ACOS Objective 1

Demonstrate computational fluency with addition, subtraction, and multiplication of integers.
  • Developing algorithms for performing operations on integers.
  • Using inverse properties of addition and of multiplication.

ARMT Possible Points = 5 (MC, GR)
  • Only one operation will be required for each item.
  • Parentheses or the multiplication symbol (*) will be used for multiplication.
  • The multiplication symbol (x) will not be used.
  • Negative integers may be in parentheses.
  • Integers will not exceed four digits in the stem.
  • No word problems/real-life situations will be used.
  • One of the options may be NH, which means "Not Here."

Sample problems from Item Specs

Integers are also tested through CS 2 (order of operations) and CS 3 (rational numbers). Division of integers is included in the sample test items for CS 3.


Objective 7.1.1: Identify numbers less than zero by extending the number line.
Objective 7.1.2: Solve problems involving basic operations on whole numbers, including addition and subtraction of seven-digit numbers, multiplication with two-digit multipliers, and division with two-digit divisors.

Additional content to be taught:
· Developing algorithms for performing operations on integers
Example: determining a systematic set of steps that can be used to subtract integers
· Using inverse properties of addition and of multiplication


CMP unit "Accentuate the Negative" gives a slow introduction to negative numbers and operations with integers.

Teaching Addition and Subtraction of Integers
Have students walk a number line. I taped paper on the wall on which I had written one number per sheet.
  • Start at zero facing the positive numbers.
  • Walk forward for a positive number and backwards for a negative number.
  • Turn around (180º) for subtraction.
This is a great way to show students that adding a negative and subtracting a positive give the same result. They can easily see that walking backwards two steps will put them in the same place as turning around and then walking forward two steps.

Rules for Multiplying and Dividing Integers
It is good (+) to love (+), and it is bad (-) to hate (-)!

If you love to love, that is good. (positive x positive = positive)
If you love to hate, that is bad. (positive x negative = negative)
If you hate to love, that is bad. (negative x positive = negative)
If you hate to hate, that is good. (negative x negative = positive)

Interwrite Lesson
Evaluate Expressions
Students will evaluate expressions using order of operations and add parentheses to get certain outcomes.

Matrix Integers


Integer Videos burst_new2.gif
Teacher Tube has two pages of videos on integers

Stand and Deliverburst_new2.gif
Jaime Escalante explains integers to his students in this movie clip.

Interesting Integers
Webquest with handouts Homework Help
Signed Integers, Adding and Subtracting Integers, Multiplying and Dividing Integers, Properties of Integers
First Glance, In Depth, Examples, Workout

Mrs. Glosser's Math Goodies
Free Lessons: Introduction to Integers, Adding Integers, Subtracting Integers, Challenge Exercises, Printable Worksheet

Amby's Math Resources
Explanation, Practice Exercises with Instant Feedback, and a great story explaining the rule for multiplication

Integer Games

Builder Ted
Put numbers in order. Levels 2 and 3 have negative numbers.

Mystery Picture Game

Fun Brain
Line Jumper
Practice using a number line for addition and subtraction.

MathCar Racing Game
Try to beat the computer by picking the expression that has the largest answer. You can choose the skill level and the operation to practice.

National Library of Virtual Manipulatives
Addition with Color Chips
Subtraction with Color Chips
Use color chips to illustrate subtraction of integers.
Circle Zero
A puzzle involving adding positive and negative integers to sum to zero.
Circle 21
A puzzle involving adding positive and negative integers to sum to twenty one.
Number Line Bounce
Number line addition and subtraction game.

Arithmetic Four
This game asks the players to add, subtract, multiply, and divide whole numbers and integers. Choose difficulty level, question types, and time limit.

Explore Learning Gizmos
Interactive "Gizmo" illustrating addition of integers on a number line. Comes with exploration guide and assessment questions. By subscription, but has Free 30 day trial account.

Choose Math Operation Game
Choose the range to include negative numbers in this fun game to get practice in how to add/subtract/multiply/divide integers.

Space Coupe to the Rescue
By choosing a positive or negative number, the player controls the vertical position of a spaceship. If the spaceship reaches the same vertical position as a virus pod, the pod is destroyed.

Flashcards with Negative Numbers