This comes via submission. Thoughts?

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…

I put “0.1″ on the board and asked students what they’d call this. A kid said “one tenth,” but that quickly became controversial.

Question: how do you think these kids are seeing 0.1?

"Find the midpoint of the line segment connecting (2,5) and (2,396)," at the beginning of the unit. Can you predict the top three responses?

— Michael Pershan (@mpershan) April 7, 2014

What would you predict? Here are some twitter responses:

@mpershan Is (0,391) one of them? That seems like a way to get an answer from those two numbers.

— Evelyn Lamb (@evelynjlamb) April 7, 2014

@mpershan (3.5, 199) (2, 200.5) (2, 198)?

— David Wees (@davidwees) April 7, 2014

@mpershan (2,198) is probably one of them. Maybe(1,198). But I am otherwise stumped. Oh! (201.5) maybe?

— Christopher (@Trianglemancsd) April 7, 2014

@mpershan er…(2, 195.5) as a top answer.

— Christopher (@Trianglemancsd) April 7, 2014

@mpershan I’ll bet at least one of the top 3 responses includes *two* points.

— Chris Lusto (@Lustomatical) April 7, 2014

—

Here’s your answer key…

**First Place:**

**Second Place:**

**Third Place**

I keep on seeing this in my Geometry classes this year. Tasked with finding the area of a right triangle, kids move toward the hypotenuse even if two of the other sides are given. Then they end up stuck looking for a height that they can’t find.

I’m pretty convinced — based on talking to kids and looking at their work — that this is all about how they see right triangles. These kids must be seeing hypotenuses as bases, and it must feel weird for them to treat the legs as bases. Or maybe instead it’s about the height? Maybe it feels strange to them to use a leg as a height?

Shared by Tracy on twitter, and a great conversation ensued.

@TracyZager @mpershan My first thought on this to see where students are making the mistake. pic.twitter.com/7X7spt0BMI

— Bryan Anderson (@Anderson02B) April 6, 2014

@mpershan @Anderson02B I think I would go concrete right away, and link it to sharing. If this were a brownie, which piece would you want?

— Tracy Johnston Zager (@TracyZager) April 6, 2014

@mpershan @Anderson02B @TracyZager This one is a bit different, tho. Kids seem to cue in on the equal widths here.

— Christopher (@Trianglemancsd) April 6, 2014

@Trianglemancsd @mpershan @Anderson02B @TracyZager OK, my turn to be an idiot, but that 3/5 triangle problem requires some tricky solving.

— Michael Doyle (@BHS_Doyle) April 6, 2014

@mpershan @TracyZager I'd bet that most 7th grade students have never seen the problem with a shape other than a circle or rectangle

— Bryan Anderson (@Anderson02B) April 6, 2014

@BHS_Doyle @mpershan @Anderson02B @TracyZager So this task needs revision and should only ask about 1/5 or 4/5.

— Christopher (@Trianglemancsd) April 6, 2014

We’ve been studying graphs of rational functions in Precalculus.

Me: “Take 1 minute with your group: what will the graph of y = x/(x+1) look like?”

One group, during discussion, asserted that it had to be a line, using a sort of process of elimination: it’s not a parabola, it’s not cubic, it’s not a hyperbola.

Interesting, right? Why does this seem like a linear equation? I guess that it sort of looks like one…