It’s here – the celebration of the positive contribution maths makes to all of our lives. If you haven’t downloaded it already, and are looking for some last minute ideas, click on this link to be taken to the Maths Week Scotland webpage and click for the activity pack suitable for your level. Remember to send us your pictures of all the fun.

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Maths Week Scotland Online Training

6 More Sleeps until Maths Week Scotland!

All sessions can be accessed through the digital hub.

Monday, 28th September 4.15pm

Games and Activities for Math Week Scotland – And Beyond!

Join us for the sharing of a small selection of games and activities designed to support Maths learning. The presentation is suitable for all levels of the Primary School.

Wednesday, 30th September 4.15pm

Listening, Talking and Numeracy?!

For this special session, we will be joined by a Literacy Development Officer. We will explore the role Listening and Talking has in the maths classroom and ideas as to how to support children to explain their mathematical thinking.

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Inset Day Digital Drop In

Tuesday, 15th September 2.30 – 3.30pm

On the Tuesday inset day, join us for an informal maths and numeracy chat session. If you have any questions or queries we’ll do our best to answer them.

Click here for the link to join, or enter via the Highland Digital School Hub.

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Outdoor Maths Kit – Maths Week Scotland Boxes


The Science Skills Academy have teamed up with Maths Week Scotland to send an ‘Outdoor Maths Kit’ to every Primary School in the Highlands.

The kit is targeted at Second-level and contains 17 outdoor activities for boosting numeracy. To help launch the kits, the Science Skills Academy are offering three CPD webinars on the inset days. Timings of the sessions are detailed below and the Tuesday is a repeat of Monday. The sessions will also be recorded and made available on the digital hub.

Please sign up on the CPD website.

**Please note – these sessions are only available to Highland Council Staff**

10:00-10:30 Outdoor Maths for Second-level

This webinar will provide a quick overview.

11:00-12:00 Numeracy games and problem solving (Second-level)

This webinar focuses on physical tasks that get pupils outside estimating, measuring, calculating and solving problems.

  1. Group games – Fast-paced games to get whole class running around and thinking on their feet.
  2. How far can we fly? – Investigated angles  using paper planes and scale models.
  3. Get your bearings – Plot a course using bearings. Measure and follow angles accurately. Draw and use a map to scale.
  4. Car Park Conundrum – Measure car park spaces and carry out calculations for total area and a proposed extension. Produce scale drawings.
  5. Explore The Perimeter – Challenge pupils to draw shapes with a specified perimeter using chalk. Accurate calculation and measuring required.
  6. Highest Heights – Estimating the height of trees and other objects that are too tall to measure.
  7. Tree-mendously Old – Measuring the girth of trees and calculating the age of trees.
  8. Maths Trail – A toolkit and example ‘bases’ to help you create a maths trail at your school

13:30-14:30  Using outside space for Data Handling, Graphs and practical maths (Second-level)

  1. Glorious Graphs – A variety of ideas for data that pupils can collect outside and then produce a graph. Looking at the graph what can we conclude?
  2. Is Faster Better? – Pupils survey cars in the car park. Research speed 0-60 and mpg then graph and compare this data.
  3. Make A Bolt For It – Pupils gather data about their stride and height then use stopwatches to test their pace. Use a scatter graph and evaluate whether there is a correlation.
  4. Pace & Distance – Pupils measure a ‘race distance’ then apply percentages to increase and decrease the race area. Stopwatches used to record pupil’s pace over each distance. Does pace increase by the same percentage as the distance did?
  5. Hopscotch Madness – Playing Hopscotch to gather data and use the stopwatch to record the time taken.
  6. Scavenger Hunt – Collect objects found outside then prepare pie charts and bar charts with the data.
  7. Shop ‘til you Drop – Pupils form two teams, shopkeepers and customers. Shopkeepers track their profit and loss. Customers calculate the balance on their debit card. Add flash sales and price increases to increase the complexity.
  8. Place value charts – Using chalk and natural objects to practice place value.

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There’s more to subitising than meets the eye!

