The goal of this lesson is to provide a concrete visual model so that students understand WHY they get a positive or negative results when multiplying and dividing integers.
Setting Up the Math Lesson:
Ideally, you will be able to project the google slides for the whole class to see as they go through the lesson.
Then you can simply print the student handout to go along with the slides and discuss as you go through.
If you don’t have access to a projector, you can also use a hands-on tool such as two-colored counters or algebra tiles.
Then students will ‘build’ each problem and manually flip the counters or tiles over as they multiply.
Multiply & Divide Integers Lesson:
Once students have the handout, you’re ready to start the lesson.
To begin, you will want to start with a simple reminder of what multiplication means. You can look at arrays, equal groups, repeated addition, etc. using whole numbers.
The lesson starts with 3 x 5, but if you feel your students need even more reinforcement before moving onto negative values, discuss a few more problems and draw a visual model.
Students MUST have a solid understanding of what multiplication represents before they can think about how that applies to negative values.
Once they understand, ask them to draw or model with tiles the expression 3 x (-5).
They should hopefully see that this means 3 groups of -5 for a total of -15, as shown on the google slide.
Again, if there are any misunderstandings about where the picture came from, or where the final answer came from, talk through and model a few more expressions before moving on.
Why Does a Negative times a Negative Equal a Positive?
Then the lesson turns to negative times negative expressions.
Hopefully by shifting the language of the negative sign to mean “the opposite,” students will be able to see and make sense of this without it being another nonsensical rule to memorize.
As the google slides show, if you think of an expression such as (-3) x (-5) as “the opposite of 3 x (-5)” then what we’re saying is that (-3) x (-5) is the same as the opposite of (-15), which would be +15.
So if we know that a positive times a negative is negative and a negative times a negative is the opposite of that, then the solution must be positive.
That may be a bit confusing to read here, but I think the google slides do a better job of showing visually what I mean.
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Divide Integers:
Lastly, the lesson shifts to division of integers, which students should see offers the same results, as division is the inverse of multiplication.
After a couple more examples of visualizing division, students have a simple “quick check” to put their new understanding of integer operations to use.
And if you need more review and practice with integer operations, check out the list at the end of this article! I have even more resources to help you help your students.
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{Click HERE to go to my shop and grab the FREE Multiply & Divide Integers Lesson!}
More Integer Operations Resources:
