Primary Maths Development: Recommendations for Parents

When children leave primary school, it is important for them to:

• Enjoy maths and see its relevance in ‘the real world’.
• Have a growth mindset about maths – developing a ‘can do’/ ’have a go’ approach. 
• Have a secure knowledge of number facts and an excellent understanding of the four operations: addition, subtraction, multiplication and division, using this knowledge to carry out calculations mentally and to be able to calculate percentages.
• Have solid mathematical thinking and reasoning – being able to choose efficient methods for a range of mathematical problems. 

In order to achieve the above, it is vital to develop children’s passion for maths and their understanding of the subject from a young age, building on their learning at school and at home. 

The CPA Approach 

CPA stands for Concrete, Pictorial, Abstract. It is a way of teaching maths to help children understand concepts in a structured way that builds confidence and understanding.

Using CPA makes maths less intimidating and helps children build a strong foundation for more complex maths. It ensures they truly understand each step before moving on, reducing the chances of them feeling lost or confused later. 

1. Concrete: Children start by using physical objects (such as counters, blocks, or toys) to represent numbers and solve problems. This hands-on approach helps them see and feel what the numbers mean.
2. Pictorial: Next, children draw pictures or look at visuals to represent numbers. For example, they might draw dots, use pictures of blocks, or look at “tens frames”. This step helps them move from real objects to pictures, bridging their understanding.
3. Abstract: Finally, children use symbols and numbers (such as 2 + 3 = 5) without needing objects or pictures. By this point, they should understand the concept well enough to work with just numbers.

Read more on the CPA approach.

Why Play Games?  

You can make a difference to your child’s learning by playing simple maths games at home. Games are effective in developing vital speaking and listening and social skills, such as turn taking and learning that we cannot always win, in addition to developing mathematical skills, all round thinking, logic, strategy and problem solving skills.

Examples of mathematical board games:

• Dominoes 
• Snakes and ladders
• Monopoly 
• Mathopoly 
• Qwirkle 
• Chess
• Cribbage
• https://juniorlearning.co.uk/products/jl425-maths-board-games 
• https://www.orchardtoys.com/collections/number-and-counting-games 

Examples of online mathematical games: 

• https://www.topmarks.co.uk/search?subject=16&ageGroup=2 (for KS1)
• https://www.topmarks.co.uk/search?subject=16&ageGroup=3&p=2 (for KS2)
• https://www.bbc.co.uk/bitesize/articles/zdjkjfr#z9cdh4j 
• https://mathsframe.co.uk/en/resources/category/22/most-popularx5 

Books to Support Mathematical Learning 

 Mathematical storybooks can be effective in developing children’s understanding of mathematical topics and ensuring that children have factual and procedural fluency.

“A story creates more vivid, powerful and memorable images in a listener’s mind than does any other means of delivery of the same material.” 

Kendall Haven, from his seminal book ‘Story Proof: The Science Behind the Startling Power of Story’ (2007)

What are the benefits of using a story? 

• There is a hook to engage your child.
• Children have an initial experience of the language, concepts and processes involved.
• It provides the context behind why we are looking at such an in-depth concept. 
• It gives a purpose for learning to work mathematically. 
• The focus is no longer simply being told to ‘do maths’ but to create the climate of maths being exciting!

Ultimately, children have an innate ability to learn stories and retain information. This allows children to engage in stories from a very young age. 

Maths Through Stories provides a list of books for children of all ages.

Supporting at home - Reception 

• Counting Everywhere: Counting objects around the home, such as steps, toys, or food items, helps build number sense.
• Play with Patterns: Use household items such as buttons or pasta to create repeating patterns and encourage your child to continue them.
• Talk About Shapes and Sizes: Point out shapes and spatial language (e.g. “Can you find something that’s taller than this?”)
• Encourage Simple Addition and Subtraction: Use language such as “one more” and “one less” with toys or food items to make learning relatable.
• Praise Effort and Reasoning: Celebrate attempts and the thought process behind answers, not just correct answers, to build a positive attitude.
• Singing songs and rhymes, reading stories and playing games 

Year 1 

Key areas of learning:  

• Number and Place Value: Counting up to 100, recognising place value in two-digit numbers, and understanding ordinal numbers (1st, 2nd, 3rd).
• Addition and Subtraction: Learning basic addition and subtraction up to 20, including number bonds and simple word problems.
• Multiplication and Division: Introducing the concepts of doubling, halving, and grouping (early foundations of multiplication and division).
• Fractions: Recognising halves and quarters in practical contexts.
• Measurement: Comparing and measuring length, weight, capacity, and time; introducing concepts of money, using coins, and telling time to the hour and half-hour.
• Geometry: Identifying and naming 2D and 3D shapes, describing their properties, and understanding position, direction, and movement.