Continuing with our ongoing theme of sharing the guidance documents that we are producing to support the new Highland Numeracy Progression Summary Documents, today will look in more detail at the document on subitising.

We frequently see the perception that subitising is just about recognising how many dots are on a five frame or tens frame or perhaps in an irregular pattern with the goal being just to know how many dots there are.  There is so much more to subitising than this and through rich discussion important mathematical ideas including can be developed including but not limited to: spatial awareness, estimation, patterns and relationships, mathematical properties and relational thinking.

The guidance document explores subitising in more depth including distinguishing between two types of subitising:

  • Perceptual Subitising 
  • Conceptual Subitising

As well as subitising in different ways including: spatial, temporal and kinaesthetic subitising.

We also explore ways in which conceptual subitising can be used to support a range of different ideas including:

  • Composition and Decomposition
  • Addition and Subtraction
  • Basic Facts
  • Place Value
  • Multiplication and Division

We discuss how subitising can be made more or less complex depending on the types of arrangements used.

We also discuss common misconceptions and things to look out for.

And finally, there is further exemplification of some of the ideas that subitising builds the foundations for.

Regardless of whether subitising is something new to you or you are very knowledgable about it already, we hope there is something in the document to start you on your journey or an idea that you hadn’t considered before that gets you thinking.

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Maths Week Scotland – One month to go!

28th September – 4th October – Pin your school on the map.


Highland schools are beginning to pin their school on the Maths Week Scotland website .   This week is an opportunity to celebrate the importance, enjoyment and contribution that maths makes to our lives.  Schools plan from the big scale – with a week of spectacular activities and maths parties, to the small scale where they plan a day of maths fun, or a special lesson.  Whatever you choose to do during the week – let’s celebrate together and remember to pin your school on the map!

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Mathematical Properties – What underpins children’s informal strategies?

This post, which follows on from the last two, forms a series of posts that aims to highlight some of the guidance documents that we’ve included in the new HNP Summary Documents for each year.  If you haven’t read the last two, you can find them here:

Making sense of part-whole strategies for addition and subtraction

Progression in Number Ranges at First Level (First** and First***)

Today’s document, Properties of Addition and Subtraction, has several aims:

  • To raise awareness of the mathematical properties that underpin the informal strategies that pupils use.
  • To highlight some of the main features of the guidance document.
  • To try and bridge a gap between Primary and Secondary.

The document is quite lengthy and it’s not intended that you read it straight through from start to end but use it more as a guide or reference document to support your planning, teaching and understanding of mathematics.

I’ll be honest, when I started teaching, my knowledge of the properties referred to in the document, some of which include:

  • the commutative property,
  • the associative property,
  • the distributive property,

was limited.  I may have had an implicit awareness of them from school, although my schooling was very much of the rules and procedures style and asking why something worked was met with the response that I didn’t need to know why, I just needed to learn it.  I may have covered them very briefly on my teacher training course but again, I’m not particularly aware of them having much prominence there although they are clearly in the main texts that were part of the course: Haylock was one and Frobisher was the author of the other.  I believe these are still the main texts used on courses today… although they may be several editions on!

So, if you read the document and think that some of the content is a bit heavy going… fear not!  I would have also felt that way at one point too.  That being said, I do feel it is fundamentally important that teachers at both primary and secondary have a deep understanding of the properties and how/where they are used.

From experience, although this is purely speculation, a lot of the recurring themes where children get stuck or have misconceptions appear to stem back to a lack of understanding about these mathematical properties.  I believe a lot of this could be mitigated if both pupils and teachers being more aware of the properties.  Algebra would be a good example of this but another good one is pupils frequently trying to solve problems like 52 – 25 but getting an answer of 33.  The document highlights issues like this and connects them back to the properties.Screenshot 2020-08-28 at 09.41.29.png

An additional point to make here is that from a really young age, an implicit awareness of the properties can be fostered as part of play based learning.  Ideas for activities that support a developing awareness of the properties is included within the document – this includes ideas for pupils in Nursery settings but extends to activities for older pupils too.Screenshot 2020-08-28 at 09.42.00

