# Maths teaching ideas and articles

Free teaching ideas and activities for your classroom.

Paul includes articles on primary maths teaching and learning, new developments and other maths topics for primary teachers.

If you have a specific maths question you want to ask, then please take a look at Ask Paul.

28/04/2022
Confused about the language to use with 3D shapes?
A question that I am regularly asked concerns the correct language to use when teaching the properties of 3D shapes. This is a typical question I had from one school:
Spheres are often referred to having one face, cones two faces and cylinders three faces. Mathematically a face on a 3D shape is part of a plane and therefore is flat. Does this means that much of the language that has been used is inaccurate?

14/03/2022
Pi day March 14th - take a look at circles
Pi day can be a whole school event, with KS1 children finding circles and KS2 children discovering a simple Pi pattern through measuring, using multiplication and division facts for x3 and rounding to the nearest whole number. Other Pi based activities include rounding decimals, looking at the format that dates are written around the world and, of course, it could include eating pies!

12/01/2022
Points of view - plans and elevations of 3D shapes
In our everyday lives we make a wide-ranging use of diagrams, maps and floor-plans which all assume an ability to interpret plans, elevations and aerial views. Giving children the opportunity to explore plans, side elevations and front elevations of 3D shapes, and represent them in different ways, is a useful step towards developing these skills.

15/11/2021
Objectives-led teaching or purposeful experiences?
An article titled 'Using local context as a hook to ignite interest and excitement’ was written a few years ago in the NCETM Primary and Early Years Magazine. I recently re-read it and it made me think about current teaching approaches, based on the curriculum advice we are getting. The curriculum is currently objectives-led, with small steps and assessment goals driving the teaching, rather than it being determined by purposeful experiences. However, the NCETM article, written by a Y6 teacher, emphasised the latter approach.

06/09/2021
How do I plan my maths using the Ready-to-progress criteria?
The Department for Education, with the support of the NCETM, produced non-statutory guidance last year to 'help teachers and schools make effective use of the National Curriculum to develop primary school pupils’ mastery of mathematics.'  They include Ready-to-progress criteria, but what is the best way of using these? Here are some suggestions to help you use these to enhance your planning and teaching.

15/01/2021
Misconceptions in maths - breaking down the problems
An aspect of teaching mathematics that can be very satisfying is spotting the reason why a child has misunderstood some maths and then being able to deal with it quickly so they are put back on the correct path in their learning. This all involves a teacher having a good subject knowledge – an understanding of the curriculum, the small steps of progression, the way a concept or procedure is represented, the connections there are and the best way of interacting with the child.

05/01/2021
Learning objectives, expected outcomes and small steps of progression
When planning a unit of maths using a mastery approach, the learning objectives are a key starting point. Teachers begin with a set of objectives, with many teachers then using statements of expected outcomes to determine the learning that has taken place. I also like to use small steps of progression alongside these. I am going to take a look at the purpose of each of them, to make the most of these linked aspects at the start of the planning process.

07/07/2020
Tracking maths progress and identifying gaps
I was sent this query from a teacher a few days ago: I am sure you have been asked this many times, but we were just wondering if you have any plans to release documents to assist with the return to school in September? We are still unsure as to whether we should continue with the plans and plug gaps where needed, start where we left off in March, or push certain areas (such as number) first before moving on. Any advice or guidance from yourselves would be really appreciated.

18/05/2020
Exploring fractions on a grid
The topic of fractions can be one of the most challenging to teach and learn in primary schools with many hidden misconceptions ready to take hold as children dig deeper into the idea of rational numbers. It is a topic that children need to have time to explore and think about, using a variety of representations to help make sense of it. Here is a simple starting point that can be used in Y4-6 as an activity for exploring fractions as quotients, improper fractions, mixed numbers and equivalence.

13/02/2020
Using love (and hate) to calculate with negative numbers
Adding and subtracting negative numbers is easy enough to put into a context, but it can be tricky to find a good way of representing the multiplication of negative numbers so that it makes sense. A teacher asked me about it recently and we talked about a nice connection to Valentines Day.

27/11/2019
Pine cones, Fibonacci numbers and Christmas
The Fibonacci sequence is an amazing mathematical pattern found in nature and there is evidence of the sequence in this layer of a pine cone. One layer of this pine cone shows 21 white marks where the seeds had been....and yes, the layer above this had 13 seeds.

