Sunday, November 18, 2012

The Number-line Code

This one grew out of some time I spent recently helping a family first-grader with her subtraction homework. I made up some sheets with numbers and letters. My original thought was just to make the practice sheets more interesting by having the answer spell out a word, but I noticed my tutoree (who naturally has very good math genes) had, without prompting, started using the code key as a number line to figure out the answers.

The more I thought about it, the more I liked the idea of using this approach for a wide range of problems. For the very early grades, it teaches numbers and letters. It has great appeal for kids (particularly if presented with the right air of mystery -- I'd suggest a pirate motif). It reinforces the number line concept and the essential idea of looking things up in tables.

Here are some sample problems

For those learning to read, present it as a straightforward code:

PIRATES LOVE 7-15-12-4

For slightly more advanced students, replace the numbers with problems

PIRATES LOVE

10 - 3

10 + 5

6 + 6

6 - 2

For even more advanced students, make it a more explicit number line exercise

PIRATES LOVE

7

+8

-3

-8

You can even play with functions by using the old SAT trick of using a circle to represent x+1 and a triangle to represent x-1 (or any other functions you can think of).

triangle 8
circle 14
circle 11
triangle 5

I'd suggest using this technique frequently enough to keep the familiarity high. It also offers extensive opportunities for teaching across the curriculum.

Anyone have any other ideas?