Adding Negative NumbersNegative numbers are another source of frustration to many budding mathematicians and scientists, and not addressing this issue can cause consistent errors throughout a child's learning in maths. To tackle this problem a clear and consistent approach is required. As always, understanding needs to be backed up with solid practice as for most students maths concepts need to be reinforced in order for them to be retained. There are several steps involved. Each step is very simple and together they allow us to break any sum into a series of simple instructions that can be placed on a number line in order, giving the correct answer to the problem 100% of the time. Step 1: Give Us A Sign!
The easiest way to learn how to add negative numbers is to start with normal sums. Every number has a sign in front of it. Unsigned numbers are all positive; we know this, but rarely do we see them with their sign in front of them. The image to the right shows four sums that have been re-written with the positive sign in front. Note that if the sum starts with a negative number, the leading number already has its sign.Step 2: Make Bubbles
The mantra for this step is "sign and number". A circle is placed around the sign and the number following it, making a bubble. This is done to EACH sign and number pair in the sum. When the process is complete, there shoud be no loose numbers or signs left. The image to the right shows this process being applied to one of the sums shown earlier.These bubbles then become the direction and distance for how to move on the number line. Let's see how this works with a short video demonstration: Step 3: Using A Number Line When using a number line for sums, one must always start at ZERO. Because we are investigating numbers with possible negative answers, the number line must have zero in the middle and go the same distance in both directions. In the examples here we will use a -10 to +10 number line, as shown below:
Number lines are best drawn by the child as this helps reinforce their learning of this topic. For convenience you can also choose a printable number line from a range of different sizes. Note that this number line has the positive and negative ends clearly marked. This is important for making the instructions in the sum easy to follow. The first bubble is the first instruction. Starting from zero, we move toward the sign the correct number of steps. In this example, we move toward the + sign three steps, as seen below:
So now we are at +3. Now we START FROM HERE and follow the next instruction which is to move toward the - sign five steps, as seen below:
We have now run out of instructions, so we cannot move any more. The answer to the sum is the place where we end up, which in this case is the value -2:
Any Number Of Instructions This method works for any number of instructions in a sum and if followed accurately, it will give 100% correct results every time. My personal experience indicates that after a few solid sessions of drawing number lines and solving sums on them they retain the concept and rarely if ever need to refer to the number line again for simple negative answers. In order to allow your child to practice this concept, please feel free to download and use this negative numbers practice sheet. Return from Negative Numbers to Basic Math Help or return to the Green Planet home page for more Solar Power Facts.
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