 2 • –3 = 60
–2 • 1 • –3 = 6
Study the problems.
What patterns do you notice?
These are multiplication problems.
All answers are positive.
Each problem has two negative
numbers and one positive.
–5 • –2 • 4 = 40
Describe the rule and give two examples.
If there is an even number of negative numbers being multiplied
then the answer is positive. So the answer is positive 12 if
positive 3 is multiplied by negative 2 and by negative 2 or if
negative 3 is multiplied be negative 2 and a positive 2.
Rule #4
3 • 4 • – 2= –24
Study the problems.
What patterns do you notice?
4 • –5 • 2 = –40
–2 • 2 • 3 = –12
These are multiplication problems.
–10 • 2 • 3 = –60
All answers are negative.
2 • 1 • –3 = –6
Each problem has two positive
numbers and one negative.
5 • –2 • 4 = –40
Describe the rule and give two examples.
If there are an odd number of negative numbers multiplied then
the answer is negative. So the answer is negative 12 if positive
3 is multiplied by negative 2 and by positive 2 or if negative 3 is
multiplied be negative 2 and a negative 2.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 24
Division of Integers
Discover the Rules!
Rule #1
–12 ÷ 4 = – 3
12 ÷ –4 = – 3
24 ÷ –6 = – 4
–24 ÷ 6 = – 4
15 ÷ –3 = – 5
Study the problems.
What patterns do you notice?
All the answers are negative.
One number is positive and one is
negative.
These are division problems.
–15 ÷ 3 = – 5
Describe the rule and give two examples.
A positive number divided by a negative number is negative.
A negative numbers divided by a positive is negative.
Rule #2
–12 ÷ –4 = 3
12 ÷ 4 = 3
24 ÷ 6 = 4
Study the problems.
What patterns do you notice?
All the answers are positive.
–24 ÷ –6 = 4
Both numbers are positive or both
are positive.
–15 ÷ –3 = 5
These are division problems.
15 ÷ 3 = 5
Describe the rule and give two examples.
A positive number divided by a positive number is positive.
A negative numbers divided by a negative is positive.
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 25
Positive or Negative?
Looking at the problem, without doing the computation, decide if the
answer to the problems is positive or negative. Explain you answer clearly.
1)
–100 • –5
Positive or Negative
Why? Because there is an even number of negative numbers
2)
15 • 4 • –3
Why?
3)
4)
6)
7)
Positive or Negative
Because there is an odd number of negative numbers
5000 ÷ –5 • –5 ÷ –5
Why?
Positive or Negative
Because there is an even number of negative numbers
–100 ÷ –2 ÷ –2
Why?
Positive or Negative
Because there is an odd number of negative numbers
–2• –2•–2•–2•–2•–2
Why?
Positive or Negative
Because there is an odd number of negative numbers
–110 • 35 • 4 • 24
Why?
5)
Because there is an add number of negative numbers
–254 • –15 • –4
Why?
Positive or Negative
Positive or Negative
Because there is an odd number of negative numbers
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 26
Review
Multiplication and Division of Integers
Based on what you have, solve the following problems:
1)
10 • –8 = –80
2)
–7 • –3 = 21
3)
4 • –3 = –12
4)
–5 • 10 = –50
5)
–3 • – 2 • – 10 = –60
6)
–3 • – 2 • 10 = 60
7)
10 ÷ –5 = –2
8)
–10 ÷ –5 = 2
9)
–25 ÷ –5 = 5
10) –25 ÷ 5 = –5
S. Mercer - Using Multiple Representations to Introduce Integers
ANSWER KEY
page - 27
Using Multiple
Representations to
Introduce
Integers
Name: ____________________
Period: ________
Date: ______________________
Opposites
Find the pair of opposites:
up
right
empty
white
have
backwards
hot
cold
no
full
left
negative
loss
down
black
south
forwards
owe
north
gain
positive
yes
S. Mercer - Using Multiple Representations to Introduce Integers
page - 1
Integers - Money
During this unit you are going to use integers to represent situations
that and problems include opposites.
For example:
having $5
is represented by +5
owing $5
is represented by –5
going up 4 steps
is represented by +4
going down 4 steps
is represented by –4
gain $12
is represented by +12
loss $12
is represented by –12
Use integers to represent the following situations:
have $10
____
owe $23
____
up 5 steps
____
down 13 steps
____
loss $23
____
gained $27
____
loss $43
____
have $1
____
forward 10 steps
____
backwards 4 steps
____
positive 7
____
negative 16
____
S. Mercer - Using Multiple Representations to Introduce Integers
page - 2
Integers - Tiles
The numbers .... –3, –2, –1 , 0, +1, +2, +3,.... are integers.
