Tag: absolute value

Posted in Number Sense

Teaching absolute value of an integer

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integers and algebraic reasoning

The tasks below are for deepening students’ understanding about the absolute value of a number and provide a context for creating a need for learning operations with integers. You may give the problems  after you have introduced the students the idea of absolute value of an integer and before the lesson on operations with integers.

Tasks (Set 1)

1) Find pairs of integers whose absolute values add up to 12.
2) Find pairs of integers whose absolute values differ by 12.
3) Find pairs of integers whose absolute values gives a product of 12.
4) Find pairs of integers whose absolute values gives a quotient of 12.

These may look like simple problems to you but note that these questions involve equations with more than one pair of solutions. The problems are similar to solving algebraic equations involving absolute values. Problem 1) for example is the same as “Find the solutions to the equation /x/ + /y/ = 12. Of course we wouldn’t want to burden our pupils with x’s and y’s at this point so the we don’t give them the equation yet but we can already engage them in algebraic thinking while doing the problems. The aim is to make the pupils  be comfortable and confident with the concept of absolute values as they would be using it to derive and articulate the algorithm for operations with integers later in the next few lessons.

Tasks (Set 2)
1) Find pairs of integers, the sum of absolute values of which is less than 12.
2) Find pairs of integers the difference of absolute values of which is greater than 12.

Encourage students to show their answers in the number line for both sets of task.
Posted in Elementary School Math

What is an integer?

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Here are some ideas pupils need to learn about integers:

•A number represents a quantity. An integer is a type of number. An integer represents a quantity.

•Integers are useful in representing quantities and includes opposite sense. For example, going up 5 floors and going down 5 floors can be represented by +5 and -5 respectively. The sign ‘+’ represents up and ‘-’ represents  down. The ‘5’ represents the number of floors.

•The integer +5 is read as “positive five” and NOT “plus five”. The integer -5 is read as “negative five” and NOT “minus 5”.

•The words positive and negative are descriptions of the whole number 5 while the words plus and minus describe operation to be done with the numbers. That’s why it doesn’t make sense to read the integer -5 as “minus 5”. From what number are you subtracting it?

•The number 0 is an integer which is neither positive nor negative.

•Integers can be represented in a number line. An integer and its opposite are of the same distance from 0. For example, -4 is 4 units to the left of zero so its opposite must be 4 units to the right of 0. This integer is +4.

integers

Problem: The distance between two integers in the number line is 4 units. If one of the integer is 3 units from zero, what could be these two integers?

•The distance of an integer from zero is called the absolute value of the integer. So the absolute value of -4 is 4 and the absolute value of +4 is also 4.In symbol, /+4/ = 4 and /-4/ = 4.

Of course, merely explaining to students these ideas and giving them lots of exercises will not work. It will never work for many of them. Teachers have to design tasks or activities pupils can work on so that students can construct their own understanding of these ideas. Teachers can help scaffold their learning through problem solving tasks and through the questions and feedback they will provide the students.

Next post on this topic will be about absolute value and operations with integers.