10/09/2019
Modelling and representing place value
To follow on from my previous article, understanding place value, I take a look at the way place value is modelled and represented. This is the key to getting a deep understanding of how our number system works. So which resources will support an understanding of place value?

02/09/2019
Understanding Place Value - 6 key aspects
Place value is a key concept for children to get to grips with as they are introduced to larger numbers. Without an understanding of it they will struggle to add, subtract, multiply or divide, let alone read and write numbers. Place value builds on from early counting and recognition of cardinal numbers to knowing the value of each digit in a number, understanding our base-10 structure and exchanging within larger numbers.

21/03/2019
Ten ways to make the most of algebra in your classroom
Ask most adults with an aversion to maths to think about the topic that turned them off the subject, and it is likely to be algebra. “I didn’t see the point…” is a common response, so what can we do to start children off with a positive view of algebra to hopefully stay with them for the rest of their lives?

14/01/2019
Creative teaching using graph stories
Graph stories are an engaging and open-ended way to explore continuous line graphs. As you know if you have heard me talk about maths planning, I feel that statistics and data handling in the primary curriculum are tools or forms of communication that can be used to support teaching and learning in all the other maths topics.

10/12/2018
Primary maths Christmas activities
Christmas maths activities for primary teachers to try with your class - a stocking full of ideas that provide children with valuable opportunities for maths learning and some Christmas festive fun. Choose from challenges that can be returned to over a few days or quick 10 minute fillers.

01/10/2018
Making sense of equivalent fractions
Being able to recognise and manipulate equivalent fractions is a key concept when working with fractions and an essential step towards ordering and calculating with fractions successfully. I find that children use models and images well to represent equivalent fractions, particularly with fraction bars. However, from observing lessons, the biggest issue seems to be a weak basic understanding of the numerator and the denominator and a lack of fluency when it comes to equivalence and proportionality.

14/09/2018
Mathematical language - using a maths dictionary
A key part of representing mathematical ideas, concepts or procedures so that it makes sense for children is about getting the language right. As teachers we each have (hopefully similar) ideas of what we mean by, say, 'product', 'divide' or 'angle' but it is not always easy to explain these to children. Using models, pictures and diagrams helps immensely, but so does accurate mathematical language. I have always had a maths dictionary at hand to help so I would suggest making use of one yourself.

29/08/2018
New content for Broadbent Maths users
I have recently updated the Broadbent Maths site which is a regular August activity for me. I'm always looking for ways to support your maths planning and at the same time help you dig deeper into mathematics teaching and learning. My MA was on the nature of 'deep' subject knowledge for primary teachers so I have built the content around my findings. This summer I have added 'Maths Topics' as a menu item.

13/07/2018
Clearing out the cupboards - make the most of old maths books
The end of the summer term is often a time for a thorough sort of your maths cupboards and resources. I heard from a past Warwick PGCE student last week and she was doing just that as a new maths subject leader. She had found some 'Broadbent Maths Boxes' that she was going to share with staff and it made me think that there are a lot of resources and books that are worth using, even if a few years old.

26/06/2018
Football - using the beautiful game as a context for teaching maths
Every two years or so I give lots of football related maths ideas to teachers. This is basically to coincide with the Euros or the World Cup when I always get excited and ultimately feel deflated. But perhaps not this year!

To help you with some ideas, here are the 'Top 5' football maths articles that I've written in the past.

16/04/2018
Enlarging shapes to explore their properties
A good way for children to understand the properties of polygons is to construct them precisely and accurately. Using a sharp pencil, a ruler and a protractor to draw and measure different shapes, they can then compare and ask questions about them. One issue with this for teachers is that progression in geometry is not clear, often because of the difficulty in breaking down the broad statements in the NC Programmes of Study. My Small Steps of Progression for geometry may help, which is followed by an 'enlarging shapes' activity.

19/03/2018
Ratio and egg sandwiches - give it a try for Easter
Teaching ratio is better understood when demonstrated, so start with a practical activity of making egg sandwiches and watch the maths roll on. This could be part of a themed maths week for Easter and include other challenges too. It also shows that maths is useful in everyday life and how ratios are used in cafes and kitchens to calculate quantities of ingredients.

