I have a big number line ($^-10$ to $10$, say) above or along the top of my whiteboard. "I believe that adding and subtracting with negative numbers makes sense. Thanks to Alan Mesfin who suggested an alternative of tying on helium balloons (as in the film "Up") instead of adding puffs of hot air to represent adding a positive number. My balloon ends up at height +5.Įventually, we want students to read the calculation as "Four add negative two, subtract positive five, subtract negative one, add positive seven" (or replacing the operation words add/subtract with plus/minus, but always insisting on positive and negative for the signs accompanying the numbers), and think to themselves "Four, down two, down five, up one, up I add two sandbags (down two), subtract five puffs of hot air (down five), subtract one sandbag (up one), then add seven puffs of hot air (up seven). We can now describe a calculation such as 4 + (-2) - (+5) - (-1) + (+7) in the following way: In this model, we represent positive numbers as 'puffs' of hot air, and negative numbers as sandbags. The first model we offer is the hot air balloon, as seen in the game Up, Down, Flying Around. There are four possibilities that we need to be able to understand with our models:
#Negative plus negative how to
We will make suggestions about how to use language precisely in order to support the understanding of the distinction between operations and directed numbers. The models for teaching addition and subtraction of positive and negative numbers that we share in this article are designed to lead to understanding. For example, we have all heard students say things like "minus four minus two equals six, because two minuses make a plus!" We are often frustrated when we hear students say "Two minuses make a plus", because it shows a rote-learned phrase that is often misapplied. The original article is contained within this version.
You would then move into in a positive direction: If you use a subtraction sign, the two negatives cancel out. In order to move in a negative direction from a smaller negative number to a larger negative number along the number line, you must use an addition sign. The equation for the line above must be written as: We have started with -1, moved three spaces to the left, and ended at -4. Here is an example where we are only using the negative number line. Since the answer is -2, we've now crossed over to the negative number line, where we do not have natural numbers. As soon as you cross over to the negative number line, you’re no longer dealing with natural numbers. It's simply a whole number that's always on the side of the number line that's right of zero. A natural number isn't a fraction or decimal. Most of the time, the positive numbers you'll see on a number line are natural numbers. Shifting right to left along the number line indicates a move in the negative direction. When you move left to right, you are heading in a positive direction. Any positive integer right of zero is part of the positive number line. Any negative integer left of zero is part of the negative number line. Number lines are linear representations of numeric values.
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