Modeling multiplication

Modeling multiplication of integers with number counters is the goal of this lesson.

Number counters


For some of the models, you will see how the concept of repeated addition can be used to do the modeling.



For example, the meaning of +3  × +2 is to put three models of 2 down. Since there are 6 blue counters now and they are all positive, the answer is + 6.

Modeling of 3 times 2 with number counters


How about  +4  × -2 ? Well, it means to put down four models of negative two.

How to multiply 4 by -2
Modeling of 4 times -2 with number counters


Since there are 8 red counters now and they are all negative, the answer is - 8.

In some cases, as opposed to adding counters, you will need to take out some counters.

For example, how do we model -4 × + 2 ?  This one is a tricky math problem! First, you need to understand the meaning of -4 × + 2.

As you can see in the illustration below, it means to take out four models of 2 (or take out four models of two blue counters).

So far though you do not have any blue counters to take. Therefore, you need to put it down. The way you do that is by putting a zero down. The zero will have 8 blue counters and 8 red counters.

Notice that by putting a zero down, you are not changing the problem since a zero is nothing.

How to multiply -4 by +2
Model of negative four times positive two


After removing the 8 blue counters, you are left with 8 red counters. The answer is -8.

Model of -8




Recent Articles

  1. How to Convert Square Feet to Acres

    Dec 14, 18 04:05 PM

    Here is how to convert square feet to acres - To convert square feet to ...

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to Convert Square Feet to Acres

    Dec 14, 18 04:05 PM

    Here is how to convert square feet to acres - To convert square feet to ...

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz