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.
As learning progresses I pose questions with numbers that can not easily be calculated on a number line. Questions such as, -15 × -8 and -60 × -10. To attempt these questions students would need have made the leap from long addition to the more efficient method of short multiplication.
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.
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