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.
-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
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.
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.
If you’re interested in teaching this lesson to your students click here to go to the lesson page.
When calculating instantaneous rates of change students need to visualise the properties of the gradient for a straight line graph. I use the starter activity to see if they can match four graphs with their corresponding equations. The only clue is the direction and steepness of the red lines in relation to the blue line […]
Fractions, decimals and percentages are ways of showing a proportion of something. Any fraction can be written as a decimal, and any decimal can be written as a percentage. In this blog I discuss how to use the place value table and equivalent fractions to illustrate how fractions, decimals and percentages are connected. You can […]
In my experience, students, in general, find the concept of a mean straightforward to calculate and understand. However, the mean alone does not provide a complete picture of a set of data. To achieve this, a measure of spread is also required. The range is the simplest measure that can be used for this. Not […]