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.
In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]
Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]
Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]