Simply Impossible

I’ve been working on a foldable for my AP Stats class for three weeks. Honest. I keep sketching it, thinking about it, discussing it with my carpool buddy.

I want my students to have a quick reference for all of the tests & intervals we’ve been learning. For proportions and means. One and two samples. My key issue was “how the heck do I set this up?” Organize it by means? Proportions? I found this awesome study guide, which helped me be sure I was catching the info I needed, but I was still stuck.

My students are getting hung up on which test to do where, and a list of tests, with conditions and calculations and calculator names, wouldn’t fix that. I’ll spare you my three weeks of circular thought process and cut to the chase–here’s what I came up with:

Some notes: It does not line up perfectly. I quit after an hour. It’s pretty darn close, at least on my printer. The margins are (intentionally) set outside the printable area, so the outer edges don’t show up (also why I center justified the tabs). When you print you get an error message that some of the document lies outside the printable margins; do you want to proceed? Just hit yes.

We started today and so far they found it very helpful. I felt kind of useless because I was basically wandering around while they started filling out the two-sample part (test tomorrow) and answering minor questions. But I think the foldable (especially the concept set up, not the technical part) has taken me longer than any lesson I’ve done in a very long time. It was especially frustrating that all that got me was two single pages–not exactly impressive looking. Here’s hoping its helpful!

What’s your favorite foldable format?

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Around the Room: Simplifying Radicals

In Honors Advanced Algebra we’ve been simplifying radicals. What’s going well? They get the concept of inverse operations, and that the power and root (they even call it the index) need to be the same. But for many of them, what comes next is just…random. Sometimes they cancel out the power and root, but leave the number under the radical. Sometimes they take it out, but also leave it in (so its there twice). There doesn’t seem to be a lot of rhyme or reason to what’s happening, so its tricky to figure out the misconceptions.

And this might be one of those places where the issue isn’t misconceptions…it’s effort.

I find that confidence issues can be one of my biggest hurdles.

Lack of Confidence: “This looks way too hard. I don’t know what you want me to do. I can’t do this. These are too long/complicated/difficult/etc” Result: Skip it. I don’t know how to do this, so I won’t.

Overconfidence: “Obviously. This is very easy. I will be able to do it, so I don’t need to actually do it right now. I will later. In fact, this will be so easy I do not even need to do my homework on it.” Result: Skip it. I don’t need to do this, so I won’t.

Sometimes, we just need to practice. I suspect most of my students are in Camp 2: Overconfidence here, so if I can make them practice in front of me, they will. But the more I make it interesting and engaging, the less annoyed at me they will be.

Solution: Around the Room. (Some call these “Scavenger Hunts”). Directions below.

Structure: Print out the full document. The first page is for the teacher, mix the others up (alpha order works nicely) and post around the room. Students start at whatever problem they choose (I always tell them no more than 4 students per problem). I have them write the problems in the notebook, with the letter in the margin, but you can also provide a template for the problems*.

Directions: Ignore the top line (we’ll come back to it later). Write the second line (larger font, this is the problem) in your notebook, with the letter in the margin. Solve the problem. Once you have a solution, look around. That will be the top line of one of the other sheets. Go there, and write the letter in the margin, and then the problem. Solve it, then repeat. If you solve everything correctly, you will end up back at the first problem when you are done.

When students are done, just check the letters. If they’ve done it correctly, they will have the sequence you see on the first page. Students find a lot of their own mistakes when they can’t find the next problem, or when they only do four before looping back.

This one was really quick for us, but some take the better part of a period. An obvious caution: Triple check. Resident (student teacher) 2 was not good about this and routinely had multiple mistakes, so students would get stuck because the right answer truly wasn’t out there. Not all of them work well as self-correcting, and it still works fine without it. I just have students come check in with me to check their answers, either in stages or when they’ve finished.

Do you use this structure? What are your favorite ways to get students some practice?

*With most things, once students are familiar with it, they no longer need the template, but the first few times it puts everything in the right place. Muscle memory, I guess?

AP Stats Project: Polling

We just started a quick little project in AP Stats, inspired by one of the extra examples in the text. The example gave two pieces of polling data from a presidential approval poll–seems like that isn’t that hard to find and real data is always better.

So a project was born–head over to RealClearPolitics for a treasure trove of polling data, often including the full report from whomever conducted the poll.

I’d like them to analyze the methodology (for review) and then do both a confidence interval and a hypothesis test on the difference of the two proportions. Put it all together and draw a conclusion…did opinions change? Why? (Both from a survey design perspective and from a timeline perspective.) Here’s what I gave the students:

I am not very good at writing rubrics, but I try. My carpool buddy told me she always writes the 3 column first, which is excellent advice but I had already written it. Oh well.

I would love any feedback–it isn’t due til Monday, so we’ll see!

How many projects do you do in your classes? Do they always seem to get squeezed out?

Equation Strips

When I saw Radical Equation Strips by Miss Calcul8, I was intrigued.

She downplayed their genius in her post, but I wasn’t fooled. I printed them out, using one color per problem, made 15 sets (split into two problems each, so enough for 30) and had them laminated (and then had to cut them all again).

Instead of giving students a format for writing down the steps I told them to write each problem in their notebook, adding in any steps I missed. They did one of the problems with a single radical, then traded with the pair behind/in front of them, then did the other single-radical problem. Then they did one of the two problems with two radicals. This was enough for them to write their own steps for solving radical equations. We did one more problem together, using it to refine the steps for solving a radical equation, and most students felt they were good to go.

This activity went so well, we tried it again, with exponential equations. These were actually made by my resident (student teacher), as well as a logarithmic set.

[OMG this is the first time I’ve ever successfully embedded something!!!!!!!]

I love that it gives students a chance to see all of the steps, and I wish I had used this with equations in my lower level classes. Especially for students that make so many computational errors, seeing and writing correct steps but with their own input is so powerful.

Can’t wait to use this in our lower class!