Monthly Archives: August 2015

“What’s a Good Question?” Activity

Today I did Alex Overwijk’s “What’s a Good Question?” activity, down to using the very same image.

Here’s the Google Presentation I made to go with the activity:

(Link to the document if the above embedding doesn’t work)

One think I did to add to Alex’s activity was at the beginning, when my students (who are seniors) were having trouble writing down more than a few questions (even though I asked for any and all questions!). I decided to talk about the paper clip challenge involving divergent thinking. They were inspired when they heard that kindergartners do the best on the “test”.

After that short 5-ish min test (I had them do the challenge and then just talked about it, but next time I might show the video!), students went back to the question-writing with more vigor, and the rest of the lesson went very well.

Here are some questions:



How much glycogen does it need to survive?

How much glycogen does it need to survive?

Best question (my opinion) and the one we actually tackled:

How many ppl would it take to hug the entire trunk?

How many ppl would it take to hug the entire trunk?

Here are some of the answers to “What makes a good question?” snowball:






And then we had time for the “tree hugging” question!





There were 15 people in the class at the time (of course nearly half the class is dismissed on a field trip when I go to do this critical lesson!) so we were able to test out and see if our estimations (ranging from 13 to 16 people) was reasonable.

One Big Tree!

One Big Tree!

They agreed that it looked pretty reasonable!


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Understanding Radicals

Vertical non-permanent surfaces (aka whiteboards hanging from command strips on the wall) gives every activity a “new look”. This activity, done during the early “let’s review our algebra” period of Precalculus gave me a new appreciation for how little students understand the procedures we teach them through the years.

Here’s the website that gave me the idea:

Nrich’s Nested Surds

Here’s the Google presentation I made from it:

(Link to the document in case the above embedding doesn’t work.)

I did visible random grouping (I’ve started to use this website because how straightforward it is. Make sure you select the “new window” output format.) in groups of 3. With 21-22 students, I had 7 or 8 groups. I showed students the first slide and had them “test out” numbers. Once they did a handful of perfect squares, I let them try it out on their calculators, for non-perfect squares.

\sqrt{a} \times \sqrt{b} = \sqrt{ab}


Here’s what shocked me: these precalculus students worked on this first problem for about 15 minutes[1]. Nobody had gotten even remotely close (okay, one group came up with a rule “if a is even and b is even, it works!”). I was within a few minutes of pulling the entire class in and having them sit down while I explain it all (as if they’d learn & understand any better, but I was panicking!). Then, within a minute or so, every group started “getting it”. It helped that they could look around (since all the whiteboards are vertical), but that didn’t help as much as I thought it would. Students must still have some inhibition along the lines of “seeing other groups’ work is cheating.”

The second problem (\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{frac{a}{b}} ) went a little faster as did the third (a\sqrt{b}=\sqrt{ab} ). I especially liked the third because it is a common mistake, so this activity gives us some ground for discussion when that type of mistake occurs in the future. Unfortunately that was as far as we got before we ran out of time.

It surprised me how difficult this activity was for these students, who should have seen radicals 2 or 3 times before in their math classes. The Alg II teacher commented that perhaps it was the open-endedness of the activity that tripped them up, but to me that simply reveals a weak understanding of the underlying math. Regardless of how open-ended an activity is, students should know and be able to apply how radicals work.

Using the vertical whiteboards, I appreciated (A) how quickly students got to work, (B) how long they worked, and (C) how I was able to quickly assess where groups were and get them back on task. Unfortunately this particular group seemed especially prone to getting off-task, distracting other groups, having conversations that were not related to math. I’m sure that standing contributed a little to this, if only because they aren’t used to standing during most classes. However, we had a good “chat” and I’m happy to report more on-task-ness more recently.

Thanks to John Golden for sharing about the Nrich site and thanks to Alex Overwijk for sharing about vertical whiteboards & random grouping!


[1] Actually, I have no idea how long it took–it might have been 30+ minutes. I just know it felt like a long time and it was at least 15 minutes.

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Hanging Whiteboards and Cards

A.k.a. “Vertical non-permanent surfaces and visible random grouping”.

Thanks to Alex Overwijk (@alexoverwijk) for introducing the idea and, as one blogger put it, “getting me fired up for this idea” and thanks to Graham Fletcher (@gfletchy) for suggesting to drill holes in the whiteboards and using command strips to hang them from the wall. This idea really hit home with me because I travel between classrooms (three!) and the teacher(s) I share rooms with are not yet sold on the idea of putting whiteboards all around the room.

When I later read his blog post about it, I realized that he only had one hole in the boards which allowed the boards to be more vertically oriented. I envisioned them being horizontal (see below) so the boards wouldn’t “wiggle”. Hopefully students still have enough room. Next time I go to Home Depot, I think I’m going to get 3′ x 6′ boards instead of 2′ x 3′. (Six 2′ x 3′ boards cost less than $15!! at Home Depot!)

Ready to go!

Ready to go!

Borrowed a door-knob-hole-driller (technical name?) from the school!

Borrowed a door-knob-hole-driller (technical name?) from the school

Lots of sawdust!

Lots of sawdust!

Final count: 15 whiteboards, but to be shared between 3 rooms :(

Final count: 15 whiteboards, but to be shared between 3 rooms

Easy to use!

Easy to use!

Command Hooks!

Command Hooks!

Sometimes I just used nails instead.

Sometimes I just used nails instead.

I did just a little bit of this (vertical whiteboards) last year, but the boards had to be propped up on tables against the wall or against a stack of heavy textbooks–not ideal. I’m going to be doing this much, much more this upcoming year!


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