At Danson, we believe that mathematical success is possible for all
As a school, maths lessons will include the use of concrete materials, pictorial representations, varied fluency, reasoning and problem solving to ensure that children are able to master the curriculum and approach abstract concepts with confidence. This process enables children to think mathematically, using their language and communication skills, so that they can independently apply their learning to a new problem in an unfamiliar situation. In EYFS and KS1, we follow the Mathematics Mastery programme for teaching and learning and, in KS2, we follow the White Rose Maths planning scheme.
Danson children are inspired to be passionate about maths and to think critically when working in a mathematical manner. They are taught to deepen their thinking through their approach to tackling challenging problems and investigating possible outcomes. Children are posed with a series of questions to increase their knowledge and understanding of specific objectives and then they are encouraged to create their own questions to make connections between different mathematical concepts and topics. We provide children with a broad and balanced range of opportunities for maths learning to take place, including but not limited to:
- Daily counting
- Quick recall of known facts
- Low stakes retrieval quizzes
- Outdoor learning
- Arithmetic fluency practise
- Mental maths quizzes
- Number games
- Data collection and statistical analysis
- Scientific graph drawing
- Storytelling in maths
- Problem solving
- Reasoning and vocabulary application
The National Curriculum for Mathematics aims to ensure that all pupils:
- Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
- Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Concrete, Pictorial, Abstract Approach
During maths lessons, we use the CPA (Concrete, Pictorial, Abstract) approach of learning to develop a deep understanding of maths as part of mastery learning. CPA is a highly effective approach that develops a deep and sustainable understanding of maths for pupils. This approach involves the use of concrete manipulatives (such as place value counters) and pictorial representations before moving on to abstract symbols and problems. When teaching for mastery, the CPA approach helps learners to be more secure in their understanding, as they have to prove that they have fully grasped an idea. Ultimately, it gives pupils at Danson Primary School a firm foundation for future learning.
Every classroom in school has a range of age-appropriate manipulatives to support learning. Some of which include:
- Digit cards
- Place value charts
- Dienes/ Base 10 equipment
- Place Value counters
- Number lines and hundred squares
- Place value arrow cards
- Bead strings
- Counters/ cubes
- Real-life objects
In the pictorial stage of learning, children are provided with a range of visual representations of key mathematical concepts. At Danson, we use the Bar Model to present children with abstract number concepts in a visual way. The visual representations of bar models become embedded in pupils’ long term memory and are helpful in making connections between other areas of the maths curriculum. Bar modelling is an effective tool in a mathematicians’ repertoire as all it requires is a pencil and piece of paper. Bar modelling begins in EYFS with pupils making towers to explore pre-counting principles, more or less, higher and lower and sizing of greater or smaller. Bar models are then used in all areas of maths throughout Key Stage One, including the use of part-whole models for exploring addition and subtraction. In Lower Key Stage Two, part-whole bar models are used to explore multiplication and repeated addition. Comparison bar models are used to discuss difference problems and division. In Upper Key Stage Two, bar models are used to explore complex multi-step problems around fractions, algebra, ratio and measure.
In the abstract stage, the final stage of the CPA approach, children use numerals, shapes, patterns and letters to represent key mathematical concepts. This stage is critical in enabling pupils to be able to apply their knowledge to a variety of problems and real life situations. Using numbers predominantly, children are taught efficient methods to solve problems and explore investigations. The ability to understand abstract concepts and think back to prior learning of visual and concrete representations is a core skill that prepares pupils for further study at secondary school and beyond.
In a previous themed Maths Week, children spent the week exploring, clarifying, practising and applying their learnt knowledge of bar models to solve problems. This was an excellent way to encourage dialogue in mathematical lessons, especially ‘Bar Modelling Buddies’, where children were able to swap with another class to teach each other how to use the bar model!
Maths Week 2022-2023
To inspire all our pupils to enjoy and value maths learning, Danson hosts a special Maths Week each year. This year, there were a variety of events, activities and lessons across the week. An important part of our curriculum at Danson is learning about money and we are proud members of the Centre of Excellence in Financial Education. This year, in Maths Week, we brought maths into a real-life context through hosting classroom shops. Children experienced the important life skill of exchanging money.
In EYFS and KS1, children took part in a ‘Bring and Buy Sale’ during Maths Week to raise money for school funds and important maths resources. Pupils kindly brought in donations that were age-appropriate and inspired purchases to be made. This ranged from toys, books, stationery, sweets or biscuits (no nuts) or homemade items. Children priced their items and were supported in buying things from the sale and acting as ‘shopkeepers’.
In KS2, children took part in the ‘£20 Shop Challenge’ during Maths Week to raise money for
school funds and important maths resources. Each class was given £20 to spend on items such as toys, stationery, sweets (no nuts) and drinks.The challenge was to sell all their items and make the most profit for their class. Children priced their items and were responsible for selling and buying things from the sale.
