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…

• How are they with connecting “half” with 0.5? I think I’d try to get more real objects. What is half an apple? One third of a pie? One fourth of the classroom floor? Then work towards one tenth. Abstract squares and grids may be hard to connect for them right now?

Maybe you can have one half of the class find one tenth of a pizza and the other half of the class find one one-hundredth then add the pictures? Sorry. I don’t have much here.

• Teachers respond really well to this activity from Anne Roche here in Australia, when I get them to trial it. http://files.eric.ed.gov/fulltext/EJ891799.pdf

• I’m curious how are decimals defined in this class. What do you want students to think the number 2.31 means? The .11 answer to the first question because if one says take a number and add 10% it one thinks about that as taking the number plus 10% of that number. If .1 is the same as 10% then .11 would be a correct answer.

• By coincidence, it looks like we are hitting the same topic at the same time.

This past weekend, I tried a slightly different introduction to decimals using binary. My thought was that binary had fewer variables and that the place value would be easier to keep track of:

http://mikesmathpage.wordpress.com/2014/04/05/fractions-and-decimals-in-binary/

Yesterday my son was asking about base 4, so we talked about the value of .11111….. in different bases and then re-watched Vi Hart’s video about why .99999…. = 1 in the evening:

http://mikesmathpage.wordpress.com/2014/04/08/the-number-0-11111/