 |
| Source: Pixabay/Erika Wittlieb CC0 Public Domain |
With all the economic, political, and cultural uncertainty in
the world today we are all looking for something with Absolute Value.
Thankfully, we can find Absolute Value in mathematics.
In a previous post, “Why
Must Some Numbers Act Irrationally?”, I briefly mentioned the set of
numbers called Integers. Integers – the set of Whole Numbers and their
Opposites, ranging from Negative Infinity to Positive Infinity counting by
ones. Along with their identification as Positive – meaning to the right of 0
(zero) on the number line, or Negative – meaning to the left of 0 (zero) on the
number line, Integers have an Absolute Value.
“The Absolute Value of an Integer is the distance between the
number and 0 (zero) on the Number Line. The Absolute Value of a number a is written as |a|.”[i] The
bars to either side of the number are known as Absolute Value Bars.
When teaching the concept of Absolute Value to my students I
have then envision a trip to the nearest sizable city to our north and the
nearest sizable city to our south. Each city is approximately 20 miles from our
city. To help them, I model the location of the three cities on a vertical
number line on the white board with our city as 0 (zero). Going north, I number
the miles with Positive Integers and going south, with Negative Integers.
Seventh graders, nearly all of them anyway, are familiar with a
car odometer. After we have our crude map on the board, I ask them how many
miles would be added to the trip odometer if they drove to the city to our
north. Naturally, they answer, “Twenty.” Then I ask them if the odometer would
run backwards and subtract the miles when they drove back to our city. I’ve
never had a student argue that the odometer would run backward. They agree twenty
more miles would be added to the odometer total.
Once the students have absorbed the first part of the lesson, I
challenge them to determine what happens to the odometer if they drive to the
city to our south and back. They usually realize very quickly that even though
the numbers on the number line are negative, the odometer will still add them
to the total both going to the distant city and coming back.
This, I explain, is the essence of Absolute Value. No matter
which way you go from 0 (zero), right towards Positive Infinity or left towards
Negative Infinity, the distance you travel is always Positive. Learning and
understanding this concept is absolutely
essential if the students are to move on to the more intricate concepts of
adding and subtracting integers.
As always, I remain,
The Exhausted Educator
[i] Larson, Ron, and
Laurie Boswell. "Chapter 1, Lesson 1." Big Ideas Math: A Common
Core Curriculum. Erie, PA: Big Ideas Learning, LLC, 2014. 4. Print.
No comments:
Post a Comment