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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#NCTMIndy day 1 feat. Dan Meyer

The MathEd Out Podcast


Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He currently studies math education at Stanford University, speaks internationally, and works with textbook publishers, helping them move from education’s print past to its digital future. He was named one of Tech & Learning’s 30 Leaders of the Future and an Apple Distinguished Educator. He lives in Mountain View, CA.

Here is a short interview with Dan Meyer following his opening session at the 2014 NCTM Regional Conference in Indianapolis

[audio https://dl.dropboxusercontent.com/u/82726094/MathEdOut/10-30-14%20NCTM%20Indy%20-%20Dan%20Meyer.mp3]

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Ep. 7 feat. Prof. Malcolm Swan

Malcolm Swan has been somewhat of a hero of mine since the beginning and so it was a great pleasure to be able to interview him for the latest episode of MathEdOut. Enjoy!

The MathEd Out Podcast


Malcolm Swan is Professor in Mathematics Education at the University of Nottingham and has been a leading designer-researcher since he joined the faculty in the Shell Centre for Mathematical Education in 1979. His interests lie in the design of teaching and assessment, particularly the design of situations which foster reflection, discussion and metacognitive activity, the design of situations in which learners are able to construct mathematical concepts, and the design of assessment methods that are balanced across learning goals – and thus have a positive backwash effect on teaching and learning. Diagnostic teaching, using ‘misconceptions’ to promote long term learning, has been an ongoing strand of this work.

He has led design teams on a sequence of internationally funded research and development projects including work for UK examination boards and the US NSF-funded Balanced Assessment project and the Mathematics Assessment Resource Service(MARS). He has designed courses and resources for…

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Walk the Line – Adding and Subtracting with Negative Numbers

I wanted an activity that would give students a deep sense of adding and subtraction involving negative numbers. Both. At the same time. I figured the best way would be for them to actually walk through what happens to a number when it goes through these operations; so began ‘walk the line’.

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The idea is simple, have students walk through various sums increasing from adding two positive numbers, going through to subtracting two negative numbers, reviewing each time.

They will first need to stand in a line, then using sidewalk chalk, draw a zero on the floor and draw out a number line to the right and left of where they are in the positive and negative direction.

Here is the general dialogue that happens:

  • I am going to call out a sum and I would like to see how quickly you can get to the result. You start with the first number I call out and are permitted to move before I have finished calling out the sum.
  • 3 + 2 (call out slowly to give students time to move)
    • Review Questions
      • Now, what did you do when I first said 3? – Run to that number
      • What did you do when I said “add”? – Got ready to run away from zero
      • What did you do when I said 2? – Ran two spaces away from zero
  • Next:  5 – 8
      • Review Questions
        • Now, what did you do when I first said 5? – Ran to 5
        • What did you do when I said “subtract”? – Turned to face the zero (Why? etc)
        • What did you do when I said 8? – Ran 8 spaces and ended up at -3
  • What about  5 – ( -8)    (call out slowly)
    • Review: What was different when I said subtract -8 instead of 8? – Had to go the other way (Why? etc.)
  • At this point I bring student thinking together and explicitly clarify the rules:
    • Whatever number I say first is where you start
    • If I then say “add” you face this way (pointing in the positive direction) and if I say “subtract” you face the other way (pointing in the negative direction)
    • If my second number is positive you walk forward by that amount, if my second number is negative you walk backward by that amount (for example: 4 would be four steps forward, -4 would be 4 steps backward)
    • Let’s try this out
  • 3 – 8 (call out slowly to give students time to think and move)
  • -4 + 10
  • 2 + (-5)
  • -9 + 12
  • 2 – (-5)
  • -4 + (-7)
  • -6 – (-10)
  • etc
  • Then return to classroom and do the same sort of thing but students write (just) their answers on their mini whiteboards. We review each time going through the 3 step process.

This activity really worked and students were doing this all in their head by the end of 50 minutes which is what I was aiming for. There was no separation of addition and subtraction or positive and negative numbers. They were just different points on the number line and different ways to move.

How do you introduce adding/subtracting negative numbers?


Classkick Review – Thoughts from the first day

I first heard about Classkick through Dan Meyer’s blog and thought ‘I have to give this a try!’ The idea is simple but the implications could be huge. A platform that lets you see what students are thinking and writing, in real time! It is so simple I can’t believe it hasn’t been done before.

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So, as soon as I finished reading the article, I downloaded it onto my iPad and emailed my students to do the same ready for the next day. I didn’t want to go another day in my classroom without trying this out.

The punchline: It’s a great idea, but it needs some work.

