Ask any Year 1 teacher what children struggle with most in early maths. Most will point to the gap between counting on fingers and understanding why 4 plus 3 gives you 7.
Addition is the foundation for every other area of primary maths, from multiplication to fractions to algebra. Getting it right matters far more than drilling answers. LearningMole is a UK educational platform founded by former primary teacher Michelle Connolly. Its curriculum-aligned educational content helps teachers and parents close that gap using structured, visual and playful methods.
Teaching addition for kids, well means moving children from holding objects, to drawing pictures, to working with numbers alone. Teachers call this the Concrete-Pictorial-Abstract, or CPA, approach. It sits behind the teaching for mastery methods now used alongside the National Curriculum in most primary schools in England. More than 70% of England’s primary schools have engaged with the NCETM and Maths Hubs Teaching for Mastery Programme.
Children meet addition first in Reception, under the EYFS framework, where they begin joining groups of objects and recording simple number sentences. The National Curriculum takes over in Year 1, at the start of Key Stage 1. By the end of Year 2, pupils are expected to add two two-digit numbers using objects, pictures or mental methods. They also need to use the inverse relationship between addition and subtraction.
The Concrete-Pictorial-Abstract framework sets the sequence that all seven methods below move through. Children who skip the concrete stage and go straight to written sums often hit a wall in Year 2 or 3. Numbers get larger, and working in the abstract alone stops being enough.
Concrete means physical objects. Children count real things: blocks, cubes, buttons, and fruit. Pictorial means representations. Children draw dots, circles, or bar diagrams. Abstract means symbols: the numerals and operation signs they’ll use for the rest of their education. Each stage should be secure before children rely on the next, though good practice moves back and forth rather than in one direction only.
| Stage | What it looks like | When children are ready to move on |
|---|---|---|
| Concrete | Physical objects: cubes, counters, Lego bricks, fingers | They can explain what the objects represent without being prompted |
| Pictorial | Drawn diagrams: dots, bar models, part-whole models on paper | They can recreate diagrams from memory and explain them |
| Abstract | Written number sentences: 4 + 3 = 7 | They can solve problems without needing objects or pictures |
“Children learn addition best when they can hold the numbers in their hands before they see them on paper. The rush to written sums is one of the most common reasons children lose confidence in maths.” Michelle Connolly, Founder of LearningMole and former teacher with over 15 years of classroom experience
The part-whole model, sometimes called a cherry diagram, shows how a whole number is made up of two smaller parts. A circle at the top holds the total; two circles beneath hold the parts that make it. One diagram covers number bonds, addition and subtraction at the same time.
In EYFS, children might place 5 conkers in the top circle, then sort them into 2 and 3 in the lower circles. In Year 1, they move to drawn diagrams. The key is that the model works both ways: children can add the parts to find the whole, or subtract one part to find the other. That two-way flexibility is why one diagram serves number bonds, addition and subtraction at once.
Give children a ball of playdough and ask them to split it into two pieces. Count the pieces in each half, then count the whole ball. Draw the part-whole model on a whiteboard together. Children then squash the pieces back together and try a different split. This physical joining and separating make the abstract concept of addition and its inverse genuinely tangible.
The part-whole model aligns directly with the EYFS framework’s requirement for children to understand that numbers can be composed and decomposed. LearningMole produces educational videos aligned with the UK National Curriculum for children aged 4 to 11. Its early years maths resources include visual guides and video explanations that bring the part-whole structure to life at school and at home.
The bar model bridges concrete and pictorial stages by representing numbers as rectangular bars drawn side by side. Where the part-whole model works best with smaller numbers, the bar model scales smoothly into two-digit addition and later into multiplication and ratios.
For addition, children draw a long bar divided into two sections. The first section represents one addend; the second represents the other. The total bar above shows the sum. Comparing the lengths lets children see relative size at a glance, which column addition cannot show them.
Bar models also help children write number sentences correctly. If children can draw the bar, they can write the equation. That link between the visual and the symbolic is what the National Curriculum asks for by the end of Year 2.
One of the most practical advantages of the CPA approach is that the concrete stage does not require expensive classroom equipment. The objects children use to count and combine at home matter less than the thinking process they go through while using them.
A standard Lego brick with two rows of four studs represents 8. Two single-stud bricks represent 2. Children can physically push them together to see that 8 + 2 = 10, then build a tower showing tens and ones for two-digit addition. The colour coding, snap-together structure, and familiar feel make Lego bricks far more engaging than generic plastic cubes for most children.
Tip a pile of mixed socks onto a bed. Ask a child to match pairs and count: 3 pairs of blue socks, 2 pairs of striped socks. How many pairs altogether? The grouping, sorting, and combining involved here directly map onto the addition of sets that children practise in Reception and Year 1. The real-world context also satisfies the EYFS requirement for children to use mathematics in everyday situations.