18/03/2018
More testing in schools - is there an alternative?
Trials for the new multiplication tables test in Year 4 start this month in selected schools, ready for a roll out in 2019 and compulsory testing in 2020. March 2018 also sees the start of a £10 million contract to develop and run Reception baseline assessment - only 2 years after trials were scrapped. There are many critics of these new assessments and the amount of national testing in primary schools. So what can be done?

05/02/2018
Using Flip-Flops to practice multiplication facts
Flip-Flops are a great resource for practising multiplication facts– simple to make and fun to use. I have had them as part of my maths kit for years (I think they first appeared in Number Work for Infants by Thomas and Bannister in 1974) and when I used them in a school recently the teacher had forgotten all about them, even though they had been one of her favourite resources in the past. So here’s a reminder.

24/01/2018
Is a structured lesson sequence the way forward for your maths planning?
A sequence of lessons is the important part of planning that organises and structures a ‘unit’ of work or medium-term plan into the reality of what goes on in the classroom. It basically involves deciding the best way of moving the children on from what they know, understand and can do now, to what they are expected to know, understand and do by the end of the unit.

04/01/2018
Ofsted - should the EYFS framework for maths be more challenging?
Ofsted has expressed concern that the EYFS statutory framework has a number of weaknesses and that expectations, especially in mathematics, are set too low. They found that children were better prepared for Y1 in schools that had more challenging expectations. So, does the EYFS framework need to change?

03/01/2018
Supporting a self-evaluation of your maths teaching
With the start of a new year and a new term, it is a perfect time to have a think about your own maths teaching. Which aspects are you happy with and which parts do you know could be a little stronger? Of course, before deciding this you need to have an idea of the criteria on which to base your self-evaluation on. I have helped you out with this by adapting a Lesson Observation Prompt Sheet so that you can assess your strengths and the areas you need to work on.

02/01/2018
Teach maths in context - what's on in 2018?
Primary maths comes to life when it is placed in context, it can spark interest and give maths purpose when used to investigate real-life situations. So what events are there this year that could inspire your maths teaching? I've listed some annual events and a few that are only happening in 2018. There are teaching ideas and resources that you can use to plan your maths around the year of 2018.

06/11/2017
Learning multiplication facts? Take a look at the products
Many hours are spent in primary classrooms on activities to help children learn multiplication facts, with varying degrees of success. I’ve seen (and used) chanting, counting patterns, songs, games, trio cards, bingo, round the class cards, tables tests… and many more strategies to try to get it to stick. So here’s another strategy to add to the mix – focus on the products.

19/10/2017
Do we need a single professional association for mathematics in the UK?
The debate has arisen again over whether there should be a single amalgamated professional association for the teaching of mathematics, with a discussion paper recently published. The proposal is that the five professional associations should be amalgamated into a single association for UK mathematics education, with a variety of Special Interest Groups (SIGs).

03/10/2017
New baseline assessment to start 2020
Baseline assessments are to be reintroduced in 2020 and it looks like the national testing system will be narrow in the skills assessed, concentrating on numeracy and literacy. It will be completed in the first few weeks of children starting in Reception classes. In addition to the new baseline testing, teachers will still be required to complete the Early Years Foundation Stage Profile. What a welcome to school!

28/09/2017
Cross-curricular maths teaching and National Poetry Day
National Poetry Day comes round each September and it is definitely a good time to introduce some poems into your maths lessons. However, thinking about it, every day is a good day to bring some sort of creative, fun, thought-provoking ideas into your mathematics. This may be in the form of poetry, but it could also be through art or stories or science or any other creative context.

05/09/2017
Inspiring your class with maths - give a problem within a context
Giving a mathematical challenge to your class can provide purpose to the maths and sparks children's interest, particularly if set in an inspiring context. The problem solving process involves reasoning and thinking mathematically, while applying the skills or concepts they are learning. That’s all great, of course – but finding appropriate problems to match the learning objectives is not always easy and they are rarely set within a context that suits your class. So where can you begin?

04/09/2017
How to make your maths displays engaging and active
A lively and engaging maths display is an important element of the classroom, helping children understand the concepts, skills or procedures of a particular maths topic and providing opportunities to celebrate their achievements. Many governors, heads and subject leaders use learning walks to get a feel of the maths going on in a class and the obvious place for them to look first is the maths display.