The interface is clean and pleasant to use. The tutorial videos are helpful as some elements are more intuitive than others. For example, i assumed that students would sign up once to a class and after that would stay signed in (as is the case for many other education apps). But with Classkick, students will sign in to each assignment you set, separately with a different code. I think this could get a little cumbersome when I am setting activities every lesson.

The idea behind the app is phenomenal and when it worked it was magical. To be able to see what students are writing, provide immediate feedback and pointers is a very powerful tool. This could be used for in class work or for homework.

The students loved knowing that I could see their work, I could give them instant feedback and they responded very positively. They jumped into the learning from my feedback. I could not only look at their answers but circle and ask questions about mistakes in their thought processes. This is so exciting!

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However, on first use I did find the app a little slow, at least from the teachers side of things. In one lesson it took around 4 minutes for the students’ work to appear on the screen when the network was working just fine. Sometimes it took a while to recognize my writing, impeding my ability to give as many students as I could, feedback. It can also take a little getting used to writing with a stylus. I found if I wrote too quickly, it simply didn’t recognize my writing at all.

This is a new app; there are going to be bugs. I for one am excited to stick with it as the wrinkles are ironed out or I find something that is doing the same thing but better. One day, this sort of app will be part of every classroom and hopefully, very soon indeed. The best of luck to the Classkick team!

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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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MathEd Out Podcast – Ep. 5 feat. Fawn Nguyen on Engaging and Rich Activities in the Classroom

The MathEd Out Podcast

Click Here to subscribe to MathEd Out on iTunes

This week we are joined by well known blogger and math teacher from Southern California, Fawn Nguyen. Known for her engaging lesson activities and honest blogposts, Fawn talks to us about how to create and execute rich and engaging lesson activities in the math classroom. We also discuss her inspiration for creating the website visualpatterns.org

[audio https://dl.dropboxusercontent.com/u/82726094/MathEdOut/07-08-2014%20Fawn%20Nguyen.mp3]

Fawn’s Blog

Visual Patterns

Illustrative Mathematics


Dan Meyer

Robert Kaplinsky

Math Munch

Math Forum – I notice, I wonder

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Book Review: ‘Playing with Math’ feat. editor Sue VanHattum

The MathEd Out Podcast

Click Here to subscribe to MathEd Out on iTunes

For this special episode we discuss the book ‘Playing with Math‘ edited by California Math Teacher and blogger, Sue VanHattum. We discuss details of the book (to be released, fall 2014), the inspiration behind the book as well as the questions it poses and the implication it has for progressive mathematics education.


From the books website:

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers has over 30 authors, who each tell their delightful stories of sharing their enthusiasm for math with others. It was lovingly compiled and edited by a teacher whose passion is to share the love of math with as many people as she can.

This 328-page book was 5 1/2 years in the making. It’s ready to head to the printers now, and can soon be in your hands.

Whether you enjoy…

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MathEd Out Podcast Episode 4 feat. Mathy McMatherson on Assessment and Feedback

The MathEd Out Podcast

Click Here to subscribe to MathEd Out on iTunes

This week we are joined by Tucson math teacher, Daniel Schneider better known in the twitter/bloggersphere as Mathy McMatherson. In Daniel’s relatively short time teaching he has built up a strong following and is known for his thoughts and ideas to do with assessment, feedback and standards based grading.


We talk to Daniel about all of the above as well as the implementation of common core across the US.

[audio https://dl.dropboxusercontent.com/u/82726094/MathEdOut/06-02-2014%20Mathy%20McMatherson%20-%20Assessment%20and%20Feedback.mp3]

Links from the show:

Everybody is a Genius

Miss Calcul8

Fawn Nguyen

Dan Meyer

Michel Pershan

Sam Shah

Common Core Standards

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Why I am Switching to Middle School


As of the next academic year I will be teaching middle school mathematics. I will be sad to leave my current school but am very excited about the prospect of teaching younger minds.  Here’s why:

  • I am looking forward to (hopefully) ‘catching’ middle school students with the wonder of mathematics before they reach high school. The most upsetting thing I hear is when students enjoyed math at elementary level but then got completely put off before they reached high school. I hope to do something to make sure this doesn’t happen for my students.
  • I am looking forward to teaching just ‘Math.’ I have enjoyed focusing on Algebra and Probability & Statistics but have missed having the time to make connections between the disciplines. My aim will be to blur the lines between algebra and geometry so that students have a very strong sense of the link between them.
  • Experience tells me that middle school math lends itself to Project Based Learning (#PBL) fairly well. This is something close to my heart and I look forward to modelling what it means to be a mathematician to my students.
  • I get to chat and share great ideas with #msmathchat peeps on Twitter

I am truly grateful to Herron High School for trusting me to teach their students for the last two years.