The activities don’t need to be dry, and if teachers really understand the properties, incorporating understanding of them while pupils are exploring different strategies can promote curiosity as to how on earth it’s possible to solve a problem in that way or how someone has solved a seemingly complex problem in a matter of seconds!  Ideas are given about how to support this kind of discussion and how to extend pupils’ understanding of these properties through the development of relational thinking (among other things).Screenshot 2020-08-28 at 09.43.04.png

And there is, hopefully, a clear explanation of what each property is and how it links to the informal strategies that pupils use.  This ties back well do the guidance document on part-whole strategies for addition and subtraction.Screenshot 2020-08-28 at 09.42.42

The final point I want to make is about bridging the gap between primary and secondary.  My feeling is, and this is a generalisation based on my own experiences and certainly not true in every case, that secondary teachers have a good awareness of the mathematical properties but not the informal strategies that pupils use and primary teachers have a better understanding of the informal strategies that pupils use but lack the understanding of the mathematical properties.  If this gap could be bridged, by both parties, then I think primary teachers would be in a better position to help guide the use of pupils’ informal strategies to increasing efficiency and sophistication, through greater awareness of the mathematical properties at play.  If secondary teachers were more aware of the informal strategies that pupils use and the mathematical properties that underpin them, it would become more apparent how these properties are the same properties at play when pupils learn algebra and so these ideas, that pupils often find so hard to grasp, can hopefully be attached to something that pupils are more familiar with and can generalise from.

I’d be interested to know people’s thoughts on this and whether this reflects other people’s experiences or not.

As ever, if anyone spots any mistakes or anything that is not accurate within the documents please do let me know so I can address this.

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Progression in Number Ranges at First Level

The post yesterday was related to making sense of part-whole addition and subtraction strategies that pupils use and showed some examples of these with concrete materials and visual representations as well as exploring the mathematical properties that underpin them.

The guidance document I’m going to link to today has a progression of number ranges at First** and First***.  The two documents could be used alongside one another to support your planning.  (We will hopefully create one of these for Second Level too, in due course.)

An overview of the document is provided below including some important points to keep in mind.

  • The numbers are all presented as bare numbers e.g. 37 + 8 (rather than in word problems or other contexts) this is purely to illustrate the numbers involved and not a suggestion that you should only provide examples in this way.
  • These numbers should be used as part of a variety of problem types as has been exemplified elsewhere, these include problems that involve comparison (and looking at the difference), situations where you are breaking a whole into parts (part-part-whole) and problems that involve the more common problem types of increasing or decreasing a quantity including varying which part of the problem is unknown.
    This also includes varying the type of practice task you give pupils.  Presenting tasks in different ways will help draw out different relationships or underlying properties.

    Screenshot 2020-08-21 at 09.40.14.png

    Screenshot 2020-08-21 at 09.40.26

  • When you use the number ranges, they should include a variety of equation representations e.g. 15 = 5 + ? or 6 + ? = 5 + 10 as well as the standard representation 5 + ? = 15.  This helps pupils make better sense of the actual meaning of the equal sign.  This should also extend to the use of inequality symbols e.g 5 + 10 < 6 + ?

Screenshot 2020-08-21 at 10.07.17

  • At each level there are several main milestones, for want of a better word, in terms of solving a particular type of problem.  These have been broken down into smaller steps but this is not necessarily so that teachers teach in these micro-steps one step at a time.  It’s more to help teachers understand the smaller skills involved in achieving the end goal.  They can then use this to help them make sense of how they are going to structure their teaching, what type of practice type might be useful, what connections they will make and how they will support pupils to understand the mathematical properties.Screenshot 2020-08-21 at 09.12.38Screenshot 2020-08-21 at 09.13.48
  • And last but not least, there is a summary of the types of numbers that lend themselves to the different strategies that were explored in the guidance document that was explored yesterday.Screenshot 2020-08-21 at 09.14.12.png

From my experience, a lot of textbooks don’t promote this level of thinking and the way the questions are organised and the types of representations they offer often limit the opportunities for really understanding and exploring the mathematics in an enjoyable way that promotes pupil questioning and curiosity.