Supporting at home:  

• Counting and Comparing: Count objects in groups (such as crayons, blocks, or leaves) and compare quantities using words such as "more" and "fewer."
• Simple Time Telling: Read the hour hand on a clock together, starting with key times, e.g. at breakfast or bedtime, to build familiarity with hours.
• Exploring Coins and Money: Let your child handle coins to identify and count values or create a “shop” where they can "buy" small household items to add and subtract with coins.
• Spotting Numbers Everywhere: Point out numbers in the environment—house numbers, prices, or numbers on packages—encouraging your child to read and identify them.
• Shape and Measure Hunt: Look for shapes in your surroundings (e.g., "Can you find a circle?") and talk about their properties, or compare lengths of items like spoons or pencils.
• Play with Simple Puzzles and Board Games: Simple games like dominoes, matching games, or board games help develop problem-solving and counting skills in a fun way.
• Praise Thinking and Effort: Focus on their approach and effort, celebrating perseverance and reasoning skills to build confidence and a love for learning.

Year 2 

Key areas of learning: 

• Number and Place Value: Extending counting to 100 and beyond, understanding the value of digits in two-digit numbers, and introducing counting in steps (2s, 3s, 5s, and 10s).
• Addition and Subtraction: Adding and subtracting two-digit numbers, understanding commutative properties, and solving one and two-step problems.
• Multiplication and Division: Developing knowledge of 2, 5, and 10 times tables, division as grouping and sharing, and simple problem-solving.
• Fractions: Extending understanding to 1/3, 1/4, and 3/4, including simple fraction calculations and recognising fractions of shapes and numbers.
• Measurement: Comparing and using standard units (e.g. cm, m, kg, g, l), telling time to the nearest 5 minutes, understanding days and months, and adding coins and solving simple money problems.
• Geometry: Recognising and describing properties of 2D and 3D shapes, symmetry in shapes, and understanding rotations and movements (e.g. turns).
• Statistics: Collecting and interpreting data through simple tables, charts, and pictograms. 

Supporting at home:  

• Counting in Steps: Count in 2s, 5s, and 10s with everyday objects like socks, pencils, or coins to strengthen their understanding of multiplication.
• Telling the Time: Encourage reading both the hour and minute hands on a clock, focusing on times such as “half past” and “quarter to” or “quarter past” to build confidence with time-telling.
• Money Games: Let your child add different coins to reach a total or give them a small budget to “buy” items at home, which helps them understand the value of coins and basic addition.
• Finding Fractions: Use food such as pizza slices, fruit, or chocolate bars to show halves, quarters, and thirds, helping them see fractions in real-life contexts.
• Shape Exploration: Hunt for 3D shapes (cubes, cylinders, etc.) around the house and discuss their faces and edges to deepen their understanding of geometry.
• Measuring Fun: Use a ruler or measuring tape to measure objects around the house, comparing lengths in cms or metres and helping them understand units. Cooking/ baking – weighing ingredients, reading scales, adapting recipes. 
• Celebrate Effort and Thinking: Encourage them to explain their thinking process, praising effort and strategies, which builds a positive and resilient attitude towards learning. 

Years 3 and 4  

Key areas of learning:  

• Number and Place Value: Understanding numbers up to 10,000, including reading, writing, ordering, and comparing them. Rounding numbers to the nearest 10, 100, or 1,000.
• Addition and Subtraction: Using formal written methods for addition and subtraction with numbers up to four digits. Solving multi-step problems involving addition and subtraction in various contexts.
• Multiplication and Division: Mastering multiplication tables up to 12 × 12. Developing fluency with written and mental methods for multiplying and dividing two- and three-digit numbers by one-digit numbers.
• Fractions (including Decimals): Recognising and showing equivalent fractions. Adding and subtracting fractions with the same denominator. Understanding and using decimal notation, including recognising tenths and hundredths.
• Measurement: Converting between different units of measure (e.g. kilometre to metre, hour to minute). Calculating the perimeter and area of rectangles. Understanding money, including solving problems involving pounds and pence.
• Geometry and Statistics: Identifying acute, obtuse, and right angles, and recognising symmetry in shapes. Interpreting and presenting data using bar charts, pictograms, and tables. 

Supporting at home: 

• Number and Place Value: Encourage games involving large numbers, such as guessing the number or ordering numbers from smallest to largest. Round numbers in real-life contexts, e.g. rounding prices while shopping.
• Addition and Subtraction: Use real-world examples, such as calculating total costs or change when shopping. Encourage mental maths by asking quick addition or subtraction questions during daily activities.
• Multiplication and Division: Revise times tables up to 12 × 12 with flashcards, apps, or songs. Relate multiplication and division to real-world contexts, e.g., dividing treats equally among family members or calculating quantities for recipes.
• Fractions (including Decimals): Use food, such as pizza or chocolate bars, to demonstrate fractions visually. Encourage recognising and using decimals when handling money or measurements.
• Measurement: Involve children in cooking, asking them to measure ingredients and convert units where necessary. Discuss time-related problems, such as how long a journey will take, or work with clocks to help with reading and calculating times.
• Geometry and Statistics: Explore symmetry in everyday objects or through arts and crafts. Create simple graphs together using data from their interests, e.g. a bar chart showing daily weather or family members' favourite foods. Point out and identify angles in their environment.

Years 5 and 6  

Key areas of learning:  

• Numbers: Understanding and using numbers up to 10,000,000, including reading, writing, comparing, ordering and rounding any whole number to a required degree of accuracy.
• Arithmetic: Solving multi-step problems using all four operations in various contexts. Performing calculations with large numbers and decimals using formal written methods. Identifying common factors, multiples, and prime numbers.
• Fractions, Decimals & Percentages: Simplifying fractions and finding equivalent fractions. Adding, subtracting, multiplying, and dividing fractions. Converting between fractions, decimals, and percentages. Solving problems involving fractions, decimals, and percentages in real-life contexts.
• Ratio & Proportion: Scaling recipes. Scale factors in maps. Using percentages to interpret data. Dividing according to ratio.
• Algebra: Using simple formulae and solving equations. Generating sequences and finding missing values. Expressing problems mathematically using symbols and operations.
• Measurement: Converting between standard units of measure (e.g. kilometres to metres, litres to millilitres). Calculating the area and volume of shapes, including triangles and cuboids. Using and applying formulae for measurement problems.
• Geometry: Nets of 3D shapes. Understanding and using angles, including calculating missing angles in triangles, quadrilaterals, and other shapes. Reflecting, translating, and rotating shapes on coordinate grids.
• Statistics: Interpreting pie charts, line graphs, and bar graphs. Calculating and interpreting the mean, mode, and range. 

Supporting at home:  

• Number and Arithmetic: Discuss large numbers found in news articles or data, such as populations or distances. Use rounding when shopping or cooking. Use quick-fire questions during car journeys or meals. Encourage calculations for budgets, shopping totals, or splitting bills.
• Fractions, Decimals, and Percentages: Use pizza slices or cake to visualise fractions and solve related problems. Work out discounts during shopping or calculate interest on savings.
• Ratio and Proportion: Ask your child to adjust recipes to make larger or smaller portions. Discuss maps and distances or scale up craft projects to create larger versions. Use real-life contexts, such as comparing quantities e.g. mixing paint colours. 
• Algebra: Challenge your child to find patterns in sequences (e.g. multiples or geometric shapes). Turn everyday situations into algebra problems, such as finding an unknown quantity (e.g. "If 2x + 9 = 12, what does x equal)?
• Measurement: Encourage using rulers, weighing scales, and measuring jugs in real-world contexts. Discuss distances, weights, or volumes in recipes or travel plans, and ask your child to convert between units.
• Statistics Encourage your child to gather data from their interests (e.g. sports results or weather) and represent it in bar or pie charts. Find the mean, median, and mode of everyday data, such as pocket money or weekly spending. Look at graphs in newspapers or online and discuss what they show.

Final Top Tips

There are many different ways that you can build your child’s mathematical skills at home. With just a few minutes of maths practice each day, children’s confidence and self-esteem can soar. 

Two of the subjects that children struggle most with in school focus on the topics of time and money, as digital watches and the use of debit and credit cards mean that children are less exposed to money and analogue time. Wearing a watch helps children develop an awareness of time passing, as they regularly check the hours and minutes throughout their day and giving pocket money introduces the real-life value of coins and notes, helping children understand saving and spending responsibly.