Now we have words and symbols that refer to amounts of things, but those words and symbols, unless arranged into something useful, is just a jumble of stuff.
Question
In what way can we arrange the Counting Numbers in a way that's useful? Something visual, perhaps.Answer
We certainly can - it's called the Number LineAnalysis
Take a moment and look at the keyboard of the computer (or texting app on your phone) and notice that the letters, numbers, and symbols are all arranged in a set manner. This is what is called standardization. (It's why, no matter where in the world you go, the burger you get in a McDonald's is the same. The burger in New York City is the same as in Tokyo is the same as in Abu Dhabi - it's thanks to hamburger standardization).
For mathematicians, having a standard way of arranging the Counting Numbers is important. Ideally, it'd be great to lay them out in a row, the next number being 1 higher than the number below it.
Enter the Number Line!
How do we make it? First we draw a horizontal (which means left to right) line. Then we make marks on that line to indicate where on the line the numbers go, then we write the numbers above those little marks. Overall, it looks like this:
I know there's a whole bunch of boxes on this view but I'd like to focus on the red line going across - that's the actual number line. I've made little blue marks to help place where the Counting Numbers are along the line.
Keep in mind that the Number Line continues to the right into infinity - if we wanted to, we could find the number 1,000,000 - we'd have to scroll a long long way but it'd be there.
We're going to use the concept of the Number Line a lot as we move forward with more and more entries.
Vocabulary:
- Counting Numbers - The set of numbers that starts with 1 and increases by 1 (1, 2, 3, 4,...)
For more information check out these links (comment to add a resource to the list!):
https://apps.mathlearningcenter.org/number-line/
Where might you have come from?
Fact-orials Index
Numbers:
Where might we go?
Numbers:
Operations:
Operations with different kinds of numbers:
Related Operations:
Relations:
Graphing:
As a resource for the page, here's a nice, interactive number line that students can play with.
ReplyDeletehttps://apps.mathlearningcenter.org/number-line/
Cool - thanks!
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