Unit 2:Integers
Grade 7 Math
Unit 2 - Integers
Section 1 – Integers and their uses
Integers: whole amounts above, below or equal to zero. An integer is any
number in the set…..-3, -2, -1, 0, 1, 2, 3…
There are many uses for integers in everyday life.
TIME ZONES
Integers can be used to indicate how many hours ahead or behind a certain
time zone is compared to the area in which you live.
Ex. Look at the time zone map on p. 50 - 51 of your textbook.
* If it is 3:30 in St. John’s, what time is it in Vancouver? _____________
* How many hours behind Newfoundland Time is Pacific Time? _________
* Write this number as an integer. _______________
SEA – LEVEL
Integers can be used to indicate how far above or below an area of land is
compared to sea level. Sea-level (the level of the worlds ocean waters) is
taken to be 0 meters.
* Write Mount Everest’s
elevation as an integer _______.
* Write the Dead Sea’s
elevation as an integer _______.
Mount
Everest
8863 m
m
Sea-level 0 m
400 m
Dead
Sea
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Unit 2:Integers
TEMPERATURE
Integers are also used to indicate temperatures above or below the freezing
point of water (0ºC).
Ex. The temperature in Gander is -3ºC. (Three degrees below freezing)
Ex. The temperature in St. John’s was + 2 ºC (Two degrees above freezing)
MONEY
Integers can also be used to indicate amounts of money gained or lost.
Money gained would be represented by a positive integer.
Ex. Susan made $15 babysitting. As an integer this is +15.
Money lost or a debt (money owed) is represented by a negative integer.
Ex. Stanley borrowed $6 from his friend last week. He now owes his friend
$6.00. As an integer this is -6.
Write an integer for each situation below.
a) Dan owes the credit card company $100.
_______________
b) Jill spent $12.00 in the arcade.
_______________
c) Tyler made $45.00 mowing lawns
_______________
d) Scott borrowed $12.00 from Mike.
_______________
e) The cost of gas went down 2 cents a liter
_______________
f) The cost of gas went up 5 cents a liter
_______________
g) Stephanie got an allowance of $20.00.
________________
h) Stephanie spent $15 on a CD.
________________
i) Stephanie borrowed $10 from Sam
_________________
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Unit 2:Integers
Modeling Integers with Integer Tiles
We can use integer tiles to model positive and negative integers.
One light tile
One dark tile
can represent +1.
can represent - 1
=
+1
=
-1
A dark and a light tile combined model zero. This is called a ZERO PAIR
+ 1 + (-1) = 0
An integer can be modeled in many different ways.
For example - 3 can be modeled in the following ways.
A)
B)
Each of the models to the left
represent -3.
C)
D)
Notice that we can keep adding
zero pairs to any integer and it
will not change the value of that
integer.
E)
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Unit 2:Integers
TRY IT.
Pick an integer and use light (positive) and dark (negative) integer tiles to
model it in as many ways as you can in the space below.
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Unit 2:Integers
Section 2 – Adding Integers
An integer has two parts, its SIZE and its SIGN
1.) SIZE - refers to how much an integer represents.
Ex. What is the SIZE of the integer modeled below? ANSWER:________
Ex. What is the SIZE of the integer modeled below? ANSWER:________
2.) SIGN – indicates whether the amount is above or below zero
Ex. What is the SIGN of the integer modeled below? ANSWER:________
Ex. What is the SIGN of the integer modeled below? ANSWER:________
What integer is modeled by the combination of tiles shown in the model
below?
ANSWER:________
Write an addition equation that represents the integer counters shown
above.
ANSWER:
(+5) + (-2) = +3
When writing equations with integers
we put brackets around the integers
being added or subtracted. This
separates positive and negative signs
from addition and subtraction signs.
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Unit 2:Integers
Write addition equations for each set of integer counters below. In each
model we are adding the second row to the first row.
1.)
1.) Equation: ___________________
2.)
2.) Equation: __________________
3.)
3.) Equation: __________________
4.)
4.) Equation: __________________
5.)
5.) Equation:__________________
6.)
6.) Equation: __________________
7.)
