Pumphrey's Math

Patterns, everywhere


Ten Webites I Check Before Starting Every Unit


There are many excellent resource sites out there with inspirational teachers making great resources. However, when it comes down to it, there are only a handful of websites I check on a very regular basis. To make it to this list, I am generally looking for tasks that:

  • Are ‘low floor/high ceiling‘ giving access and challenging everyone at their own level
  • Have multiple approaches, giving students room for creativity
  • Are challenging and hence interesting
  • Will give me permission to teach skills
  • Make skill practice, more interesting
  • Have a story for students to follow

There are many activities out there that fit these descriptions, but there is only so much time in the week. During breaks I have more time to explore but these are the sites that I can check quickly with high yield for your classroom (in no particular order):

1. Mathematics Assessment Project – A website produced from a partnership with the Shell Centre (University of Nottingham, UK) and the University of California at Berkley. Here you will find tasks that will help the common core standards come alive in your classroom. Full of rich activities that encourage discussion and investigation.

2. Standards Unit – This has been around for a while but is still one of the first publications I look at and is close to my picture of what mathematics education should like. A rich, dense set of activities that will give you great ways to work on various skills and topics.

3. YouCubed – A relatively new site that has come out of Prof. Jo Boaler’s (Stanford) efforts to encourage the ‘growth mindset’ in the classroom. I am interested in anything that comes from the idea that anyone can be good at math.

4. Open Middle – I came across this site relatively recently and am sad that I didn’t find out about it sooner. it’s tag-line is: ‘Challenging Math Problems Worth Solving’ and tips the proverbial hat to the school of thought that says that you don’t need to have tenuous links to real world problems in order to get buy-in from students. It appeals to the problem solver in all of us.

5. Emergent Math – With its routes in Problem Based Learning (PBL), emergent math is useful not only for those who want to tear up the textbook and start again with an integrated curriculum, but also for people who just want great projects that they can slot into their established curriculum. Lots of links to sites not mentioned here so worth a look.

6. Mr. Barton Maths – Lots of great resources and activities that will make your classroom a more interesting place. Enough said.

7. Tarsia – Sometimes students just need to practice. There I just said it. But using Tarsia you can avoid ‘death by worksheet’ and get students to practice without really realizing it. It also great for discussion and you can tell very quickly if students have answered everything correctly or not. For more, see Why I Love Tarsia.

8. NRich – Great site for ‘low floor/high ceiling’ problems that will challenge anyone in your classroom. Students may like to explore this outside the classroom, too. Sortable by topic and I believe they are coming out with a common core curriculum map, quite soon.

9. Dan Meyer 3 Acts Spreadsheet – Act 1 –  You show a video or picture prompting discussion, prediction and estimation as well as the all important step of coming up with the variables that are to be investigated. Act 2 – Students get the information they need to solve the problem. Act 3 – Once students have solved the problem in various ways and presented you show them the solution. There is a lot more to it than this and to pull these lessons off well is a true art form. But the only way to get better at these is to try them. So try them! More info here.

10. Mathalicious – Math lessons based on the real world problems. $185 for 12 months subscription (I think currently they are also doing pay-what you can) but well worth it. Excellent for creating the need for the math you teach.

It takes me around 90 minutes to trawl through these websites at the beginning of a unit but is well worth it when it comes to lesson planning and I know half of the activities I am going to do already. As with any of these activities they will need to be (and should be) adapted for your classes and situation but they provide an excellent starting point from which to plan.

What websites are a must-check when you are planning a unit? Leave a comment, below.

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The Great Wall of Questions

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Any strategy that raises the level and status of questioning in my room is useful. I found that there were times when a student asked a great question but that it was just no the time to go into that topic too deeply. I have also found that there are times when I have a 5-10 minutes gap in my lesson where these topics would fit into nicely.

The Great Wall of Questions is my attempt to solve these two problems at once. If a student asks a great question, then I proclaim ‘get it on the board!’ to the delight of the person that asked. They know that if it goes on there I think it is an important question, one that is worth thinking about for a longer period of time. When there is a good moment I will take a question and try to get students thinking about some answers or at least ways to find the answers (I am going to avoid just answering the questions as much as I can). Here are the rules:

  • A question only goes on the board if it has come out of genuine curiosity (rather than an attempt to get their name on the board)
  • Their name goes with the question and the color of the stickie determines which class it came from
  • When the question has been addressed (different from answered), a small dot goes on there so we can see what needs to be looked at in the future.