Line up tins and packets from a cupboard and give each a simple price tag (2p, 5p, 3p). Ask children to fill a basket with two items and calculate the total cost. Start with totals under 10; progress to totals under 20. This activity practises addition in a context children already recognise from shopping trips.
Bridging through ten is the technique children use when they cannot add two numbers directly without losing track. To add 8 + 5, a child using bridging first asks: how many do I need to reach 10 from 8? The answer is 2. They take 2 from the 5, reach 10, then add the remaining 3 to get 13.
Bridging matters because it comes directly before column addition and mental arithmetic with larger numbers. Children who learn to bridge confidently in Year 2 have a reliable strategy that scales up through KS2 without requiring rote memorisation of facts beyond number bonds to 10.
Draw a number line from 0 to 20. Ask children to place a finger on 8. Jump 2 spaces to land on 10. Ask how many of the 5 they have used. Then jump the remaining 3 to land on 13. The physical movement along the line makes the two-step process visible. Children can then practise the jump on their own with different starting numbers.
A 100-square grid works for counting, place value and addition alike. In addition, children use it as a map: find your starting number, count forward by the number you are adding, and read your answer. Adding 10 always moves you one row down; adding 1 always moves you one cell to the right.
The ‘detective’ framing works particularly well with children who are anxious about maths. Rather than solving a sum, they are following clues on a grid. Starting with single-digit additions and building up to crossing tens boundaries gives children repeated low-stakes wins that build confidence alongside skill.
For home learners, a laminated 100-square with a dry-wipe marker doubles as a reusable activity that takes less than two minutes to set up. Children can mark their starting number, draw arrows to show their jumps, and wipe clean for the next attempt.
For children in Reception and children with sensory processing needs, adding numbers through touch, movement, and texture provides an entry point that visual or symbolic methods cannot replicate. For some children, sensory addition is the most direct route to understanding.
Fill a shallow tray with sand or fine salt. Ask children to draw 3 dots on one side and 4 dots on the other, then sweep the two groups together and count the total. The act of physically sweeping reinforces the mathematical meaning of addition as combining two quantities into one.
A small squirt of shaving foam on a waterproof surface lets children write numbers with their finger, combine groups, and smear them away without the pressure of permanence. For children who are reluctant writers or who find pencil-and-paper tasks frustrating, this reduces the emotional barrier to practising number work considerably.
LearningMole’s educational resources include video-based approaches that support sensory and visual learners, with explanations broken into short segments that match children’s attention spans at EYFS and KS1.
One of the most useful things a child can learn early in their addition journey is that order does not matter. 3 + 7 gives the same answer as 7 + 3. This is the commutative property, and understanding it cuts the number of addition facts children need to learn almost in half.
Teaching this as a ‘magic trick’ works well from Year 1, though the National Curriculum sets commutativity as a Year 2 objective. Show them 2 + 8 on a number line, then ask them to predict what happens if you start at 8 and add 2 instead. The surprise that the answer is identical, even though the journey looks different, is a genuine mathematical insight that children remember.
Once children are fluent with commutativity, they can pick whichever order makes counting on easier. Adding 1 + 9 becomes much simpler when a child knows they can just start from 9.
One of the most common barriers parents face when supporting addition at home is unfamiliar vocabulary. Below are the terms teachers use most often, with plain-English explanations.
| School term | What it means at home |
|---|---|
| Partitioning | Splitting a number into smaller parts, e.g. 14 = 10 + 4 |
| Number bonds | Pairs of numbers that add together to make a target total, e.g. 3+7, 4+6 and 5+5 all make 10 |
| Addend | One of the numbers being added. In 4 + 3 = 7, both 4 and 3 are addends |
| Regrouping (carrying) | When digits in a column add up to 10 or more, the extra ten moves to the next column, which older parents may remember as ‘carrying the one’ |
| Counting on | Starting from one number and adding the second by counting forward, e.g. for 6 + 3, starting at 6 and counting ‘7, 8, 9’ |
| Sum | The answer you get when you add numbers together. In 4 + 3 = 7, the sum is 7 |
A child who appears to have ‘switched off’ during addition is almost always telling you that the current method is operating above their current stage of understanding. The most reliable response is to step back, not push forward.
If a child cannot add reliably using pictorial methods, they are not ready for drawn diagrams. Return to physical objects and check whether they can accurately count out a set, then count out a second set, then count the combined group from 1. If counting from 1 is insecure, that is the starting point, not the addition.
Ask children to add smaller numbers than they have been working with. A child struggling with 7 + 5 may be completely secure with 3 + 2. Building confidence with easier problems first lays the foundation for the harder ones.
