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  • Writer's pictureAlex Box

(Uni)fixing lessons to include and celebrate all learners

What made this maths investigation so valuable?

How many different ways can you make 5? How about 6? How about 7?

This week I had the pleasure of observing a Year Foundation / 1 maths exploration in action. It was a great example of differentiating to a group of individuals, each with unique mathematical histories, through one, shared task.

Here are some reflections on key elements that made it a successful session.

1. A tactile, conversational and collaborative opening

Together in a circle, everyone grabbed five unifix cubes and created a stick of five. The teacher, who sat in the circle also, had a small whiteboard.

Group members were invited to break their stick of five into two parts. Then share what they noticed about the different models.

The questions posed (by the teacher) were open - they were genuine and they sparked thinking and discussion. (There was no sense of anyone 'being tested').

  • What do you notice about your model?

  • Tell us about how you broke your number into parts.

  • How else can five be broken into parts?

All learners had the tactile experience of breaking blocks up in different ways. A clear method of recording both visual models, and related number models, was modelled on the whiteboard.

2. Plenty of time for hands-on exploration

Students extended on the idea at their tables. All grabbed a set of six unifix - same-coloured, to avoid the distraction of making repeating patterns (an important and beautiful mathematical thing, but not the focus of today).

These young explorers found different ways of breaking and making six. They had the added challenge of recording (on paper) their discoveries in ways that made sense to them. Some used pictures, others numbers and symbols, some a combination of both.

Some were preoccupied about making mistakes and 'having to start again'. So there was a particular mindset to practise: See mistakes as part of the process. These could be picked up along the way and corrected. This often happened when explaining a recording.

Checking and adjusting our recordings...🌱🧠

One of the things I LOVE about creating habits of reasoning is how they support precision... 💙🎯

Keeping mistakes visible in the working is a way of acknowledging and showing the learning that is happening.

These young explorers were leading their own investigation. Interested in pursuing other numbers? Go for it!

The teacher here was a 'guide on the side', posing nudging questions along the way and modelling curiosity about the various recordings.

Sure, this investigation was rich in that these young explorers were interacting with number in various ways. For instance, they were:

  • using and describing part-part-whole understanding

  • counting small collections in different ways: by ones, by twos, subetising and adding or counting on

  • using number names and writing numerals

But they were also:

  • making choices

  • working at a 'just right' level for them

  • organising and communicating their ideas

  • engaged in an investigation with no end - just like mathematicians do 🔢💙 No 'early finishers' here!

3. A timely, conversational and collaborative sharing of strategies

After some time investigating, the group came together to share and discuss some of the findings so far.

It was an opportunity to spotlight and celebrate different ways of recording.

It was timely discussion because afterward was more time to investigate. And so learners had the opportunity to draw on the ideas and recordings shared.

What in this lesson resonates for you? What would you do the same / differently and why? I'd love to hear.

Playfully learning,



Thanks to Marissa Cashmore for allowing me to observe her in action. It was such a joy to be in a such warm, welcoming and playful learning space.

You can learn more about Marissa's teaching approaches via her page Motivating all Maths Learners to Succeed. Connect with her on Twitter here.

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