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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Summer Reading 2014

Summer is rapidly approaching. A great time to reflect and decide what I want the next 12 months to look like. Time is precious and I want to read books that will not just improve my philosophy but that will help on a day to day basis. I am currently looking forward to devouring these two books:

I’ve been thinking a lot this year about how to teach my students how to learn, how to think for themselves and direct their own learning. I’ve skim read ‘Making Thinking Visible’ before but I’ve been looking forward to going through this with a fine toothed comb and extracting every word of worth from its pages. The philosophy statements in the first couple of chapters is worth a read all on its own. It seems clear that students who can name and show their thinking processes do a lot better than those that just go with the flow. I would like my classroom to foster the former. Thoughts to be blogged/tweeted as I go along.

This is the other book I’m really looking forward to going through. It has come highly recommended and anything that is going to help me become better at asking questions and promoting debate and discussion is worth a look. I haven’t even opened this yet so watch this space for highlights online and in my classroom.

Because LeCarre is amazing.

What will you be reading this summer? Any recommendations?


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Virtual Filing Cabinet 1.0

I trawled, I tweeted, I tried to find the best of what was out there. I have posted the first draft of my virtual filing cabinet here and in the process, learned the following:

  • There are so so many great lessons and activities out there!
  • There are far too many to include them all
  • It is hard to choose which ones to include
  • There are some incredible teachers who I would like to be more like
  • I’m really excited about trying just a handful of things I found
  • I want to do a lot more project based lessons
  • This is a working document and will evolve with my teaching

If you haven’t already I highly recommend you trawl some websites and create one of these yourself. Chances are, it will be unique to you and your teaching style and philosophy. Here is a list of websites to get you started. 

Let me know if you think there are any glaring emissions.


What my students think of Khan Academy

Recently, I used this and this Khan Academy activity to test my students’ understanding of graphing inequalities as part of our Linear Functions Unit. Having not broadly used KA before, I wanted to gauge my students’ reaction and try and work out if I should use it more regularly to give me and the student, good feedback. After the activity, I gave a quick Google Form Survey to ask my students what they thought. The results are below:

KA Activity Survey

Other student comments included:

I think this really helps envision the problem, and it really helped me. I would thoroughly enjoy doing this again, although it is kind of hard to maneuver around on it.

I liked the system, but I really hated the fact that we had to get three right in a row, because if you accidentally make a mistake, you can’t go back, you’ve just permanently failed.

It was good for practice but too easy to make technical mistakes. Graphing is harder to do on Khan academy.

This feedback, coupled with talking with students during the activity told me these things:

  • We are a Bring Your Own Device (BYOD) school with many varieties of device. Laptops were fine but some tablets were pretty difficult to use with KA. It was hard to move things across the screen
  • The instant feedback is awesome and students really enjoyed/were frustrated at (in a good way) knowing immediately whether they got things wrong or right.
  • I think in the future, I will mainly use KA for homework where students can do things at their own pace and use their home computers rather than tablets.
  • The idea is great but I’m going to have to think about the most useful way to implement it as part of the wider experience, for the student.

Have you used Khan Academy in the classroom. Any good tips on how it can be integrated without the frustrations above?


Seven Squares – The Essence of Mathematics

This post is my attempt at being part of the ExploringtheMathTwitterBlogosphere community.

This week (or last weeks) challenge is to post your favorite rich/open ended math task.

Without doubt mine is nrich’s Seven Square’s problem. To my mind, this captures the essence of what mathematics is all about: Patterns. I love starting my Algebra 2 course with this to give them a sense of why we do the Math.

In class I will give each group a set of toothpicks. Some use them, others go straight to the drawing but all seem to get into it at their level/pace straight away. It’s amazing what comes up from students of all abilities.

A great extension to this is Dan Meyer’s toothpick activity. There is no end to shapes that students can investigate. It is one of those ideas that is great for all ability levels and really does help when you are dealing with the content skills throughout the course. I find that I refer back to this lesson, often.

What I learned from Dan Meyer

Yesterday I realized, many of my students are currently motivated by the threat of:

  • Getting a bad grade
  • Not getting into college
  • Getting yelled at by parents.

This is not good. In my mathematics classroom I would like my students to be motivated by a need for math, a hunger for math. I want them in a position where they are begging me to give them the mathematical tools they need to solve problems. Yesterday, I came a little closer to understanding how to get to this point by attending a conference given by the inspirational educator, Dan Meyer.

He has pioneered what are known as the 3acts lessons where students are presented with a photo or a video that inspire questions leading to a multilateral problem solving environment. I’m not going to go into detail here; I just wanted to share one or two thoughts from the day.

There is a common theme throughout his videos and that is the word ‘per’. How does one thing change with another? Miles per hour, Mass per Volume, hot dogs per minute. This is the heart of mathematics and something we all meet every day. Present a problem with changing variables (without just giving them what they are looking for) and you are presenting them with a problem that will need mathematical modeling to solve.

The difference is, whereas in textbooks, all the information is given to you at the start, in Dan’s lessons, hardly anything comes from the teacher. A nugget of information here and there to aid the process and to give something for the students to use, but mainly it is the students that have to identify variables, come up with the process in order to solve the problem (that they came up with) and hence make conclusions, with no mention of standards at all. What an amazing process!

The whole thing is a great validator also. With a lot of space for making predictions and coming up with ideas, the glory is not given to ‘the clever one’ but to those who make the effort of contributing. Every student has intuition.

Finally, I learned that Dan Meyer is human. I’ve been to conferences before where you leave feeling bad if you are not producing every lesson based around super rich tasks with resources that take hours of pain staking work to produce. Dan agreed that sometimes lectures are needed to fill in the gaps, that time needs to be spent preparing students for specific standardized assessments and that teachers often have little time with which to work. This was refreshing.

What was inspirational about yesterday was that this was not a plan to change everything about the way I teach. It was about elegant strategies to introduce the need for and the process of mathematical modeling; to create the hunger for the mathematics so that students then want to know how to e.g. divide rational expressions.

Good math is like a good movie; you know the point throughout the whole thing.

I’m really excited to give these lessons a try.

The three acts lessons mapped with common core standards can be found here.

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Why I love Tarsia

Apparently it takes 10,000 hours to become an expert at anything you put your mind to, although not everyone agrees. A great pianist, however talented, does not become a virtuoso overnight. What is clear is that to become proficient in mathematics, yes, we need rich tasks and activities to build connections but sometimes you just need to ‘practice the scales.’ Many lessons out there are full of worksheets and textbooks where students can practice the same idea over and over again to their hearts content. The trouble is, this can be so boring for the individual and really demotivating for learning.

I want my mathematics classroom to be a place where students can get the practice they need but not get bored. That is why I love Formulator Tarsia.

Endless questions are boring, but put those questions in the context of group-work (possibly including competition) and suddenly it becomes a project where the task is to build a shape and the students find they are learning by accident. This is the best type of learning.

A download of this crucial program can be found here.

Pre-made files can be found here

I recently made a Tarsia activity for finding common denominators of rational expressions; this can be found here (right click and ‘Save Link As’).