Tag: negative integers

Posted in Elementary School Math, Number Sense

Teaching negative numbers via the numberline with a twist

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One popular way of introducing the negative numbers is through the number line. Most textbooks start with the whole number on the number line and then show to the students that the number is decreasing by 1. From there, the negative numbers are introduced. This seems to be something easy for students to understand but I found out that even if students already know about the existence of negative numbers having used them to represent situations like 3 degrees below zero as -3, they would not think of -1 as the next number at the left of zero when it is presented in the number line. They would suggest another negative number and some will even suggest the number 1, then 2, then so on, thinking that maybe the numbers are mirror images.

Here is an alternative activity that I found effective in introducing the number line and the existence of negative numbers.  The purpose of the activity is to introduce the number line, provide students another context where negative numbers can be produced (the first is in the activity on Sorting Situations and the second is in the task Sorting Number Expressions), and get them to reason and make connections. The task looks simple but for students who have not been taught integers or the number line the task was a problem solving activity.

Question: Arrange from lowest to highest value

When I asked the class to show their answers on the board, two arrangements were presented. Half of the class presented the first solution and the other half of the students, the second solution. Continue reading “Teaching negative numbers via the numberline with a twist” →

Posted in Elementary School Math, Number Sense

Who says subtracting integers is difficult?

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Subtracting integers should not be difficult for most if they make sense to them. In first grade, pupils learn that 100 – 92 means take away 92 from 100. The minus sign (-) means take away or subtract.

After two or three birthdays, pupils learn that 100 – 92 means the difference between 100 and 92. The minus sign (-) means difference. The lucky ones will have a teacher that would line up numbers on a number line to show that the difference is the distance between the two numbers.

After a couple of birthdays more, pupils learn that you can actually take away a bigger number from a smaller number. The result of these is a new set of numbers called negative numbers. That is,

small number – big number = negative number

The negative numbers are the opposites of the counting numbers they already know which turn out to have a second name, positive. The positive and the negative numbers can even be arranged neatly on a line with 0, which is neither a positive nor a negative number, between them. The farther left a negative number is from zero the smaller the number. Of course, the pupils already know that the farther right a positive number is from zero the bigger it is. It goes without saying that negative numbers are always lesser than positive numbers in value. This is easier said than understood. When I tried this out, it was not obvious for many of the learners I have to give examples of each by comparing the numbers and defining that as the number gets further to the left the lesser in value.

Now, what is 92 – 100 equal to? The difference between 92 and 100 is 8. But because we are taking away a bigger number from a smaller number, the result must be a negative number. That is 92 – 100 = -8. Notice that the meaning of the sign, -, before 8 is different from that between 92 and 100.

What about -100 – 92? Because -100 is 100 units away from the left of 0 and 92 is 92 units away from the right of 0, the total distance or difference between them is 192. But because we are taking away a bigger number, 92, from a smaller number, -100, the answer must be negative (-). That is, -100 – 92 = -192.

And -100 – -92? Easy. Both are on the left of 0. The difference or distance between them is 2 but because -92 is bigger than -100, the answer should be a negative number. That is, -100 – -92 = -8.

We  shouldn’t have a problem with 100 – -92. These numbers are 192 units apart and because we are taking away a small number from a bigger number, the answer must be positive. That had always been the case since first grade.

Who says we need rules for subtracting integers?

Click the links for other ideas for teaching integers with conceptual understanding