Monday, January 30, 2012

Double Number Line Diagrams

6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

UPDATE (see below)

I just created a 9-minute video on the basic idea of double number line diagrams. Although double number line diagrams are specifically mentioned in a Grade 6 standard, if we want students to use them to solve ratio and rate problems in Grade 6, they really need to be familiar with the representations by then. That means they should be really introduced in elementary schools.

Anyway, I hope to create additional videos to elaborate how double number lines may be used to represent students' own reasoning, and eventually become their own thinking tools.

UPDATE: February 4, 2012
I just uploaded another video on double number line. I apologize for some background noises. Also, at one point I said something like "to go from 0.8 to 0.1..." when I really should have said "to go from 0.8 to 1..." The app I'm using does not allow me to edit the video, and I didn't want to re-do the whole video. So, please excuse my errors.


Claire E. Hallinan said...

I have missed Double Number line diagrams in CCSS since I have focused on k-5 so much. It is a very interesting approach. I agree with we should start teaching the concept in the early grade to prepare but I am a little confused. How do you determine multiplication and division?
Thank you for sharing.

Leigh Ann said...

My daughter is taking sixth grade math and learning all this. So in your video with the length and weight of the wires you show how to make the two lines, one for length and one for weight, but I don't see how you use the lines to solve the problem.

Tad said...

Leigh Ann,

Thank you for your comment.

When teaching (or learning) about the four arithmetic operations, there are two ideas we need to keep in mind. The first is that students need to understand which of the four operations is needed to solve a problem. The second is that students need to understand how to carry out each of the four operations. Neither one is sufficient by itself - although the availability of calculators make the second one perhaps a bit less crucial. There are no replacement for the first one, though.

Different representations are often useful for helping students with one of these two ideas, but not necessarily with both. As you noted, double number lines are probably much more for the first purpose - knowing what operation to use.

When students represent their reasoning on a double number line - and when they get comfortable with the representations - some may start reasoning with double number lines. However, I think their own reasoning must precede the representations on double number lines. You can see some examples of this in my discussion on multiplication and division of decimal numbers I wrote in November, 2008.

Anonymous said...

Thank you for this video.

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Elaboration of Georgia Performance Standards by Tad Watanabe is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.