7.) Equation: __________________
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Unit 2:Integers
Integer counter tiles can also be used find the sum of two or more integers.
Example: Find the sum of the following addition sentence and write an
equation to represent it.
(-10) + (+14)
STEP 1: Model each integer.
(-10) 
(+ 14) 
STEP 2: Cancel out all zero pairs.
(-10) 
(+ 14) 
There are 4 negative tiles left over after all the zero pairs are removed.
This means the equation would read;
(-10) + (+14) = (-4)
PRACTICE PROBLEMS
Use coloured tiles to find each sum and complete each equation.
a) (+6) + (–12)
= _____
b) (–10) + (–4) = _____
c) (–8) + (–9)= ______
d) (+11) + (+7)
= _____
e) (–13) + (+5) = _____
f) (+12) + (–6) = ______
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Unit 2:Integers
Section 3 – Adding Integers on a Number Line
We can represent the size and sign of an integer by drawing an arrow on a
number line.
SIZE – how many units the arrow will cover
SIGN – the direction the arrow will point.
 NEGATIVE will point left
 POSITIVE will point right
Ex. Represent (-5) on the number line below.
PRACTICE PROBLEMS
Represent the following integers on the number lines provided.
A) (-3)
B) (+6)
C) (-9)
D) (0)
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Unit 2:Integers
We can also add integers using a number line.
EXAMPLE 1.
Model (+4) + (+3) on the number line below.
STEP 1: Start at zero and jump 0 to the first integer.
STEP 2: Starting at the first integer draw an arrow representing the size
and direction of the second integer.
Therefore, (+4) + (+3)= +7
EXAMPLE 2.
Model (-2) + (+5) on the number line below.
STEP 1: Start at zero and draw an arrow from 0 to the first integer.
STEP 2: Starting at the first integer draw an arrow representing the size
and direction of the second integer.
Therefore, (-2) + (+5) = +3
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Unit 2:Integers
EXAMPLE 3.
Model (-2) + (+7) + (-4) on the number line below.
STEP 1: Start at zero and draw an arrow from 0 to the first integer.
STEP 2: Starting at the first integer draw an arrow representing the size
and direction of the second integer.
STEP 3: Starting at the end of your second arrow draw a third arrow
representing the size and direction of the third integer you are adding.
Therefore (-2) + (+7) + (-4) = +1
TRY IT.
Model (+6) + (-7) + (+2) on the number line below.
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Unit 2:Integers
PRACTICE PROBLEMS –
1.) Use a number line to add. Complete the equation for each.
a) (+4) + (–6) = _____
b) (-5) + (–4) = _____
c) (-7) + (+8) = _____
d) (-10) + (+3) = _____
e) (+9) + (–6) + (–7) = _____
f) (-1) + (+8) + (-15) = _____
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Unit 2:Integers
2.) Write an addition statement for each situation. Find the sum.
What does the sum represent?
a) The temperature in Victoria was +15ºC in the afternoon.
By midnight, the temperature had dropped 8ºC.
b) The temperature in Calgary was –10ºC.
A Chinook caused the temperature to rise 12ºC.
c) The temperature in Ottawa was –3ºC.
A cold front passed and the temperature dropped 8ºC.
d) The temperature in St. John's was –4ºC at 4 a.m.
By noon, the temperature had risen 10ºC.
3.) Represent each sentence with integers, then find each sum.
What does the sum represent?
a) The elevation of the base of the building is 345 m above sea level.
The building is 50 m high.
b) The elevation of the base of the building is 75 m below sea level.
The building is 15 m high.
c) The elevation of the top of the trench is 237 m below sea level.
The trench is 10 m deep.
4.) These are the scores on each hole of mini-golf. Find the total score.
Score
–2
+1
0
+3
–1
+2
–1
0
–2
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Unit 2:Integers
Section 4 – Subtracting Integers
To subtract integers we remove integers tiles from an existing group.
Ex. (+7) – (+2)
Remove 2 positive tiles
There are 5 positive tiles left.
Therefore,
(+7) – (+2) = (+5)
What if one of the integers is negative?
EXAMPLE 1. (+5) – (-3)
STEP 1: Model the first integer
(+5)
STEP 2: Add zero pairs until there is enough to represent the integer we
want to subtract.