We also held a dressing-up competition for the whole school related to NumBots and Times Tables Rock Stars, where pupils and staff dressed up as robots and rock and rollers!
We raised an astounding £1868.66 during the week - thank you so much for your support!
Here is what some pupils had to say...
Pupil Voice - Maths Week 2022:
‘I loved maths week. We used our learning to buy the right amount for our budget and get change if we needed it.’ – Year 6 Pupil
‘ I went to the maths shop two times and bought sweets, pencils and toys. The prices were reasonable and it was really fun.’ – Year 4 Pupil
‘It was good to raise money to help our school and help our learning about money. Everyone’s happy!’ – Year 5 Pupil
Children at Danson focus on vocabulary in every maths lesson and in relation to all maths tasks. The correct terminology is modelled for children and it is discussed in context and related to real life situations. ‘Star words’ are used at the start of, and within, all lessons for children to practise using crucial vocabulary. Children will have many opportunities to discuss maths language with their peers and ‘talk as thought’ dialogue is promoted in all lessons. Children are supported with sentence stems, word banks, visual displays and additional resources when appropriate. Parents are provided with a list of key maths vocabulary when children enter a new year group.
By the end of Year 4, all children should have a quick and accurate recall of all multiplication facts up to 12 X 12. This vital knowledge supports children in other areas of mathematics, such as fractions and division. Also, children in Upper Key Stage 2 must have a secure grounding of times table facts to successfully solve problems. For depth of learning, we believe it is important that children are given the opportunity to see, explore, and understand the mathematical structures, patterns and relationships within the times tables.
The table below shows which times tables facts are learnt in which year groups at Danson:
|Progression of the Teaching of Times Tables|
|Reception||Year 1||Year 2||Year 3||Year 4||Year 5 and 6|
I can count in steps of 1 I can count in steps of 2
I know all of the reception
I know all of the Year 1
|I know all of
I know my 4
I know my 8
I know my 6
I know my 11
|I know all of
I know my 9
I know my
I know my 7
Online Resources to Support the Teaching of Mathematics: NumBots and Times Tables Rock Stars
At Danson, we believe that technology plays an important part in our society and it should be reflected in our practice of teaching and learning. We use a variety of technology software and hardware to inspire children and enhance the teaching of mathematics.
This software is aimed at pupils in EYFS and Key Stage One who are practising crucial place value and arithmetic skills. NumBots supports every child in achieving the understanding, recall and fluency in mental addition and subtraction, so that they move from counting to calculating. Pupils choose their own avatar of a ‘Bot’ before launching into ‘Story’ and ‘Challenge’ modes, where pupils can practise different addition and subtraction methods and calculations. As they progress, pupils collect achievement badges and unlock hundreds of new levels and challenges. In the Story Mode, they will also discover parts, helping RustyBot upgrade from Rust to Diamond - so he can shine inside and out. Tables and charts enable teachers to keep track of progress and usage at a class and individual level.
Times Tables Rock Stars (TTRS)
We use Times Tables Rock Stars as a resource to support children in improving their accuracy and speed when recalling multiplication facts. Times Tables Rock Stars is a fun and challenging programme designed to help students master their times tables. It is accessible at home and school and children earn coins for correctly answering questions. Each child creates their own rockstar avatar and, by playing in different game modes (such as ‘Garage’, ‘Gig’, ‘Rockslam’, ‘Arena’ and ‘Stadium’), earns coins to buy special items to modify their avatar. The platform is safe for children to use and encourages a competitive element when ‘battles’ are arranged between groups. ‘Battles’ are low-stakes competitions that can be against classes, year groups, teachers, other local schools or even against other classes and schools in the country as part of national battles. Furthermore, children are able to practise specific times tables that they need to consolidate as the programme makes use of a meticulous automatic training mode which tracks children’s success and gaps in knowledge to set times tables questions.
Pupil Voice - Times Table Rockstars
“I enjoy playing Times Table Rock Stars because it is fun and competitive when I play against my friends and people around the world.”
“I like that when I’m using Times Table Rock Stars I can solve multiplication and division equations.”
“Times Table Rock Stars is fun while learning the times tables that I don’t know.”
Danson as a 'Centre of Excellence' in Financial Education
Danson Primary School is proud to be recognised as a 'Centre of Excellence in Financial Education' by Young Money. Across the school, the teaching and learning of financial education is incorporated into many different areas of the curriculum, notably in Maths, PSHE and Citizenship lessons. In line with Young Money’s planning frameworks, pupils’ learning is covered across four different strands: how to manage money, becoming a critical consumer, managing risks and emotions associated with money and understanding the important role money plays in our lives.
Young Money's planning frameworks enable teachers to gauge pupils’ starting points in financial education, map existing provision and ensure there is progression across different year groups. As part of Danson's commitment to developing pupils' financial literacy, the school often involves external organisations in order to raise children's aspirations, such as by inviting volunteers from the banking sector to support children in NatWest workshops.
