Fractions become much easier when the learner has a picture to attach the symbols to. Resist rushing to rules. Ask them to show, compare, rebuild and explain before asking them to memorise a procedure.

Useful prompt: “Can you show me what that fraction means?”

You do not need to remember every fraction rule to help. Sit alongside the learner, try things together, and give each idea time to become familiar. One small idea understood is worth more than a page of answers copied from a method.

Keep learning aids within reach: handmade paper squares and circles to fold or cut, strips of paper, beads, counters, or sweets to share into equal groups. These are useful mathematical tools, at any age. Let the learner keep using them for as long as they help.

Use shapes for parts of one whole and beads or sweets for parts of a collection. Always agree what counts as one whole. When comparing paper fractions, begin with wholes of the same size; when sharing a collection, make equal groups.

Try together: fold two matching squares into halves and quarters. Cover one half with two quarters. Then share 12 beads into four equal groups: one quarter of the collection is one group of 3 beads. Ask, “What is our whole this time?”

When we explored fractions with our son, we made our own paper circles and squares together. He enjoyed using them, sometimes in situations where we had not expected him to reach for them. They became a reassuring, familiar tool: something he could check, a little like his own cheat sheet.

The making mattered too. Drawing the divisions, choosing colours and tracing how one fraction connected to another gave him a part in building those visual paths. The finished aid was useful, but the thinking involved in creating it was just as valuable.

You can try this together. Start with a paper whole and add the fractions you are exploring. Let the learner choose useful colours, mark connections and explain what they want to remember. Help with accurate equal divisions where needed; it does not have to look professionally made to be worth keeping.

Keep it available during later work. Reaching for a familiar aid can be a way of checking an idea and continuing independently. There is no need to take it away to prove that learning has happened.

The ten lessons below follow a deliberate progression. Stay close to that order, returning to an earlier picture whenever it helps. A lesson is an idea to explore, not a deadline: it can take several short sessions.

Addition may sound like the easy starting point, but adding fractions with different denominators is one of the most demanding parts. It brings together equivalent fractions, multiplication facts and matching the size of the pieces. That is why we begin with familiar additions and leave general addition until Lesson 8.

Multiplication is often simpler to calculate. Finding a fraction of an amount, and then a fraction of a fraction, gives it meaning before the general addition method. Do not assume a learner who finds addition difficult will also struggle with multiplication.

If the focus is fractions, do not make recalling every times-table fact another test. Keep a multiplication grid or the Times Tables resources available to help answer the calculations. Practise recall separately when it needs attention.

For example, to find three quarters of 20, first share 20 into four equal groups, then take three groups. If 3 × 5 is uncertain, look it up together. The fraction reasoning still belongs to the learner.

Likewise, accept an unsimplified answer while learning a new operation. Come back to simplifying in Lesson 10. Begin with small, familiar numbers and change one feature of a question at a time.

Use money often. Many children find £ and $ arithmetic more intuitive than abstract numbers because the quantities already have meaning. £1 = 100p and $1 = 100¢ give immediate examples of halves, quarters, tenths, hundredths, addition, subtraction, equivalence and regrouping. Use pounds and dollars as parallel familiar contexts rather than comparing their exchange values.

Give them thinking time. Then try a question that brings the meaning back: “What is the whole?” “Can we make it?” “Are these pieces the same size?” “How could we check?” Invite an explanation through objects, a drawing or words; it need not be a polished sentence.

If they write 1/2 + 1/3 = 2/5, rebuild the amounts using matching paper wholes. Ask whether adding a positive amount to one half could give less than one half. Use the mistake to find the missing idea, then try a simpler example together.

Move on when they can show what is happening, explain a familiar example and try a slightly different one with less support. Speed is not the deciding factor. If frustration grows, stop and return another day.