The numbers +1, +2, +3 are positive integers.
The numbers –3, –2, –1 are negative integers.
When working with integers we are going to use the tile model.
a white tile will represent
+1
a black tile will represent a –1
a white tile and a black tile represent the number 0.
Therefore
represents the number –3.
represents the number +5
represents the number +2
( this is the same as 2 + 0 )
Using tiles, represent the following numbers:
+4
–6
–3
+1
10
–10
0
S. Mercer - Using Multiple Representations to Introduce Integers
page - 3
Integers - Number Lines
During this unit you are going to use number lines. Label each number
line and place the integer in its appropriate place.
4
–6
–2
–9
0
7 and –7
+7 and –7 are opposites
Place the number and its opposite.
–5
+2
–8
0
S. Mercer - Using Multiple Representations to Introduce Integers
page - 4
Integers - Sea Level
During this unit you are going represent above and below sea level
using integers. Represent each number. Remember to start at Sea Level.
Sea
Level
Sea
Level
0 (Sea Level)
+6 (going up 6 steps)
Sea
Level
Sea
Level
+4
–2 (going down two steps)
Sea
Level
Sea
Level
–5
+5
Sea
Level
Sea
Level
+7
S. Mercer - Using Multiple Representations to Introduce Integers
–2
page - 5
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
4+5
Problem
+5
+4
Sea
Level
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
1+6
Problem
Represent Using Money
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
page - 6
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
–3 + –2
Problem
–3
Sea
Level
Represent Using Money
–2
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
–1 + –7
Problem
Represent Using Money
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
page - 7
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
–3 + –5
Problem
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
–3 + 6
Problem
+6
–3
Represent Using Money
Sea
Level
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
page - 8
Addition of Integers
Represent Using Tiles
Represent Using a Number Line
5 + –5
Problem
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
–4 + –6
Problem
Represent Using Money
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
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Addition of Integers
Represent Using Tiles
Represent Using a Number Line
0 + –5
Problem
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
–7 + –5
Problem
Represent Using Money
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
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Addition of Integers
Represent Using Tiles
Represent Using a Number Line
5 + –3 + –4
Problem
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
–8 + 2 + –4
Problem
Represent Using Money
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
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Addition of Integers
Represent Using Tiles
Represent Using a Number Line
0 + –4 + 2
Problem
Represent Using Money
Represent Vertically
Represent Using Tiles
Represent Using a Number Line
10 + –2 + –6
Problem
Represent Using Money
Represent Vertically
For each representation, clearly label the answer.
S. Mercer - Using Multiple Representations to Introduce Integers
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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
Write a math expression of the problem
Answer the question in a complete sentence.
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
Answer the question in a complete sentence.
S. Mercer - Using Multiple Representations to Introduce Integers
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Word Problems
3)
At midnight the temperature was 48˚F. By midday the temperature
had risen 36˚. What was the temperature at midday?
Represent the problem using a picture
Write a math expression of the problem
Answer the question in a complete sentence.
3)
Sabrina owes $5 to her mother and $16 to a friend, how much money
does Sabrina have?
Represent the problem using a picture
Write a math expression of the problem
Answer the question in a complete sentence.
S. Mercer - Using Multiple Representations to Introduce Integers
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Word Problems
Comparing Addition and Subtraction
1)
Sabrina earned $15 babysitting. She spent $6 in candy. How much
money did she have left?
Represent the problem using a picture
Write a math expression using subtraction
1)
Write a math expression using integers
2)
Solve the problem.
1)
Answer the question in a complete sentence.
2)
2)
Duncan invested in the stock market. The first year he gained $150.
The second year he lost $80. What was his net gain?
Represent the problem using a picture
Write a math expression using subtraction
1)
Write a math expression using integers
2)
Solve the problem.
1)
Answer the question in a complete sentence.
2)
S. Mercer - Using Multiple Representations to Introduce Integers
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Word Problems
Comparing Addition and Subtraction
1)
Duncan has $30. He spends $12 on a CD. How much money does he
have left?
Represent the problem using a picture
Write a math expression using subtraction
1)
Write a math expression using integers
2)
Solve the equations.
1)
Answer the question in a complete sentence.
2)
2)
Sabrina’s mom gained 15 pounds during the summer vacation. During
fall she lost 12 pounds. What was her net weight loss or gain?
Represent the problem using a picture
Write a math expression using subtraction
1)
Write a math expression using integers
2)
Solve the problem.
1)
Answer the question in a complete sentence.
2)
S. Mercer - Using Multiple Representations to Introduce Integers
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Subtraction of Integers
1-2-3-4 Method
1)
10
1) Copy the
same
number
5
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
2)
5
1) Copy the
same
number
-2
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
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Subtraction of Integers
1-2-3-4 Method
3)
-4
1) Copy the
same
number
8
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
4)
-7
1) Copy the
same
number
-1
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
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Subtraction of Integers
1-2-3-4 Method
5)
0
1) Copy the
same
number
-5
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
6)
0
1) Copy the
same
number
8
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
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Subtraction of Integers
1-2-3-4 Method
7)
10
1) Copy the
same
number
15
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
8)
3
1) Copy the
same
number
-8
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
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Subtraction of Integers
1-2-3-4 Method
9)
-4
1) Copy the
same
number
4
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
10)
6
1) Copy the
same
number
-6
2) Change
subtraction to
addition
3) Write the
opposite
4) Add the integers
S. Mercer - Using Multiple Representations to Introduce Integers
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Review
Addition and Subtraction of Integers
Based on what you have learned so far, solve the following problems:
1)
10 + –8
2)
–7 + –3
3)
4 + –9
4)
–10 + 15
5)
–3 + – 5 + – 9
6)
10 + –9 + – 4
7)
10 – 15
8)
10 – (–3)
9)
–5 – 10
10) –5 – (–3)
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Multiplication of Integers
Discover the Rules!
Rule #1
–3 • 4 = – 12
Study the problems.
What patterns do you notice?
5 • –2 = – 10
–6 • 3 = – 18
2 • –3 = – 6
1 • –3 = – 3
–10 • 4 = – 40
Describe the rule and give two examples.
Rule #2
–3 • –4 = 12
Study the problems.
What patterns do you notice?
5 • 2 = 10
–6 • –3 = 18
–2 • –3 = 6
1•3= 3
–10 • –4 = 40
Describe the rule and give two examples.
S. Mercer - Using Multiple Representations to Introduce Integers
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Multiplication of Integers
Discover the Rules!
Rule #3
–3 • 4 • – 2= 24
Study the problems.
What patterns do you notice?
4 • –5 • –2 = 40
–2 • – 2 • 3 = 12
–10 • 2 • –3 = 60
–2 • 1 • –3 = 6
–5 • –2 • 4 = 40
Describe the rule and give two examples.
Rule #4
3 • 4 • – 2= –24
Study the problems.
What patterns do you notice?
4 • –5 • 2 = –40
–2 • 2 • 3 = –12
–10 • 2 • 3 = –60
2 • 1 • –3 = –6
5 • –2 • 4 = –40
Describe the rule and give two examples.
S. Mercer - Using Multiple Representations to Introduce Integers
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Division of Integers
Discover the Rules!
Rule #1
–12 ÷ 4 = – 3
Study the problems.
What patterns do you notice?
12 ÷ –4 = – 3
24 ÷ –6 = – 4
–24 ÷ 6 = – 4
15 ÷ –3 = – 5
–15 ÷ 3 = – 5
Describe the rule and give two examples.
Rule #2
–12 ÷ –4 = 3
Study the problems.
What patterns do you notice?
12 ÷ 4 = 3
24 ÷ 6 = 4
–24 ÷ –6 = 4
–15 ÷ –3 = 5
15 ÷ 3 = 5
Describe the rule and give two examples.
S. Mercer - Using Multiple Representations to Introduce Integers
page - 25
Positive or Negative?
Looking at the problem, without doing the computation, decide if the
answer to the problems is positive or negative. Explain you answer clearly.
1)
–100 • –5
Positive or Negative
Why?
2)
15 • 4 • –3
Positive or Negative
Why?
3)
–254 • –15 • –4
Positive or Negative
Why?
4)
–110 • 35 • 4 • 24
Positive or Negative
Why?
5)
–2• –2•–2•–2•–2•–2
Positive or Negative
Why?
6)
–100 ÷ –2 ÷ –2
Positive or Negative
Why?
7)
5000 ÷ –5 • –5 ÷ –5
Positive or Negative
Why?
S. Mercer - Using Multiple Representations to Introduce Integers
page - 26
Review
Multiplication and Division of Integers
Based on what you have, solve the following problems:
1)
10 • –8
2)
–7 • –3
3)
4 • –3
4)
–5 • 10
5)
–3 • – 2 • – 10
6)
–3 • – 2 • 10
7)
10 ÷ –5
8)
–10 ÷ –5
9)
–25 ÷ –5
10) –25 ÷ 5
S. Mercer - Using Multiple Representations to Introduce Integers
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