At Danson, we believe that developing pupils’ financial literacy from a young age will set them up for whatever future path they endeavour to follow. We incorporate financial literacy with storytelling in mathematics and teachers read a class text once per year that has an element of financial education that can be explored and discussed with pupils. Children are supported through the use of manipulatives, including pretend coins and notes that look realistic.
The role of parents does not just mean supporting and facilitating homework. It is vital that parents show a positive attitude towards mathematics and share the need for it in real life with their children. Negative mindsets towards maths can become a barrier to learning for pupils and parents/carers should aim to enthuse their children about the subject.
The maths curriculum has greatly changed over the last two decades and Danson supports parents with this through workshops, information on the school website, homework letters and suggested digital and non-digital resources to use at home. Parents and carers can positively impact their child’s mathematical understanding by engaging with the suggested materials from school and discussing maths with their child.
- Talk positively to their children about their maths learning on a regular basis
- Engage with homework and newsletters to see what topics are being taught
- Ensure regular rapid recall of key facts are practised at home (e.g. times tables or number bonds)
- Ensure regular real life maths is drawn attention to (e.g. telling the time on an analogue clock, paying with coins and notes or measuring ingredients while cooking)
- Encourage the practice of new and alternative written methods
- Encourage the use and application of the correct vocabulary related to maths topics
Maths Homework and Supporting Your Child At Home
Regular practise at home of key facts can support children with their maths learning at
school. We recommend that parents/carers and children make use of our online learning
platforms, NumBots and Times Tables Rock Stars each week so that pupils are able to recall
key facts with fluency, speed and accuracy.
The table below shows which calculation methods we teach at Danson across school. (For
more information and examples please click on the following link:
|Progression in the Teaching of Calculations|
|EYFS||Year 1||Year 2||Year3||Year 4||Year 5||Year6|
|Addition||In EYFS the main focus is on the concept of number. The four operations are explored (at an age related level) but children will leave EYFS with a secure mastery of number||Combining two parts to ake a whole: part whole model. Starting at the greater number and counting on. Regrouping to make 10.||Adding three single digits. Number lines Bar Method Partitioning||Expanded column method. Column method - no regrouping. Column method-regrouping (up to 3 digits)||Column method- regrouping (up to 4 digits and including decimals to 2dp)||Column method-regrouping. (with more than 4 digits)(Decimals-up to 3dp)||Column method-regrouping. (Decimals- with different amounts of decimal places)|
|Subtraction||Taking away ones counting back Find the difference Part whole model Make 10||Counting back find the difference Part whole model||Expanded column method. Column method with no regrouping ( up to 3 digits) Column method with regrouping ( up to 3 digits)||Column method with regrouping (up to 4 digits and including decimals to 2dp)||Column method with regrouping (with more than 4 digits) (Decimals- up to 3dp)||Column method with regrouping (Decimals- with different amounts of decimal places)|
|Multiplication||Doubling Counting in multiples Arrays (with support)||Doubling Counting in multiples Repeated addition Arrays- Showing commutative multiplication partitioning to X (GD)||Counting in multiples Repeated addition Arrays- showing commutative multiplication Grid method||
Short multiplicaion (up to 4 digits)
(2 and 3 digit multipled by 1 digit)
|Short multiplication (up to 4 digit numbers multiplided by 1 digit) Long multiplication (up to 4 digit multiplide by 2 digits) X with decimals||Short and long multiplication (multi digit up to 4 digits by a 2 digit number) X with decimals|
|Division||Sharing objects into groups Division as grouping||Division as grouping Division within arrays Division with a remainder (GD)||Division within arrays Division with a remainder Short division (2 digits by 1 digit-concrete and pictorial)||Division within arrays Division with a remainder short division (up to 3 digits by 1 digit- concrete and pictorial)||Short divsion (up to 4 digits by a 1 digit number interpret remainders appropriately for context) -with decimals||Short division Long division (up to 4 digits by a 2 digit number-interpret remainders as whole numbers fractions or round) -with decimals|
Expanded column method
Expanded column method
Partitioning/ grid method
Expanded long multiplication
Short division with remainder
Short division with decimal remainder
Websites to support children’s learning in maths are many and varied. Some recommended sites are listed below.
These games help make learning times tables fun!
Exciting fun games suitable for Early Years and KS1 children.
An excellent website including games and activities for a variety of maths topics for Early Years, KS1 and KS2 children.
Lots of fun activities and games for a wide range of maths topics and ages.
Fun games that help KS1 children practise a variety of maths skills.
Fun games that help KS2 children practise a variety of maths skills.
A variety of games to develop your child’s maths skills whatever their age.
A variety of maths audio resources specifically focussing on helping children develop their mental maths skills.
An exciting way for 4-8 year olds to learn at home while having fun.
A wide range of games, activities, videos, advice and songs for children aged 4-7 and their parents.
Lots of maths games where the emphasis is on fun!