An Innovative, Open-Ended Approach to Mathematics Teaching Pedagogy

I am incredibly excited this week to be procrastinating from report writing by taking up the opportunity to write for Education Services Australia, and their incredible online resource: maths300.

For those of you who haven’t heard of the resource, here is an excerpt from their ‘About‘ page, below:

“maths300 is less prescriptive than traditional pedagogy.  The lessons build on important algorithmic skills, but also encourage students to develop reasoning and communication skills beyond the textbook. Students are often required to work in groups, to think creatively and to apply a number of different strategies to solve a problem. This process is called Working Mathematically and features in most lessons. The extensions section provides huge scope for extended investigations and cross-curricula activities.”

The lessons are presented as mathematical adventures, and all of them contain rich activities that promote discussion encouraging students to work like a mathematician (one of our numeracy catch-cries!). In our classroom, I have used them exclusively with Kevin Cummins’ Maths Toolbox which he shares on his superb education resource, Edgalaxy.

‘maths300 lessons are presented in an illustrative style based on the Mathematics Curriculum and Teaching Program (MCTP) style. The MCTP is arguably the most successful professional development program prior to maths300.’

In combination with this, schools are able to download the accompanying software package which, although simple looking, allows students to complete investigations with a real-life contextual edge. One example is the Footy Finals lesson (great for September, AFL or NRL!) where students have the opportunity to investigate the chance of their team winning the premiership starting from 1st-8th position.

When I submit my maths300 lesson plan, I also plan to make it available via OpenEdToolbox, so watch this space!



Have you used MCTP or Maths300 in your schools/classrooms?

What sorts of maths ‘adventures’ have you taken your students on?

How do you apply real-life context to your numeracy classroom?

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Maths Lesson Ideas – Smarties!

I always try and include some extra fun lessons in the last week of term that revise a range of topics students are familiar with. In addition, it is always extra special to be able to introduce some new concepts at the same time. I got the idea for this lesson from the Black Douglas Mathematics Centre, an incredibly rich resource closely linked to Maths 300, but it is free! If you haven’t had the opportunity to look at these resources as a school, please take the time to do so. They are just packed with open-ended, purposefully engaging lessons with a focus on problem solving throughout.

I taught this lesson in the last week of Term 3, and found myself wishing we had the time to investigate more!

Smarties! Introducing Negative Numbers.


  • 600g pick n’ mix smarties
  • paper bags with random selection of approx. 30 smarties per pair of students
  • 10x10mm grid paper (enlarged to A3)
  • calculators

Lesson content:

Our Learning Intention was based on using our number skills to experiment with negative numbers (which my students weren’t familiar with previously), but the learning experience included so much more, including: data-collection, chance, graphing, number patterns  and calculator use. Our Success Criteria was to effectively show addition and subtraction using negative numbers on a number line.

I went to my local supermarket and bought 600g of pick n’ mix smarties, which was enough for around 30 smarties per pair in a class of 24 students. I also gave each pair a 10x10mm sheet of grid paper, enlarged to A3, to assist them with the graphing of their random selection of smarties.

The rules of the game were as follows:

  1. Each pair was to count their smarties and each player record this number in their own scrapbooks as their starting score.
  2. All of the smarties are placed back into the paper bag.
  3. Students take smarties out one by one, each student guessing which colour will come out next.
  4. A correct guess scores +2 points
  5. Incorrect guess scores -2 points

The students kept a record of the addition and subtraction in their scrapbooks:

Prior to this, I encouraged each group to build a simple column graph to refer to during the game – I had little input, simply observing and taking some anecdotal notes about graphing skills, axis labelling etc. Some of the graphing was interesting!

The students amazed me with their creativity when they began playing the game. Nobody ate any, they were far too valuable! Instead, they rebuilt their graph to assist them with correct guessing.

We had a great discussion about which strategy/strategies we were using from our Mathematicians’ Toolbox (an invaluable tool from, which can be found and printed here)

As students waded into unfamiliar negative number territory, some were able to successfully apply prior knowledge. I stopped other students and encouraged them to use a calculator and a number line to support their calculations.

The discussion at the completion of the lesson was based on meeting our Success Criteria, but also somewhat disturbed by the munching of half-melted smarties (‘no thank-you, I don’t want one’). As I said, I wish we could have used this as a springboard for a follow-up lesson, but it was a great one to explore in the last week of term nonetheless.



I’d love to hear your comments, suggestions and reflections below:

What resources do you use to enhance your maths classroom?

Have you found any other open-ended resource banks like Maths300? 

What makes a great maths lesson? 


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