Write down 0.1, and add a tenth to it. Write that number down. Then add 0.2 to 0.1. Write that down. Then add one to 0.1.

In case it’s hard to see, in response to “What’s one tenth added to 0.1?” these students responded

- 1.1, then crossed out with a “2” written over it
- 0.01
- 0.11

When asked “What’s 1 added to 0.1?” they responded

- 0.2
- 0.2
- 1 0.1 (which looks like a mixed decimal to me which is pretty cool)

I’m trying to think through what class looks like tomorrow. It seems that I’ve got kids who certainly need time to work with 0.1, 3/10, 0.4 and other tenthy ideas. I also have students who don’t really have much of a grasp on how to use the hundredths place.

I’m going to take a page out of “Extending Children’s Mathematics” and give kids a version of this problem tomorrow:

Francine is making chili. She adds .1 grams of her secret ingredient to each liter of chili that she makes. If she has 5 grams of her secret ingredient, how many liters of chili can she make?

But what numbers would be most helpful to use in this problem? I’m struggling with that question right now. It seems like anything involving 0.1 or any tenths would be good, I guess. I think it’s probably most important for these students to relate decimals to whole numbers.

…and then the more practical concerns arise. What do I do for the quick finishers? They’ve done a lot of problems like this — will this problem feel tedious to them? Should I retrench with some of the part/whole stuff that we worked on yesterday? Maybe spend the first half of class solving chili problems and plan for a discussion, and then try this shading in activity again during the second half? Ooh, we could structure the second half of class around comparing 0.25 and 0.3, like my textbook says, or maybe the kids won’t be ready to discuss decimals that go into the hundredths…