Today I’m presenting with @pcipparone at the CGI Seattle conference. Our presentation is entitled “Bringing out the Unit Across Mathematical Domains.” You can check out the slides here.

One of the things we’ll be talking about is a new routine I created this year, called Unit Switch. The idea behind Unit Switch is to have students repeatedly explore the idea that when you change the size of a unit, you need more or less of them to make the same length. My interest in creating this routine came from a lot of work with 3rd and 4th graders around unit fractions, and seeing the struggle they had with understanding the idea that 1/4 is smaller than 1/3, because it takes four 1/4ths to make one whole unit, so the pieces are smaller than thirds, which require three to make one whole unit. In one of my student’s words:

I hoped that by giving my kids repeated experiences around changing the size of the unit, I could lay some groundwork for the important work they would need to do in the upper grades and into middle school around fractions, multiplication and division, and proportional reasoning. What I didn’t realize is that talking about units with my kids would also be a way to connect SO MANY different mathematical domains that we tend to teach discretely in elementary school. More about that in the presentation. But here, I wanted to share the Unit Switch routine, and I would love to hear your thoughts if/when you try it out with your own kids. Could I start my own #unitswitch hashtag? That would be crazy.

Here’s a quick rundown of how to lead a Unit Switch:

- Show an object (or a picture of an object).
- Show the first unit.
- Ask, “How many of these will it take to make this length?”
- Collect estimates – too high, too low, just right.
- Reveal (or collectively determine) how many – discuss if their estimates were close or not, why or why not.
- Show the second unit. Ask, “How many of THESE will it take to make this same length?” Again have kids turn and talk about estimates and share thinking. This time, when collecting estimates, compare to the original unit … do they think they’ll need more or less of the new unit? Why?

- Reveal how many. Ask, why did it take (more/less) of these? Focus discussion around the idea that as the size of the unit gets bigger/smaller, you need more/less of them to make the whole.

Here are a few photos of some Unit Switches we did in my classroom this year, to give you a mental image.

There’s more I’d like to say about this, but it’s time to go present. Looking forward to hearing your thoughts!

My suggestions are:

1. Kill off the name “unit fraction”. The confusion with “the unit” is dire.

2. Until kids are comfortable with for example “a fifth” of ” they should avoid “arithmetic” apart from “greater, or less, than …///////”.

3. “How many times as big as” is a lead in to fractions as numbers.

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