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Your email address will not be published.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

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]