Grade 9 Gap Closing & Explore Learning Gizmos Strategies
Topic 3.2: Integers- Adding and Subtracting Integers
Student Book: Open Questions p. 10, Think Sheet p. 11-14, Facilitators Guide p. 14-20
Big Idea: The operations of addition, subtraction hold the same fundamental meanings no matter the domain in which
they are applied.1
Gizmo:
Description:
Learning Goal:
Adding and Subtracting Integers
Add and subtract integers on a number line
using dynamic arrows.
Selecting a strategy to add or
subtract integers depending on
the values of those integers.
Assessment Quiz:

Demo Movie: 
Topic Key Questions:
How can you quickly decide
whether a - b is positive or
negative?
How can you quickly decide
whether a + b is positive or
negative?
Open Questions
This Gizmo is well designed for visualizing adding and subtracting integers.
1. Start with students working with the Gizmo to add positive and negative integers. For example, 2 + (-3)
2. Then have students subtract positive and negative integers. For example, (-2) - 3, (-2) - (-3)
User Lesson Materials : Check out this worksheet adapted from the Exploration Guide by Susan McCoy, Ontario.
Ask Students: How are adding and subtracting with negative integers like adding and subtracting whole numbers? How
are they different?2
Think Sheet
Use this Gizmo to:
a. solve and model each subtraction:
i.
ii.
iii.
iv.
(-7) - (+7)
(+7) - (-7)
8 - (-4)
4-8
b. explain why -(-10) is the same as +10
1,2
Small, Marian and Amy Lin. More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction. Teachers College, Columbia University, 2010:
64-73. Print.
Grade 9 Gap Closing & Explore Learning Gizmos Strategies
Topic 3.2: Integers- Adding and Subtracting Integers
Student Book: Open Questions p. 10, Think Sheet p. 11-14, Facilitators Guide p. 14-20
Big Idea: The operations of addition, subtraction hold the same fundamental meanings no matter the domain in which
they are applied.1
Gizmo:
Description:
Learning Goal:
Adding & Subtracting Integers
with Chips
Use chips to model addition and
subtraction of positives and negatives.
Explore the effect of zero pairs. See how to
use zero pairs to help special cases of
addition and subtraction.
Selecting a strategy to add or
subtract integers depending on
the values of those integers.
Assessment Quiz:

Demo Movie: 
Topic Key Questions:
How can you quickly decide
whether a - b is positive or
negative?
How can you quickly decide
whether a + b is positive or
negative?
Open Questions
By selecting “Explore” students can use this Gizmo to explore possible integer pairs.
Think Sheet
a. Have students:
i.
model the Zero Principle: -4+4=0
ii.
add a number to (-2) and the sum is negative. List three
possible numbers you might have added and three you could not have added.
b. Have students model and solve addition problems:
i.
(-6) + (6)
ii.
(-2) + (-3)
iii.
(-7) + (+6)
iv.
Select “Addition” and the Gizmo will
generate questions.
c. Have students model and solve subtraction problems:
i.
(-6)-(+6)
ii.
8 – (-4)
iii.
10 – (+12)
iv.
10 – (-12)
v.
Select “Subtraction” and the Gizmo will
generate questions.
d. Have students work in groups to answer the following:
i.
Katie added all the integers from -15 to +15 in her head. Explain how she could have done that.
ii.
Subtract two integers and the difference is -4. What could those integers be?
iii.
Use a model to explain why any number -(-3) is the same as that number +3.
Small, Marian and Amy Lin. More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction. Teachers College, Columbia University, 2010: 6473. Print.