Mathematics Unit Strand(s) & Areas: NS & Numeration: Integers
Quantity
Relationshi
ps
Grade 7
Grade 8

Identify & compare integers found in real-life contexts


Represent and order integers, using a variety of tools

Represent, compare & order rational numbers [including integers]

Use estimation when solving problems involving operations with whole numbers,
decimals, percents, integers, and fractions, to help judge the reasonableness of a
solution

Operational Sense
Grade: 7/8 Timeline: Spring

Add and subtract integers, using a variety of tools



Represent the multiplication and division of integers, using a variety of tools


Solve problems involving operations with integers, using a variety of tools


Evaluate expressions that involve integers, including expressions that contain
brackets and exponents, using order of operations
Big Ideas:
1. The negative integers are the “opposites” of the whole numbers. Each integer is the reflection of its opposite across a line that is perpendicular to the
number line at 0.
2. In a number of ways, integers are more like whole numbers than like fractions or decimals.
3. The zero property (i.e…..) plays an important role in many integer operations.
4. The meaning for the operations that apply to whole numbers, fractions, decimals also apply to all integers. Each meaning can be represented by a model,
although some models suit some meanings better than others.
Culminating Task / Problem:
Formative Problems / Tasks Related to Culminating task:
Vocabulary
Positive
Negative
Zero pairs
Integers
Mathematics Unit Strand(s) & Areas: NS & Numeration: Integers
Day
Big Idea &
Learning Goal
Big Idea - In a number of
ways, integers are more like
whole numbers than like
fractions or decimals.
Grade: 7/8 Timeline: Spring
Minds On
Action
Who’s in the NHL playoffs? How is this
decided?
Here are different types of stats for hockey teams.
According to this, are the best teams currently in
the playoffs?
Is that a true determination of who
the best teams are?
Learning Goal – We are
learning to understand the
values of numbers.
Provide students with the regular season team
stats (Goals For, Goals Against). Have students
determine how to rank the teams using the
information.
2 (Probably do 2 & 3 on same day)
1
3
Big Idea:
The zero property (i.e…..)
plays an important role in
many integer operations.
Show picture 4 (+) = 4 (-), Ask: Is this
true (Turn & Talk with partner)?
Watch the Integer video.
Does this balance? How do you know?
File:
Integer Video.mp4
Consolidation
Gallery Walk – Focus on Question 1:
“How did different groups rank the
teams? Was it consistent with your
method?”
“How did the different groups
represent negative numbers? How
did they deal with negative
numbers?”
Highlight:
Bigger negative numbers
have a lower value/ranking
A negative ranking means
the team was scored on
more than they scored
Summarize:
Both negative & positive
numbers can be found on a
number line, and 0 is in the
middle.
Gallery Walk:
Highlight –
- Matching one +ve to one –ve
- Value on opposite side of = sign is
the same
Summarize
Zero Principle – the sum of
a negative integer and its
opposite is always zero
Define Zero Pairs
Big Idea:
Show one positive integer tile.
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
How much is here? (1)
(add 3 zero pairs) How much is here
now? How do you know (turn & talk).
-
No change b/c you are just
How can you use the tiles to find the answer to any
negative number added to a positive number?
Prompt:
Does your strategy always work?
Does it work if you add a negative number to a
positive number?
Bansho / Gallery Walk / Congress
Highlight
How to represent an
adding question (drawings)
How to record +ve, -ve
numbers
Assessment
Practice:
Math Notebook –
create a horizontal
number line using
values -10 to +10.
Vertical?
Practice – Choose at
least one of the other
integer pictures. How
would you make it
equivalent to zero.
File:
Integer Pictures.doc
Reflection – Jessie says
adding negative
numbers is the same as
subtracting positive
numbers. Why might
she think this? Do you
agree?
Mathematics Unit Strand(s) & Areas: NS & Numeration: Integers
be represented by a model,
although some models suit
some meanings better than
others.
adding zero
Grade: 7/8 Timeline: Spring
Could you start with one example?
-
Positive and negative
numbers added together
will cancel out
Summary:
Learning Goal – We are
learning how to show to
adding integers with tiles.
4
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
– using “zero pairs” strategy, and see
how much you have left over
Eyes on Math p. 174