I only have four questions on there so far this semester (after 8 school days). I am hoping that by the end of the semester the board will be full. Here goes….

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How to fake a Jackson Pollock

Convergence (1952) by Jackson Pollock (from about.com)

It’s the end of summer school session 1 and I wanted to give my students a taste of the beauty and power of fractal geometry. Rather than just play a TED talk (although this helped with the introduction) I wanted them to live through the process.

I know that fractal geometry has been used to spot fake Jackson Pollock paintings and thought it would be fun to look at the method behind this and to see if my students could use what they have learned to try and create their own ‘Jackson Pollock’. Here is a summery of what we did, spread out over a 2 day period (in between normal curriculum activities).

  1. For a link from Geometry, semester 1 work, we used this nrich task to start them questioning what a fractal was.
  2. We had a discussion on where you might see such shapes in the real world, e.g. lungs, coastlines, cauliflower etc.
  3. We watched this TED talk from Mandelbrot himself (recommend using subtitles with this, he can be hard to understand)
  4. Before getting crazy with the paint, we watched this video on how Pollock painted his work and how people have tried to replicate the motion
  5. Time to head out to the front lawn of the school where students were greeted by a large canvas and a lot of paint where they were tasked to try and create their own Jackson Pollock, but not before reading the following quote from Nature Notes to help them think through the process, rather than just splash a load of paint around.

‘There were two reasons to suspect that Pollock’s paintings might obey fractal geometry. Moving around a large canvas laid on the ground, the artist let paint fly from all angles, using his whole body. Human motion is known to display fractal properties when people restore their balance, says Taylor, and films of Pollock seem to show him painting in a state of ‘controlled off-balance’. Second, the dripping and pouring itself could be a chaotic process. 

“Pollock was in control,” says Taylor. The large-scale fractals are a fingerprint of the artist’s body motion, he notes. “But the small-scale fractals are also to do with his choices — his height over the canvas, the fluidity of his paint, angle and force behind the trajectory, and so on.”’

The real magic was when we took a photo of the canvas and zoom in several times to see if we have replicated the infinite properties that Pollock created so well. Here is a video of the class starting the painting (and getting pretty covered in paint in the process).

Here is the end result and the zoomed-in versions.


I appreciate we’re not going to win any awards with this art but from a geometry point of view, I was really happy with the results and so were the students. The zoomed in photos do not look all that dissimilar to the painting as a whole.

I will be, of course, asking the school to display this somewhere. There is part of me that hopes they decline so that I can take it home with me. Apart from anything else, it was great fun!

A huge shout out to local artist, Quincy Owens, who helped me to set this up and provided all the materials we needed.

Have you done something similar? Any suggestions on how I can improve on this for the future?


What motivates my students to learn?

I used Google Forms to survey 56 of my students (I know, it sounds like a statistics textbook question already!). I wanted to know what motivated them in my classroom. The survey was anonymous and I encouraged them to be as honest as possible.

The question: What motivates you to learn in the mathematics classroom?

The response: 1 – No motivation, 4 – Highly motivating


Any other comments? (here is a sample):

  • I would like to work in groups of my choice
  • Competition only puts stress on me
  • I find the mathematics interesting, but I feel immense pressure to get a good grade and get into college
  • I like working on my own with music playing
  • I need one on one help and lots of time to practice

My initial thoughts:

  • Clear patterns here are motivations of getting to college and getting a good job. I wish it was the same for ‘the mathematics covered’
  • Also clear is that students want lesson activities to be fun
  • Not so clear is the motivation of groupwork, individual work and working on practice problems. This just highlights the diverse nature of how my students learn and how to get the best results I need to cater for different learning styles. This is an art form, for sure.
  • Also interesting is that not all students appreciate competition. Even more interesting is how this graph changed with different classes. For example, for the first class that took this survey, there was an intense dislike of competition. This leveled out as the day progressed.


  • College and career is more of a motivator than the math. I would like this to level out somewhat; for the math to be its own motivator. I’m still working on this point.
  • My students are very different in terms of how they learn and what motivates them. Some appreciate individual work, some appreciate group work. In a math ed world where the group-work-is-the-only-way team is by far the loudest, I have to remember that this is not always the biggest learning engine for all of my students.

This process reminded me of the following TED talk on ‘The Power of Introverts’. An important idea to think about if we want to tailor education to the individual student: