Making sense of missing number problems… at Early Level!!!

Hopefully that’s got your attention!

The mystery of why missing number problems are so maddening for many pupils is not really so mysterious when you begin to unpick why they might be having difficulties with them.

From experience, and this is purely anecdotal, it usually comes down to problems like
4 + ? = 9 or ? – 3 = 8 frequently being explored with digits alone… not a context or a concrete material in sight… no wonder it’s so difficult.

For context, I frequently carry out the basic facts diagnostic assessment with pupils from P1 to S3.  This includes both pupils who appear to be experiencing difficulties and those who are appear more confident in maths.  The most common answer to the missing number problem which is similar to this one: ? – 6 = 6 is… ZERO!  If I had to guess I would say for pupils that get this far in the assessment, the percentage of pupils answering zero for this is somewhere in the region of 90%.

It doesn’t need to be this hard though and early understanding about equivalence can be explored through engaging stories and activities.  Erikson Institute have conveniently collated ideas to use with 3 such stories that explore the idea of equivalence and which build the foundations for this type of problem before we even need to think about getting pupils to see this written down.

The three books mentioned include:

A Balancing Act by Ellen Stoll Walsh

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Twelve Ways to Get to Eleven by Eve Merriam

One is a Snail, Ten is a Crab by April Pulley Sayre

Click on the article to find out the ways these books could be used to explore this concept.

Do you know of any other books that explore these ideas?  If you do, feel free to share them.

After reading and exploring the stories, what other follow up ideas could you use to explore these concepts further?

Thanks to Seonaid, our Early Years expert for sharing this article.

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Maths Week Scotland – Maths v Sport

On Thursday this week, I was fortunate enough to attend the Maths v Sport presentation given by Dr Tom Crawford from the University of Oxford.

It was great to see a mix of adults and kids there.  It was a bit of a blast from the past for me as it turns out that I taught some of the kids in the audience 8 years ago when I first moved to Inverness!

The content certainly peaked my interest and the kids seemed equally engaged, especially with the penalty shoot out that occurred after learning the secrets of taking the perfect penalty!

I’ve also got a few ideas on how to shave some time of my marathon PB and I also now know where the best place would be for me to set a 2km rowing PB should I ever take up rowing.

It was really interesting to see so much maths going on in sport and beyond the usual things you might think of!

Let’s get more of this type of thing into our schools so those that haven’t yet seen the light can see what a fascinating subject it really is!

For those of you that missed it or who maybe aren’t into sports you can check out Tom’s website: Tom Rocks Maths or you might like to visit his page I Love Mathematics where you can find the maths behind some intriguing questions.
Being a bit of a Monopoly lover I thought I’d hone my strategy by watching the video below… hopefully nobody I play in the near future watches this!

Sadly that’s the end of Maths Week Scotland for this year but hopefully teachers, pupils and anyone else reading or engaging in any of the many Maths Week Scotland activities has been inspired.  Let’s strive to continue to help everyone see how relevant, intriguing, creative and fun maths can be for all between now and next year… and beyond!

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Math’s Week Scotland – Friday’s Challenge

Well, it’s not so much of a challenge today and more of a game to continue on with our weekly theme of bringing you a game a week that can be adapted to teach pupils working from Early through to Third Level and sometimes beyond.

This week we bring you Dotty to…  This is another game we’ve adapted from NRICH so thanks to them for the original idea.

Click on the link to see our adaptations of Dotty to… (you can also click on the image below).

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Click on the links below to find templates for:

I have played this with quite a large number of kids and they go mad for it!  When I return to schools where we’ve introduced it, it is often reported to be the ‘go to’ game.

You can use it for all sorts of things from copying patterns to addition and subtraction facts within 10, those missing number problems that kids often find tricky and all the way up to making sense of fractions, decimals and percentages!  We’ve even got an outdoor version we’ve called ‘Stones and Cones’.

We hope you enjoy this one, we’ve certainly had a lot of fun playing it!

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Math’s Week Scotland – Thursday’s Challenge

Great to see some photos on Twitter from classes solving some of the problems from earlier in the week!  We hope you’re having fun so far… here’s today’s challenge.

The Four Coins Problem

You’re creating a new coin system for your country.
You must only use four coin values and you must be able to create the values 1 through 10 using 1 coin at a minimum and 2 coins maximum.

What four coins do you choose?

Can you think of a second set of four coins that achieves the same goal?

I’m not sure of the original source of this problem so can’t credit the creator however if you’re looking for more of the same to challenge yourself or your pupils then I got this one from Mr Barton’s Maths and Logic Puzzles page.  It also appears in Jo Boaler’s Mathematical Mindset book and can be found on the Numberplay Blog from the New York Times.

Send us or tweet us @HNumeracy photos of your solutions and how you worked it out.

Did you use a trial and error approach?
Did you use a more systematic approach?
Did you think about any connections or relationships you know already about the numbers 1 to 10?



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Math’s Week Scotland – Wednesday’s Challenge

Today we bring you a problem solving task from NRICH called Four Colours

This would be suitable for both Primary and Secondary pupils.

Less experienced problem solvers may take more of a trial and error approach to this while others may try to find a more systematic way to approach this.

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If you were able to solve it with Four Colours… can you challenge your self with Nine Colours

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Math’s Week Scotland – Tuesday’s Challenge

Today we bring you a strategy game: The Shannon Switching Game from the University of Edinburgh.

This games is aimed at Upper Primary and Secondary.

There are 10 different game boards to choose from (two examples are below).
The rules can be found here.

Take it in turns to ‘join’ or ‘cut’ a line… can ‘join’ make a path between the two red dots or will ‘cut’ ruin their chances?

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Find a partner and get stuck in… can you find a winning strategy?

Is the game fair or does someone have an advantage?
Does it matter who makes the first move?

If you’ve been solving any of your own problems, let us know what the problems were and how you went about it.

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Maths Week Scotland – Monday’s Challenge

This activity has been inspired by the work of John Mason’s More/Less Grids and is almost an exact replication of his original More or Less Perimeter and Area Task.

The original task can be found here with other ideas for adaptations.

I was reminded of these at the Improving N5 Conference on Saturday when Chris McGrane mentioned them in his presentation.  Here is a link to his blog: Starting Points.

The activity below would be suitable for upper primary and into secondary.  Click on the image below to get a copy of the full PDF with instructions of what to do as well as prompt for things to think about.Screen Shot 2019-09-30 at 01.09.04.png

If you or your pupils have a go at this activity, send me a photo of their end result and we’ll collate these on the blog for others to see.

Could you adapt this More/Less Grid to promote mathematical thinking in a different area?

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