Investigating Quantity
Arithmetic with Integers
Name________________________
Use colored chips to explore arithmetic with integers. All numbers should be easily identifiable and any zeros
that may occur must clearly identified as a zero.
I. Addition of Integers
Using the set model of addition illustrate the following addition problems.
1. -4 + 7
2. 3 + 2
3. -3 + -5
4. 5 + (-8)
II. Subtraction of Integers
Illustrate subtraction of integers using the Take-Away model of Subtraction on the following problems.
1. 7 – 4
2. – 3 – 2
3. -5 – (-2)
4. 5 - 8
III. Multiplication of Integers
Illustrate multiplication of Integers using a Repeated Addition model for Multiplication.
1. 3  4
3.
 3   4
2.  3   4
4.
 3   4
IV. Division of Integers
Illustrate division of integers using the indicated model of division. Clearly explain the answer to the division
problem.
1. 12  4
3. 12  4
(The Partition Model of Division)
(The Repeated-Subtraction Model of
Division)
2. 12  4
(The Partition Model of Division)
4. 12  4
(Either model of division)
V. Summary of Arithmetic with Integers using the Chip Method
1. Explain how to model addition of integers using the Chip method. Include in your explanation any issues
that must be addressed when using the Chip method to model addition.
2. Explain how to model subtraction of integers using the chip method. Include in your explanation any issues
that must be addressed when using the Chip method to model subtraction.
3. Explain how to model multiplication of integers using the chip method. Include in your explanation any
issues that must be addressed when using the Chip method to model multiplication. Also include in your
explanation how you showed that a negative times a positive is negative, a negative times a negative is
positive.
4. Explain how to model division of integers using the chip method. Include in your explanation any issues
that must be addressed when using the Chip method to model division. Also include in your explanation how
you showed that a negative divided by a positive is negative, a negative divided by a negative is positive and
why you were unable to show that a positive divided by a negative is negative.