## Opportunities to notice – developing number sense and reasoning

I have long been a fan of Steve Wyborney’s blog where he shares plenty of engaging and different ideas to develop mathematical thinking. Although based in Oregon, the ideas are still very relevant to the UK curriculum.

I recently came across his use of dot patterns to promote ‘noticing’ – not something we necessarily spend a lot of time on, but I now wonder why we don’t.

One big focus in mathematics teaching currently is the use of small step and space to let children think. This sort of activity undoubtedly lends itself towards these ideas.

Steve has created 10 pages of dotted patterns, the purpose of which is to promote a wide variety of partitioning, seeking different perspectives and recording observations in ways that can be very useful. I would guarantee there will be children in every class who see a different pattern or way of breaking things up to draw out different mathematics every time.

He recommends using 18 copies of the same pattern with the space underneath being vital to allow plenty of working room and many opportunities to explore the same thing in different ways.

The following image is from his explanation video of how to use the patterns (found here), demonstrating 4 ways to investigate one such pattern.

For a greater challenge, once children are used to working with these, you could develop more complex images with different coloured dots – each colour being worth a separate value – to explore larger numbers, perhaps. Each dot doesn’t need to necessarily only be worth 1, either.

The 10 patterns and some further information can be found at the link below.

## Prime Number GIF

This lovely animated GIF makes me feel like there is something worth getting children to investigate further – either as a lesson activity or as a project to create short films showing other numbers.

As always, I’d love to hear if you use the idea, or it has inspired you to do something different in a lesson.

## Venn Diagram in the wild!

I recently saw this on Twitter (via @MrATeachesMath) and just had to share it. I’ve copied the image below and embedded the original tweet too.

A nice reasoning question here would be: “What labels would this Venn diagram have?”

I’m not quite sure why I’ve never thought of this before now, but… using sticky notes to highlight the partitioning of a number after an addition to show how to deal with numbers larger than 9 is a complete revelation to me!

This idea (and associated images below) is from The Classroom Key.

Show students how to add up the numbers in the ones column and write the answer on a sticky note.  In the beginning, it is probably worth labelling the left side of the note “tens” and the right side “ones.”

Use a pair of scissors to cut the note in half vertically.

Put the “tens” half of the note on top of the tens column.  Put the “ones” half underneath the ones column.  Add up all the numbers in the tens column and there’s the answer!

I will certainly be using this with my pupils in future when introducing this concept. I’d love to hear how you get on if you try it too.

The following ten files are a straightforward set of mathematical vocabulary flashcards. I have grouped them by topic and have written on in small lettering where in the curriculum the term is introduced.

A sample page from the addition and subtraction group is shown below. All of the pages share the same design.

Feel free to share with colleagues – I would love to know how they are being used.

## Tessellation: M.C. Escher – Metamorphosis Machine

The work of M.C. Escher is full of tessellation and he was inspired – he referred to a ‘mania’ he had – to fill a page with shapes.

With this site, you can make your own metamorphosis and techniques which Escher developed by hand over the years are built into the ‘Metamorphosis Machine’.

Children can make their own Escher work and become part of the endless metamorphosis.