Here you will find fully-resourced mathematical art lessons as well as displays I have created to brighten up my classroom and support my students’ learning. I have archived my modular origami projects here, and offer some advice on using origami in lessons or setting up origami clubs. And there is also a page where I recommend some of the beautifully elegant logic and visuo-spatial iOS puzzle games I have happened upon and enjoyed.

Puzzle of the Week is a free international puzzle competition for schools.

Students submit answers to a puzzle which is published weekly on Mondays. School and student performances are recorded and leaderboards are published on the results page. You can sign your school up for free on the ‘About Puzzle of the Week’ page.

One of the things I always find difficult when teaching fractions is finding accurate ways to create the images I desire. I have found two sites which create the representations I want in my lessons.

The first is part of a large suite of online materials.

VisualFractions.com has a large range of tools linked to fractions. The page above is the basic fraction maker which I use a lot. The site has clear instructions for each area and works really well. The downsides, for me, are the lack of colour choice and no possibility to change the orientation of the final image. It can, however, create improper fractions.

This has the option to make shapes as polygons or circles, provides space to apply a custom colour and can rotate the images. Unlike my other option, this cannot make images for improper fractions.

As always, if you use these links in your lessons, I’d love to hear how you get on!

MathsBot is a recent discovery of mine which has a few great tools aimed at older maths learners – on loading, it displays resources for GCSE pupils, for example.

However, it also has a section of online manipulatives which are great to use in the Primary classroom – particularly one which may be lacking somewhat in concrete resources.

Now, I know that online and virtual pictorial representations are no substitute for hands on experience, but they still have a place in the classroom.

Right now, there are 12 available:

algebra tiles

bar modelling

counters

counting stick

Cuisenaire rods

Dienes blocks

fraction wall

geoboard

number frame

pentominoes

place value counters

unit box

Of those, a handy way to create place value counters and Dienes blocks, will prove invaluable to me.

Old folk like me will probably remember the National Numeracy Strategy (NNS) Interactive Teaching Programmes (ITPs) – some of which were great and some of which were horrible.

It turns out, they were great tools to show loads of mathematical ideas on whiteboards – but because they were made in the late 90s, and in Flash, lots of them no longer work.

Ted Burch of mathsframe.co.uk has very kindly remade them all in html5 but retained their original look.

The reworked programmes should work on tablets and most modern devices.

There are currently 25 remade tools which are all available for free here:

A great way to think about conceptual variation is to ask children when something doesn’t fit into a specific set of criteria – knowing not only the properties of a maths topic but being able to explain why particular objects don’t belong in that topic too is a feature of maths mastery.

Conceptual variation means the opportunity to work on different representations of the same mathematical idea. This might be, for instance, looking at multiple representations of a number with Diennes equipment, place value counters, Gattegno grids, place value grids, arrow cards etc. These numerous representations demonstrate to pupils the different conceptual ideas that underpin a mathematical concept.

So, in the context of place value, some will reveal the quantity or value of a digit, some will show the importance of the position of a digit, others will support the order of the number and some will reveal the additive or multiplicative nature of place value.

The use of conceptual variation can be applied to all areas of the mathematical curriculum.

One website I’ve found to aid in this aspect of conceptual variation is nonexamples.com.

The site has a range of mathematical topics to choose from and will display a variety of appropriate images of both examples and non-examples relating to it. There are two modes currently: question and compare.

I feel the initial question mode would be useful for opening lessons, possibly mid-way through a unit of work. They would also be a wonderful resource to develop and assess children’s reasoning skills.

Compare mode, however, is something I would use to introduce a new concept – perhaps even just displaying examples and non-examples side by side as above and asking children what they notice.

Numberblocks is a pre-school BBC television series aimed at introducing children to early number.

These NCETM materials use each episode as a launch pad. They are designed to assist Early Years (and also Year 1) practitioners to move on from an episode, helping children to bring the numbers and ideas to life in the world around them.

You don’t even need to register with the NCETM to use them!

The materials are designed to be used in conjunction with the Numberblocks episodes. They highlight and develop the key mathematical ideas that are embedded in the programmes. Each set of materials comes in the form of a PowerPoint file, and includes the following features:

The episode description summarises the story and the key things that happen

The maths in the episode explains the key mathematical concepts that are featured in the episode

Using mathematical language – because it is important that practitioners model precise and correct mathematical language, there are suggestions of key sentences that you might use and have repeated; they provide a language structure to connect each mathematical idea to different contexts. Children will initially use their own language to talk about the mathematics, and will develop correct and precise language if this is modelled by adults.

Overviews of each series, their storylines and the mathematics addressed, are available as downloadable PDFs from the link below.

More materials are available on the CBeebies’ Numberblocks page, also linked below.

This has always been one of those problems that I have loved exploring. I recently found a website that will model the outcome in a brilliantly beautiful way. Here’s a little more about it from the Birthday Problem Wikipedia page:

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.

It may seem surprising that the probability is above 50% when there is a pair with the same birthday for a group as small as 23 individuals. This is made more plausible when considering that a comparison will actually be made between every possible pair of people rather than fixing one individual and comparing him or her solely to the rest of the group.

https://en.wikipedia.org/wiki/Birthday_problem

The Pudding’s Russell Goldenberg has created this website to demonstrate this paradox.

Have a visit, have a play and contribute to the data.

I would absolutely use this as a hook the next time I need to tackle statistics with an upper Key Stage 2 class!