Pencil Sharpener Problem

Let’s start with a student sharpening a pencil as quickly as he can.



Let’s add a second student sharpening a pencil as quickly as he can.



And then, we’ll add one more student sharpening a pencil as quickly as he can.



If all these guys kept going at the same rate they were in the video, how long would it take for them to grind away 100 pencils?


The Best Classroom Management

Okay, blogosphere: I need your help. Seriously.

For the last couple of years, when I get asked about my classroom management, I’ve responded:

The best classroom management is a meaningful curriculum.

I love that line. What I want to know is if it’s a quote that I have stolen from someone that I haven’t remembered or recognized.

Can you help me out? Are you aware that the above line belongs to someone else? Let me know in the comments so that I can start giving credit where it’s due.


Thanks everyone.



Three-Ring Binder Problem

This is a bit of a sequel to The Bowl Problem, which was one of the first video problems I ever made. But I gave the bowl problem to a group of students and a handful of them were skeptical of measurements taken straight from the video. So, I gave them a chance to solve the problem right in my classroom.

To solve this one, you may want a close-up shot of the cabinet. So, here:

The cabinet in question in my classroom

The cabinet in question in my classroom

You may also want a close-up shot of the binders. They are basic 1-inch, empty three-ring binders. So, here:

photo 22

Two of the three-ring binders stacked in an alternating manner

photo 21

A end view of the three-ring binder

You may also want a shot of the two together. So, here are a few of these:
photo 25 photo 24

Do your best. Let me know what you find out.

The Train Set Problem

My daughter's birthday present

My daughter’s birthday present

My daughter got a new train set for her birthday. Today we opened it up and put it together. As we got to playing with it, it seemed that the two loops were becoming a focus. We had two trains on the tracks at the same time and every so often, there would be  bit of a collision at the short stretch where the two loops intersect.

Now, that got me thinking. I thought of two questions. Both relating to comparative speed.

1. How much faster would one train have to be for the trains to complete the loops in the same amount of time?

2. If the trains started at the same spot and traveled the same speed, when would they both be at the same spot again?

There are mountains of math problems we could do with this train set. It would be okay with me if you filled the comments with possibilities beyond my two.

An overhead shot, if you think it will help.

An overhead shot, if you think it will help.

The Citrus Problem


If we are going to convince our students that math is usual in everyday experiences, then we need to show them everyday experiences and have them do math.

And a box of oranges like that is an everyday experience for me. In fact, that’s my kitchen in the picture. So, how many oranges will fit in that crate?

And for a real challenge, how many will fit into the dark brown basket beside it?

Remember, the power is in the explanation.

The best change of 2012

Ladies and gentleman: As we wind down this year of updates, changes and additions to my teaching, I am proud to present the most universally beneficial change of 2012.

The Supply Nook. (cue trumpet fanfare)

The Supply Nook

One thing that I’ve known for a while is that if you are going to expect students to own their learning, you have to be prepared for the effects. Students will want to individualize their experience. They will want to be who they are. So, I try to make as much stuff available as possible. Visible in this shot of the supply nook is paper (line, grid, dot, white, patty and construction in multiple colors), crayons, colored pencils, scissors, rulers, protractors, tape, stapler, highlighters, and when I took the photo, my calculator bin was on loan to the algebra teacher downstairs, but that’s usually there, too. I also keep a pencil cup so that my students don’t have to wait for me to help them deal with that.

Two years ago, I tried having everything in unlocked drawers, but the students forgot that they had resources available.

Last year I tried putting resources on the student pods, but I found that they students were pretty disrespectful to the resources. Lots of garbage was left in the bins. Items were getting stolen. Also, when the students had the resources, but didn’t necessarily need them, they would play with them (ruler helicopters… stuff like that), which led to resources getting broken.

Now that the geometry curriculum has been rewritten, I have found that the students are doing a lot more than they were. We moved away from textbook problems in favor of stuff the students can put their hands on. This change has amplified the need for resources. So, this year, I started with having the resources out along the counter top on the side of the room, but it wasn’t very streamlined. The configuration above has worked the best, yet. It is convenient, but not convenient enough to inspire frivolous use. The stuff is holding up well.

There it is. Best change of 2012.