Children with dyscalculia often find it difficult to hold numbers in working memory while counting. Three supports help. Keep a number line permanently visible. Colour-code manipulatives by value. Break each calculation into two explicit steps: reach 10, then add the rest. Together these lower the memory demand, so the child can focus on the concept rather than the recall.
“Every child who struggles with addition is showing us something: the method we’re using doesn’t match where they are yet. The question is always ‘what does this child need to see or hold to make this make sense?’ not ‘why can’t they just get it?’, Michelle Connolly, Founder of LearningMole and former teacher with over 15 years of classroom experience
LearningMole is a UK educational platform providing curriculum-aligned video resources and teaching materials for primary schools, designed by educators who have taught these concepts in real classrooms. Its addition and early maths resources cover every stage of the CPA sequence. Videos demonstrate each method visually, and the activities need no preparation.
For teachers: LearningMole’s resources are mapped to the UK National Curriculum and include year-group-specific materials for EYFS, Year 1, and Year 2. Each resource is designed to save planning time while maintaining the depth and rigour that Ofsted expects. Explore the full teaching resource library.
For parents: the platform’s home learning materials translate the methods above into activities families can try together using everyday household items. Video explanations make it easy to understand what your child’s teacher is doing in school and how to reinforce it at home.
Children meet addition in Reception, aged four to five, under the EYFS framework rather than the National Curriculum. They start by combining groups of physical objects. Formal written number sentences usually arrive in Year 1, once children have had time to handle objects and explore number relationships through play.
Four appear most often: counting on from the larger number, number bonds to 10 and 20, partitioning into tens and ones, and bridging through ten. The CPA approach sequences these from concrete objects through pictures to symbols, so children meet each strategy at a stage they can handle.
Step back to physical objects. Ask the child to count out each group separately before combining them, and reduce the numbers to ones they handle confidently. Check that number bonds to 5 and 10 are secure, because bridging and partitioning both depend on them. Avoid timed practice.
CPA stands for Concrete, Pictorial, Abstract. It draws on Jerome Bruner’s enactive, iconic and symbolic modes of representation from the 1960s, developed into the CPA sequence in Singapore from 1979. Children work with objects, then pictures, then symbols, moving between the three rather than climbing a fixed ladder.
Number bonds are pairs that make a target total: 3 and 7, 4 and 6, and 5 and 5 all make 10. They matter because bridging through ten and partitioning both rely on instant recall. A child secure with bonds to 10 can handle much larger additions confidently.
Start concrete, whatever the year group. The part-whole model with physical objects suits Reception and Year 1. The bar model and bridging through ten suit Year 1 and Year 2. Choose by what the child can already do rather than by the year group on the register.
Match what school is doing. If your child uses a number line or part-whole model in class, use the same tool at home. Real objects work well: coins, pasta shapes, toy cars. Keep sessions to five or ten minutes, and ask your child to explain their method aloud.
A part-whole model is a diagram showing how a number breaks into two smaller parts. The total sits in a circle at the top; the parts sit in circles beneath, joined by lines. Sometimes called a cherry diagram, it presents addition and subtraction as one relationship.
Year 3. The National Curriculum introduces formal written methods there, for numbers up to three digits. Move only once place value is secure and your child can explain what each digit represents. Children pushed into columns early follow the procedure but cannot check or explain their answers.
Ask them to explain addition without using numbers. Can they give a real-life example? Can they check an answer a second way? A child who produces correct answers but cannot explain, adapt or check them is working procedurally. Returning to objects usually shows where the gap sits.
Teaching addition well is about pacing as much as method. The seven approaches here, from part-whole models to sensory sand trays, aren’t meant to be used all at once. Nor in rigid sequence across a single lesson. They represent a range of entry points, each suited to a different stage of understanding or a different kind of learner. The teacher’s job, and the parent’s job at home, is to read where a child is and choose the method that meets them there.
LearningMole’s curriculum-aligned resources are built around that principle. Children learn maths best when the approach matches their stage, and when concepts are made visible before they turn abstract. Michelle Connolly founded LearningMole after more than fifteen years teaching in primary classrooms, including two years in Dubai. She developed its videos and teaching materials to support the move from concrete understanding to flexible number sense. That confidence carries children through every year of primary maths.
If one parent finds the jargon buster useful, these methods have done their job. So has one teacher trying the Lego place value activity and watching a child’s face change when it clicks. Addition is where mathematical confidence begins. It deserves the time and care to get it right.
LearningMole provides free and subscription-based educational videos and teaching materials aligned with the UK National Curriculum. Whether you’re a teacher planning your Year 1 maths unit, a parent supporting homework, or a teaching assistant working with a small group, LearningMole’s resources are built to help.
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