# Maths - Negative thinking

If there is one rule that pupils of all ages and abilities remember, it is that two minuses make a plus, writes Craig Barton. This all well and good when multiplying and dividing, but can lead to a whole world of problems when applied to addition and subtraction problems.

Rules, without understanding, can be very dangerous and are the root cause of many misconceptions. You have to get pupils early and get them thinking about the questions themselves.

I have found that young pupils respond quite positively to thinking about a bowl of soup. Imagine you have a lovely bowl of soup that has a current temperature of 10 degrees. We also have ice cubes, each of which takes one degree off the temperature, and we have fire cubes (bear with me here!), each of which adds 1 degree to the temperature. Now, what happens if we add three ice cubes to our soup? Well, our soup gets three degrees colder, and we have 10 + -3 = 7. If we now dip our hand in and take out 4 fire cubes, we have 7 - +4, which must equal three degrees.

Once pupils have got their heads around this, it is time to progress to the likes of 4 - -5 (a temperate soup of four degrees has five ice cubes removed, so the temperature goes up to nine degrees), and the potentially deadly -4 + -5 (a chilly soup of temperature -4 degrees has a further five ice cubes added and goes down to -9 degrees).

Where to find it

www.mrbartonmaths.com. On the TES website, Negative numbers (MEP, Year 7, unit 15).

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