You add two numbers and the answer is negative.
What two numbers might you have added?
What do all of these pictures show?
Highlight:
Use of tiles
Use of number lines
Reflection – When
might the principles
we’ve discovered help
you?
Partner. All pictures have a value of 0.
Summarize:
The sum of 2 –ves is always –ve
The sum of 2 +ve is always +ve
The sum of +ve and –ve can be either
+ve or –ve.
Learning Goal – We are
learning how to model
addition of integers with
integer tiles and number
lines.
5
6
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
Learning Goal – We are
learning how to model
subtraction of integers with
integer tiles.
Big Idea:
The meaning for the
operations that apply to
What could a negative value mean in
real life?
Debt
Cold
Golf score (below par)
Loss on stock market
Hockey player / team rating
Below sea level
Time zones?
-
You have a positive number. You subtract another
number and end up with a negative number. How
is this possible? Show you thinking.
Highlight
Use of Number line
Use of tiles
Practice Questions
- Integer Black Jack
- Intergo (Gr. 7
Nelson text p. 206)
Summarize
You can add in zero pairs to
take away the amount
needed.
You can change a
subtraction question into
an addition question with a
missing value.
Would you calculate (-10) – (-3) in the same way
you would calculate 10-(-3)? Explain your thinking.
Summarize
Practice: Magic Square
(Making Math
Meaningful p.267)
Mathematics Unit Strand(s) & Areas: NS & Numeration: Integers
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
Learning Goal – We are
learning how to model
subtraction of integers with
integer tiles.
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
Learning Goal – We are
learning how to model
subtraction of integers with
integer tiles.
7
Grade: 7/8 Timeline: Spring
-
Practicing Adding & Subtracting (mini
quiz, problem) –
good activity (Spinning Spinners, Gr. 8
Nelson Text p. 180 – what is the
greatest sum, least sum etc. Take
away sub steps)
When subtracting a
negative value, the answer
will be more than with
what you started
Mini Quiz:
1. Write an addition
sentences that
represents each
statement:
a) All addends are
negative
integers and
the sum is -7
b) At least one
addend is a
positive integer
and the sum is
-7
c) Which
statement has
the most
answers?
Explain.
2. Tell whether each
statement is
sometimes, always,
or never true.
Explain how you
know.
a) Positive – positive =
positive
b) Negative – positive =
negative
c) Negative – negative =
negative
Mathematics Unit Strand(s) & Areas: NS & Numeration: Integers
Grade: 7/8 Timeline: Spring
d) Positive – negative =
negative
8
9
10
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
Learning Goal – We are
learning to multiply
integers.
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
Learning Goal – We are
learning to multiply
integers.
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
Learning Goal – We are
How can you represent 3 x 4?
Would represent 3 x (-4) the same way as 3 x 4?
Manipulatives?
Real life?
Diagram?
Grouping?
Repeated Addition
How is 3 x (-4) the same / different as
(-4) x 3?
Highlight
Different representations
(adding, manipulatives,
group, real life)
Summarize
- Positive x positive = positive
- Positive x negative = negative
If 3 x (-4) is adding groups to a “pot”, what might
(-3) x (-4) mean? How could you represent or
model this?
Turn & Talk

Allow students to create a video? Ipad,
phone or Laptop?
Prompt –
How can you represent zero in a pot, but change
how much is in there? (add zero pairs)
Practice multiplying integers (Integer
Flip Game)
Reflection – Explain
why the following
statements are true or
false:
Positive x positive =
positive
Positive x negative =
negative
Practice questions?
Highlight
Different strategies (tiles,
number line)
Summarize
Negative x negative =
positive
(Review summary of
multiplying principles)
Mathematics Unit Strand(s) & Areas: NS & Numeration: Integers
11
learning to multiply
integers.
Big Idea:
The meaning for the
operations that apply to
whole numbers, fractions,
decimals also apply to all
integers. Each meaning can
be represented by a model,
although some models suit
some meanings better than
others.
What is dividing?
-
Sharing
Grouping
Opposite of multiplying
Learning Goal – We are
learning to divide integers.
12
Performance Task -
Grade: 7/8 Timeline: Spring
Do the rules for multiplying integers stand true for
dividing integers? Explain your thinking.
Highlight –
1. understanding of inverse
operations
2. Use of understanding about
positive number
relationships
Summarize
1. Rules stand true for
division