Tuesday, January 8, 2013

Birds On A "Number" Line

What do you see?  

Call me crazy or math nerdy but I see a number line!

The traditional number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point.

In contrast to a traditional number line, an "open" number line is just an empty line that can be used to record children's addition and subtraction strategies. Only the numbers children use are recorded and the addition or subtraction is recorded as leaps or jumps.

Here are some examples of open number lines:

This example shows a student using incremental strategies. This means adding up in "chunks" or increments. One benefit is the students decide the "chunks" depending on the number choices.

This example shows a student using compensation. This means they add or subtract to adjust a number to make it friendly, solve the problem, and then readjust to find the solution.
This example shows a student a counting up for a subtraction problem. Look at the place value the student uses to compose and decompose the numbers.

Aren't open number lines awesome?  What a great way to model thinking!

So how do the birds on a line remind me of a number line? The birds just alway seem to be evenly spaced on the line so it just got me thinking about number lines!

Here is a problem to ask your students:
Name points A, B, C and D on the number line.  Justify your solution.

The next time you see birds just hanging out on the lines, I dare you not to think of a number line!

Can you think of any other real-life objects that remind you of number lines?

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