05/06/2017
Using mobiles to explore complements of numbers
The visual representation of balanced mobiles is a great way to explore the complements of sets of numbers. Children need to be able to quickly recall the complements of 10, 100 and 1000 as well as the decade numbers to give them mental agility when calculating. Mobiles are also useful for practicing complementary addition to work out the difference between two numbers. This challenge to balance the mobile is open ended and is a great starting point that can be accessed by all abilities before progressing in complexity.

30/05/2017
Teaching money - include financial education too
Teaching money in primary maths involves recognising the values of coins and notes, making totals and giving change, understanding decimal notation and calculating with money to solve problems. It is also a good opportuntity to include financial education, looking at where our money comes from, what we use money for and how it makes us feel. Research from the Money Advice Service finds that habits around money are often formed by the age of 7 so this is an important topic to cover across the whole primary age range.

02/05/2017
Statutory assessment consultation - have your say
There is an opportunity for teachers to influence future statutory assessment in primary schools. The Department for Education and the Standards Testing Agency are asking for your views about assessment, the best starting point for measuring progress and the role of teacher assessment. A cross-party Education Select Committee report, published last week, suggests that current testing is having a negative impact on children’s education and well-being. So, while testing happens in schools this month, keep up to date with current findings around assessment and have your say.

27/04/2017
Chanting activities and interactive maths
Chanting activities involving a unison response can be a good way to practise aspects of maths that involve some sort of repetition. It is fun to do, but needs to be well managed by the teacher and this includes identifying the areas of maths it works best with and careful planning to include all abilities in this whole class activity.

07/03/2017
Multiplication - exploring Gelosia and Russian methods
As a follow up to the article on Napier’s Bones, I thought it would be useful to look at other historical (and interesting) methods for multiplication. There were two in particular that I used in my own teaching - the Gelosia and Russian Peasant methods. They were both great for exploring different ways of handling numbers when calculating and practising key skills, but I wouldn’t necessarily use either as a chosen standard method.

07/03/2017
Maths around a Roman theme
The Ancient Romans as a theme offers such a rich context for mathematical starting points. The 2014 NC programmes of study includes reading and using Roman numerals which would obviously fit in, but here are a few more quick maths ideas to add to your topic on the Romans.

07/02/2017
Logical reasoning in the primary maths classroom
On a visit to a school in Switzerland I was pleased to see a whole range of logic games and activities being actively used by a group of 8 year olds. The teacher explained that sorting by different attributes, reasoning and logical thinking were all key to the children having mathematical success so these games were used daily.

07/02/2017
Planning Assessment for Learning (AfL) questions and activities is an important part of good teachingHowever, AfL type questions need not be complex - a focus on learning and depth of understanding is the focus. A basic question structure that can be used for any maths topic can be very helpful and 'Give me a pair...' is a versatile start for questions to ask.

23/01/2017
Multiplying with Napier's Bones - new maths collection at the Science Museum
The Science Museum has a new maths collection and one of the artefacts is a wooden set of Napier’s ‘Bones’, you can visit the new maths collection online. Set your class the challenge of discovering how to multiply large numbers using Napier's numbers on a grid. A great problem solving activity that holds children's interest while reinforcing quick recall of mulitplication facts.

03/01/2017
Reflect on your maths teaching and take a look at the bigger picture
Once the term has started it is likely that you focus on your teaching for each day or week with little chance to reflect and look at your teaching in a wider context. If possible, take some time to reflect on what education is all about for you and then look at the best way you can make this happen in action.

03/01/2017
Interactive maths kits - add a geoboard for 'show me' activities
'Show me' activities are great for whole class starters and each child having their own maths kit helps your classroom management as well as making maths motivating for children. On a training course recently, where I give out maths kits with counters, number cards,100-squares and other manipulatives, a teacher suggested adding a geoboard to help with shape 'starter' activities.

03/01/2017
Calculate the day of the week for any date in 2017 - inspire your class
The 'doomsday rule' is a way to mentally calculate the day of the week for any date - without the use of a calendar. Looking at the patterns and rules and then using them to predict the day of any date gives children a reason to learn the order of months, the positional and ordinal number for each month, as well as developing a desire to play with numbers. A great maths motivator for the new year.

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