Multiplying and
Dividing Integers
7th Grade
Module 2
The Destination
Standards
7.NS.A.2
Multiply and divide integers.
7.NS.A.3
Solve real-world and mathematical
problems using all four operations
with integers.
7.EE.B.3
Solve multi-step problems with
integers in any form.
Module 2 continues to build on student
understanding of whole number multiplication by
representing groups of an object. When multiplying a
negative number and a positive number, students use
the Commutative
Models
 Horizontal
number lines
 Vertical
number lines

Integer chips
Property to show a positive number of
groups with a negative value. For
example, when multiplying -3 and 7, think
7 groups of -3. We use our knowledge of
opposites when multiplying two negative
numbers. For example, (-3)(-7) can be
thought of as the opposite of 3 groups of
(-7) which can still be represented in a
concrete way. After investigating integer
multiplication students can apply the
same rules to division, the inverse
operation. Tying together Module 1 and
Module 2, students solve problems
involving all four integer operations.
Must-See-Attractions
Integer Chips
Division can be interpreted in two ways:
partitive and quotative. Partitive is the
fair-share model that focuses on splitting
the objects into groups of equal size, like
dealing a deck of cards. When simplifying
(−8) ÷ (−2), ask “if you split -8 into -2
groups, how many will be in each group?”
Since it is impossible to have -2 groups,
students should think about integer
division problems as quotative or as
measurement.
They repeat the group size as many
times as needed to get the dividend:
(−8) ÷ (−2) can be interpreted as
“how many -2s fit inside of -8?”
This conceptual understanding of
division can be modeled using integer
chips:
There are four -2s in -8:
Related Places to Visit
Number lines
Write a multiplication equation and comparison
statement to relate the temperatures in Anchorage,
Alaska to Winnepeg, Canada.
(-15 x 2 = -30; Anchorage is two times as cold as
Winnepeg)
For clip art or worksheets:
http://www.commoncoresheets.com/Math/Temperature
/Finding%20Differences%20(With%20Thermometer)/Engl
ish/All.pdf
Data Analysis
PGA Golf Scores (Round 1)
(−15)(2 ) = −30
−5, 0, 1, 2, −4, 1, −1, −1, 0 , 3, −1, 4, 5, 8, 6
1) Plot these scores on a line plot.
2) Describe the data using measures of center (mean, median, mode).
3) Describe the variability of the data (range, MAD).
Rates
EXIT
Jet Blue airplane’s altitude changed -378 over
7 minutes. Skyliner’s airplane changed
PARCC
-215 over 5 minutes. What is the mean change
of altitude in feet per minute for each
airplane? Which plane is descending faster?
Exponent Patterns
Evaluate and discuss the answers to the
following:
SMP
1. 34
2. the opposite of 34
3. −34
4. (−3)4