How to check maths learning gaps: five worked examples
When maths homework becomes difficult, “practise more” can feel too vague. A more useful question is: which step is causing the difficulty? Your child may understand the new topic but need help with an earlier idea, such as place value or equal parts.
These five checks give you a starting point for that conversation. They are original practice activities, not a standardised assessment or a way to assign a school year. Choose examples your child has already met. Skip unfamiliar topics rather than treating them as gaps.
Start with the explanation, not the score
Use paper and a pencil. Let your child draw, use counters, or talk through a method. Ask, “How did you work that out?” before showing an answer. If you help, note the help you gave. An answer reached alone tells you something different from one reached after a prompt.
Keep the first check short. One wrong answer may reflect a misread question, a slip, or tiredness. Look for the same difficulty in another example before choosing what to practise. The activities below move from number ideas to early algebra; completing all five is not the goal.
1. Check what each digit means
Try: What is the value of the 6 in 462? Write 462 as hundreds, tens, and ones.
Worked answer: The 6 represents 6 tens, so its value is 60. The whole number is 400 + 60 + 2. A drawing of four hundreds, six tens, and two ones is another way to show this.
What to notice: An answer of “6” might mean your child named the digit rather than its value. Ask them to show the number using a drawing. This helps separate unclear wording from an unclear idea.
Next check: What is the value of the 6 in 406? It is 6 ones. If the two positions cause confusion, practise making and breaking apart three-digit numbers before moving on to larger calculations.
2. Check subtraction across a ten
Try: Work out 52 − 27 and explain one way to check the result.
Worked answer: Subtract 20 from 52 to get 32. Then subtract 7 to get 25. To check, add back: 25 + 27 = 52. A written method can also work: exchange one ten so that 52 becomes 4 tens and 12 ones, then subtract 2 tens and 7 ones.
What to notice: If your child gets 35 by subtracting the smaller digit from the larger digit in each column, ask them to estimate first. Taking away 27, which is close to 30, should leave an answer close to 22.
Next check: Try 61 − 24. The answer is 37. Use tens and ones drawings if the exchange is the difficult part.
3. Check the link between multiplication and division
Try: Four bags each hold six apples. How many apples are there? If those apples are shared equally between four people, how many does each person receive?
Worked answer: Four groups of six give 4 × 6 = 24 apples. Sharing 24 into four equal groups gives 24 ÷ 4 = 6 apples each. Draw four circles and put six marks inside each to connect the two calculations.
What to notice: Your child might recall 4 × 6 but not recognise the division. That suggests a useful next conversation about equal groups. If the grouping makes sense but recalling the fact takes time, practise that fact without assuming the whole concept is missing.
Next check: Share 30 counters into five equal groups. Each group contains six.
4. Check equal parts before adding fractions
Try: Find 1/2 + 1/4. Explain why the answer is not 2/6.
Worked answer: The pieces need the same size before you count them together. One half is two quarters. Two quarters plus one quarter makes three quarters: 2/4 + 1/4 = 3/4.
Draw two identical rectangles. Divide one into halves and the other into quarters. Then divide each half into two equal parts. The drawings show why changing 1/2 to 2/4 changes the name of the fraction but not its size.
What to notice: Adding both the top and bottom numbers can reveal confusion about what the bottom number means. It names the number of equal parts in one whole.
Next check: Try 1/3 + 1/6 using equal-sized wholes. The answer is 3/6, or 1/2.
5. Check whether an equation stays balanced
Try: Solve 3x + 4 = 19. Explain what you do to both sides.
Worked answer: Subtract 4 from each side to get 3x = 15. Divide each side by 3 to get x = 5. Check by putting 5 into the original equation: 3 × 5 + 4 = 19.
What to notice: If your child guesses 5 correctly, ask for a method too. If they change only one side, use the idea of a balanced scale. Equal amounts stay equal when you make the same change to both.
Next check: Solve 2x + 5 = 17. The answer is x = 6. Skip this check if equations are not yet part of your child’s learning.
Turn one finding into a small plan
Make three notes: the question, your child’s explanation, and any help needed. Choose one idea to revisit. Show one example, work through another together, then try a fresh question without prompts on a later day. Keep the original notes so you can compare methods, not just totals.
England’s mathematics programmes of study include fluency, reasoning, and problem solving. These checks draw on those broad areas, but they do not cover the full curriculum or establish your child’s level.
If the same difficulty keeps returning, share the examples with your child’s school teacher. For the platform options, explore FutureSchool maths, read the assessment information, and see how FutureSchool works.