Hopefully this document alongside the other ones we are sharing will mean people feel better equipped to understand the progression of learning and also plan meaningful, engaging experiences for their pupils.

As always, if anyone spots any mistakes or disagrees with anything then please do let us know!

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Making sense of part-whole strategies for addition and subtraction

Yesterday we shared the (draft) materials for the HNP Summary Documents for the rest of First Level.

Over the next few days, we’ll highlight a few of the guidance materials and example activities that are contained within the Summary Documents to help people know what is available and how it can help.

Today we’ll look at the the document:

Addition and Subtraction: Part Whole Strategies Summary Guidance First**/First***

Firstly, it’s important to know that if you are teaching pupils below or above these levels the document is still relevant.

  • For those working with pupils below First**, it is important to know what’s coming next so you can make sense of why certain skills that your pupils are working on are relevant and how they feed into future strategies.
  • For those working with pupils above First***, the strategies that pupils will use to solve addition and subtraction problems are the same, so this document will still help you to make sense of content relevant to Second Level and above.  The difference between First Level and Second Level and above will be related to:
    • The number range the pupils work within.
    • The pupils’ ability to more effectively choose an efficient strategy based on the numbers within a particular problem.  It should be noted though, that there is still an expectation at First Level that they are reflecting on and justifying their choices.
    • The pupils’ greater understanding of the mathematical properties that underpin these strategies and their subsequent application to algebra.

Within the document you’ll find information related to the following areas.

General Guidance which includes:

  • A general look at how to approach pupil understanding of part-whole strategies (although ideas for teaching is covered in more detail in another document).
  • Information about whether pupils need to learn all the strategies!
  • Information about language and making connections.

Jump and Split Strategies

  • Have you ever wondered why your pupils answer problems like this: 63 – 25 with incorrect answers like 42?
    This is explored in the Jump and Split strategies section.

The Part-Whole Strategies:

The part-whole strategies, that pupils might use to solve addition and subtraction problems, are explored in more detail including:

  • Prior knowledge that may be required.Screenshot 2020-08-20 at 15.11.39
  • Common misconceptions.
  • Representations with concrete materials and visual representations that might support understanding.Screenshot 2020-08-20 at 15.13.54.png
  • The mathematical properties that underpin certain strategies.
  • A video example of a pupil using the strategy to solve a problem mentally.
    While most of the videos show examples of number ranges and strategies at First** and First***, this particular video is highlighting an example of a pupil using a strategy to solve a problem in a number range that is more closely related to Second***.


We hope you find the documents useful and we’ll share some more detail about what’s inside some of the other materials over the next week or two.

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Highland Numeracy Progression Summary Documents: First Level

The Highland Numeracy Progression Summary Documents for the rest of First Level are now available on the Shared Drive, as well as on the blog.  They will be added shortly to the Highland Digital Hub.

A huge amount of work has gone into the documents and the additional supporting Guidance Documents.  We hope that people find them useful for their own knowledge and understanding as well as to support their teaching.  We’ll share some of the features of the Guidance Documents over the week to help people navigate their way around some of the additional materials.

As a reminder, if you haven’t already, please read the HNP Summary Documents: Overview and Rationale before using the documents so you understand them better and use them appropriately alongside other resources we have available.

These are ‘live’ documents which means additional supporting documentation and resources will be added on an ongoing basis.  As such, we suggest you use them online (or regularly check that you have the most up to date version) rather than download them.

Although we are adding the rest of First Level, the section on Multiplication and Division is still being constructed and will be added to the document soon.

We are currently working on Second Level and hope to have this out within the next three weeks.


First** HNP Summary Document.png


First*** HNP Summary Document

As always, if anyone happens to spot any mistakes, please do let us know and if you disagree with any of the points we’ve made then we’d be more than happy to have a discussion about this.  

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