Multiplying with Negatives

I like to teach multiplying with negatives in a similar way to how students learned multiplication at primary school.  As a quicker and more efficient form of long addition. This way students consolidate addition and subtraction with negatives and extend that to multiplication and later division.

Multiplying with negatives

-2 x 3 is three lots of negative two or more precisely, positive three lots of negative two.
So -2 × +3 = + -2 + -2 + -2 = -2 -2 -2 = -6

2 × -3 = – +2 – +2 – +2 = -2 -2 -2 = -6

-2 × -3 = – -2 – -2 – -2 = + 2 + 2 + 2 = +6

Multiplying with Negatives

We work through a couple of problems this way on mini-whiteboards. I ask the students to show their working only when they need to as I’m aiming for them to naturally progress on to mental methods rather than written working. When the students generate their own rules of arithmetic as a natural progression of what they already understand they are more likely to apply that learning correctly in the future.

Differentiating for abilities

The less able students have a laminated number line to work on along with a timetables grid. The main learning point here is writing out the multiplication as a long addition or subtraction not necessarily being able to perform the arithmetic.

I challenge the more able students to investigate what happens when a negative is raised to an even or odd power. This continues their exploration of multiplying with negatives into index notation.

Related Lessons

Revising Calculations with Negative Numbers

Revising Calculations with Negative Numbers

Students revise how to add, subtract, multiply and divide with...
Read More
Adding and Subtracting with Negative Numbers

Adding and Subtracting with Negative Numbers

Adding and subtracting with negative numbers is taught through the...
Read More
Dividing with Negative Numbers

Dividing with Negative Numbers

Students learn about dividing with negative numbers using written methods. ...
Read More
Multiplying with Negative Numbers

Multiplying with Negative Numbers

Students learn about multiplying with negative numbers.  As learning progresses...
Read More

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Area of Compound Shapes

To find the area of compound shapes students need to understand what the word compound means.  Therefore, I ask students to discuss in pairs a definition for the word compound and to extend it to include the shapes below.  As a result of their learning in science students agree that a compound can be defined […]

Priorities for the Spring Term

At the start of the Spring Term these are three main priorities for me as the Head of Mathematics.

Mutually Exclusive Outcomes and Events

I teach mutually exclusive outcomes directly after students have encountered Venn diagrams. This is the fifth Year 8 Probability lesson.