Back to teaching

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Well, seems like I couldn’t stay away from teaching after all. Starting this fall I will be teaching at the local university – I will be teaching student teachers how to teach math.

It’s only fitting that I start blogging about teaching math again. Right now it is only an ambition, so we’ll have to see what happens.


My last post


I just quit my job and will not be going to back to teaching. So this will probably be my last post on this blog.

One last math problem

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This will be my last post about teaching math. In a day or two I will explain why.

For now, here is one last problem that I made up that I like. It is to help highlight the difference between percent change and percentage points:


Alfred and Anna have savings accounts at The Bank of Hubert’s Left Toe (a very respectable bank). They notice that the interest rates have gone up this year.

Alfred says, “That was lame, we are only earning 1,5% more money now.”

Anna responds, “No, you are mixing up percentage points and percent change. We are actually earning 24% more money now. That’s a big change!”

Assuming Anna is right, what percent is the interest now after it has gone up?

Bad math in society

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I have always had a low tolerance for bad math out in society – if you can’t do your (often simple) job then let someone else do it. Since becoming a math teacher I find I have even less tolerance. So to the student whine of “why do I need to know this?” I would really like to answer “so you don’t look like a total moron doing the low-skilled job you thought didn’t require even basic math skills to do“.

True story number one:

A few years ago my wife was shopping at a jewelry store. They were having a necklace sale: buy 3 and get the cheapest one for free. The woman in line in front of my wife bought 6 necklaces. The cashier tried to give her the cheapest two for free. The customer argued and said that she should get a more expensive one for free. The cashier didn’t understand. The customer was quite frustrated at the stupidity and incompetence of the cashier who clearly could not do her job because she could handle the incredibly simple logical thinking required in this situation.

To illustrate for those having trouble picturing this, imaging the following size prices (in Swedish kronor):

2000, 1800, 1600, 1400, 1200, 1000

The cashier wanted to give her the 1000 SEK and the 1200 SEK necklace for free. The woman wanted the 1000 SEK and the 1600 SEK necklace for free instead. I’ll let you figure it out if you haven’t already (I even arranged the numbers nicely for you).

True story number two:

The following picture is from our local supermarket.


In case you are having trouble reading the blurry text. These are 50g packages of yeast. They cost 7.90 SEK each. The price in yellow is what is the called the “comparison price”, which is given in cost per kg. Listed in this case as 15.80 SEK. Seeing the problem yet?

Practice apps update

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I’ve created a whole bunch of new math practice programs since last I posted about them. I thought it might be useful to anyone who cares to put publish a link where you can find almost all of them in one place. They can be gotten to through the links in the ThingLink image, or from the explicit list underneath. As usual, these are mainly just for basic skills practice (and some harder skills). Let me know if you find any of them useful:

Group discussion with post-it notes

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I tried a new idea today that I borrowed from Andrew Knauft, found vid Dan Meyer’s blogg.

I divided my 7th graders into groups of 4 and asked each group to decide which of the number in the set {9, 16, 25, 43} didn’t belong and why. They stuck the post-it on the whiteboard when done and then took another group’s note. They then had to say whether or not they agreed with the reason the other group gave for their decision.

At least that was the plan. The reality was that three of the groups had exactly the same number and reason (43 because it is the only prime number), a fourth group had 43 because it is the only not perfect square. Only the fifth group had anything different.

So then I pulled out another harder problem and set them to work on it. I showed the following picture with this question

“Each of the four cards below has a solid color on one side and a number on the other side. What is the smallest number of cards you need to turn over to decide whether or not the following statement is true: if a card has an even number on one side then the other side is red?”


That gave rise to a lot more lively discussion and a lot of disagreement between the different groups on what the right answer was. It was a very fun lesson.

Math video prompts

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In case any of you don’t already follow Dan Meyer, I highly recommend his math teacher blog – best around:

In line with his theories about trying to create video or picture prompts to stimulate natural questions that require math to really answer, I have a couple ideas. The problem is I’m not really good at video editing and suspect I might not get around to actually making them.

So this post is a request for anyone interested in seeing if they can/want to produce one or two short videos.

  1. This one is of two people running around a track. I think it should be a standard 400 meter running track so that distances are known, though the 100 meter marks should maybe be added to the videos. Two runners/joggers start facing each other a short distance from each other. When they pass each other they smack hands and at that moment a timer starts on the screen. The video is stopped after a short time (before they meet on the other half). The question you are hoping for is where will they pass each other again? The timing information and known distances on the track should provide enough information for estimates. The rest of the video is then shown afterwards to show the answer.
  2. In this one you need a full class of students to help out. The students are standing in a line outside a room, each is holding a big bag of presents. One student is in the room. The first student in line walks in and shakes hands with the student there, and they give each other a present from their bags. They put their presents on a big table maybe (or maybe just keep them in a pile at their feet). The next student comes in and does the same (shakes hands and exchanges gifts) with EVERY student already in the room. The video would show the first two or three students doing this, then pan down the line of students. The exact number in line should be a bit unclear. The questions to answer here are how many presents total (which is why they should maybe be on a big table) and how many handshakes total (for those who don’t know, this is showing an easy connection between these ideas and which later is used to easily motivate the Gauss formula for adding up sequences of integers easily).

Any takers?

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