We must add three zero
pairs in order to get (-3).
STEP 3: Remove the integer tiles being subtracted. The remaining tiles
represent the difference (answer of the subtraction problem).
We remove the (-3)
8 positive tiles remain
Therefore,
(+5) – (-3) = (+8)
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Unit 2:Integers
EXAMPLE 2. (-2) – (+5)
STEP 1: Model the first integer
(-2)
STEP 2: Add zero pairs until there is enough to represent the integer we
want to subtract.
We must add five zero
pairs in order to get (+5).
STEP 3: Remove the integer tiles being subtracted. The remaining tiles
represent the difference (answer of the subtraction problem).
Remove 5 positive tiles
7 negative tiles remain
Therefore,
(-2) – (+5) = (+7)
EXAMPLE 3. (-4) – (-5)
STEP 1: Model the first integer
(-4)
STEP 2: Add zero pairs until there is enough to represent the integer we
want to subtract.
We already have four negative
tiles. We only need one more to be
able to take away (-5), so we add
one zero pair.
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Unit 2:Integers
STEP 3: Remove the integer tiles being subtracted. The remaining tiles
represent the difference (answer of the subtraction problem).
Remove the 5 negative
tiles
1 positive tile remains
Therefore,
(-4) – (-5) = (+1)
Practice Problems
1. Use tiles to subtract.
a) (+7) – (+4)
b) (–9) – (–5)
d) (–3) – (–8)
e) (+7) – (–3)
c) (+8) – (+12)
f) (–5) – (+4)
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Unit 2:Integers
2. What do you subtract from each integer to get the answer +4?
Use coloured tiles if they help.
a) +6
b) –3
c) +1
d) 0
3. What do you subtract from each integer in question 2 to get the answer –
4?
4. Subtract.
a) (–5) – (–8)
b) (–12) – (–4)
c) (+8) – (+11)
d) 0 – (+3)
e) (–8) – (–5)
f) (+11) – (+8)
5. Complete the magic square for a magic sum of 0.
Subtract –2 from each entry. Is it still a magic square?
–1
–3
+2
+3 –4
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Unit 2:Integers
Section 5 - Subtracting Integers Using a Number Line
Integers can be modeled on a Number Line. There are two methods that can
be used.
METHOD 1: The Comparison Method
Ex. (+6) – (+4)
Start at the second integer and determine what must be added to it in
order to get the first integer.
+2
So the difference between (+6) and (+4) is (+2)
(+6) – (+4) = (+2)
Ex. (+1) – (-2)
We start at the second integer (-2) and determine what must be added to it
to get the first integer (+1).
+3
Ex. (-9) – (-7)
We start at the second integer (-9) and determine what must be added to it
to get the first integer (-7).
-2
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Unit 2:Integers
Practice Problems
Subtract the following integers using the comparison method.
1. (+9) – (+3)
2. (+4) – (-2)
3. (-2) – (+5)
4. (-2) – (-6)
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Unit 2:Integers
METHOD 2: Adding The Opposite
To understand how this method works complete the problems in the table
below.
(+4) – (+2) =
(+7) – (-3) =
(-3) – (-2)
(+4) + (-2) =
(+7) + (+3) =
(-3) + (+2) =
What do you notice about the equations in each row of this table?
_________________________________________________________
_________________________________________________________
_________________________________________________________
What do you notice about the solutions (answers) to the equations in each
row of this table?
_________________________________________________________
_________________________________________________________
_________________________________________________________
We can re-write any subtraction statement as an addition statement without
changing the answer.
Ex. Solve (-5) – (-8) using the comparison model.
+3
Now solve (-5) – (-8) by adding the opposite.
We re-write as (-5) + (+8)
Start at (-5) and move 8 units right. We still land on (+3)
OR
+3 remain
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Unit 2:Integers
Practice Problems
1. Re-write as an addition statement and then solve using a number line or algebra
tiles.
a) (–5) – (–4)
b) (–6) – (+3)
a)
b)
c) (+8) – (+12)
d) (+7) – (+2)
c)
d)
e) (–3) – (+5)
f) (–7) – (–8)
e)
f)
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