A gap in maths is almost never the topic your child is struggling with this week. It is a specific skill from an earlier year that was never fully secure, and the current topic quietly depends on it. Identifying it means working backwards from a wrong answer to the skill underneath, rather than practising more of whatever produced the wrong answer.
In short: collect a few weeks of marked work, look for the same error appearing more than once, trace each error back to the earlier skill it depends on, then confirm it with short questions that change one thing at a time. A gap is real when it survives being retaught and shows up in more than one form of question.
This is work parents can do without teaching anything. It needs marked work, a few careful questions and a willingness to look further back than feels reasonable.
1. Signs a Student May Have a Gap in Maths
Gaps rarely announce themselves. They show up as a pattern in ordinary work, and the pattern is easier to see once you know what to look for.
- The same kind of error appears in different weeks, on different pages, in the same place in the method.
- Questions are left blank rather than attempted, which usually means no method was available at all.
- Number facts come out right but slowly, so longer calculations run out of working memory before the end.
- A right answer cannot be explained, or the explanation is a list of steps with no reference to what the numbers mean.
- A topic that looked secure in class collapses when the question is worded differently or set without a diagram.
- Marks fall when the topic changes but the arithmetic inside the questions has not.
2. Collect the Errors Before You Look for Patterns
Start with evidence rather than impressions. Gather three or four weeks of marked homework, any recent test paper, and a page or two of classwork. One wrong answer tells you very little. The same wrong answer appearing in three different weeks tells you a great deal.
Two things are worth noticing that parents often skip past. The first is blank answers. A question left empty usually means no method was available at all, which points at a more fundamental gap than a question attempted and failed. The second is hesitation. A child who arrives at 7 × 8 correctly but takes eight seconds to do it has a recall problem that will surface later as an accuracy problem, because the working memory spent retrieving the fact is no longer available for the rest of the calculation.
3. Trace the Error Back to the Skill It Depends On
The Department for Education’s non-statutory mathematics guidance for key stages 1 and 2 sets out what it calls ready-to-progress criteria: a set of core concepts from Year 1 to Year 6 where understanding each one is treated as a prerequisite for later content and for making connections between concepts. That is the useful idea for parents. Most content sits on top of something earlier.
Take 4003 − 1856 done in columns and answered as 2257. The error looks like subtraction. Look at the working and the child has lent from each zero without reducing it afterwards: 13 − 6 = 7, then 10 − 5 = 5 and 10 − 8 = 2 where there should have been 9 − 5 = 4 and 9 − 8 = 1. The skill is exchanging across a zero, which rests on flexible partitioning of numbers, taught in Year 2 and applied to formal columnar subtraction from Year 3. Reteaching Year 6 subtraction will not fix it. Ten minutes on what 4003 can be broken into probably will.
The table below maps difficulties parents commonly see onto the skill underneath and the point in the national curriculum where that skill is introduced.
| What you observe | Likely underlying gap | Where it is introduced |
|---|---|---|
| Column subtraction goes wrong only when there is a zero in the calculation | Exchanging across place value, flexible partitioning | Partitioning in Year 2, columnar subtraction from Year 3 |
| Thinks 0.7 is smaller than 0.65 | Decimal place value, tenths against hundredths | Tenths in Year 3, hundredths and comparing two decimal places in Year 4 |
| Can add three eighths and one eighth but stalls on a half plus an eighth | Equivalent fractions and common denominators | Equivalent fractions in Years 3 and 4, unlike denominators in Years 5 and 6 |
| Hesitates on 7 × 8, 6 × 9, 7 × 6 | Recall of multiplication facts rather than method | 2, 5 and 10 in Year 2, then 3, 4 and 8 in Year 3, all facts to 12 × 12 in Year 4 |
| Short division is fine, long division collapses | Deriving multiples of a two-digit divisor | Short division in Year 5, long division by two-digit numbers in Year 6 |
| Confuses area and perimeter, or adds when scaling | The distinction between the two measures | Perimeter from Year 3, area by counting squares in Year 4, area of rectangles in Year 5 |
| Can find 50% and 25% but not 15% of 360 | Percentage as parts per hundred, linked to fractions | The per cent symbol in Year 5, percentage problems in Year 6 |
| Answers reverse in word problems, subtracts where division is needed | Choosing the operation, multiplicative reasoning | Two-step problems in Year 4, multi-step problems in Years 5 and 6 |
4. Read the Year Column as a Guide, Not a Timetable
Curriculum content is set out year by year for key stages 1 and 2, though schools are only required to teach the relevant programme of study by the end of the key stage, so they can introduce content earlier or later within it. Treat the year column as an indication of where a skill belongs rather than a statement about when your child’s school taught it. The Study by Year Group pages show how each strand builds from one year to the next, which is the order that matters when you are tracing a gap.
5. Confirm the Gap With Short, Targeted Questions
Once you have a candidate, four probes will usually settle whether it is real. Each takes under a minute and none requires you to explain anything.
- Strip the context. If a word problem about coach seating failed, ask the bare calculation. A correct answer means the arithmetic is fine and the difficulty is in interpreting the problem. A wrong answer means the arithmetic is not fine.
- Change one number. If 4003 − 1856 failed, try 4523 − 1856. If the second is correct, you have confirmed the zero, not subtraction generally.
- Ask for an estimate first. “Roughly, what should this come to?” A child who cannot say that 4003 − 1856 is somewhere near 2000 has a place value gap regardless of what the written method produces.
- Ask them to explain a right answer. Correct answers hide gaps well. If the explanation is a recital of steps with no reference to what the numbers mean, the method is being followed rather than understood, and it will fail as soon as the question is presented differently.
6. Careless Error, Fluency Problem or Genuine Gap
Not every error is a gap, and the three kinds call for different responses. A careless error disappears the moment the child slows down or reads the question again, and it does not come back in the same place next week. Nothing needs reteaching; it needs a habit of checking.
A fluency problem is a correct method run too slowly. The child knows what to do but retrieving each fact costs so much attention that the later steps go wrong. This matters, but it is fixed with short, regular retrieval practice rather than a lesson: a few minutes a day on Daily Maths Practice does more for it than an hour on Saturday.
A genuine gap survives being retaught, appears in more than one form of question, and shows up when the topic is not the current unit. An error that persists after a clear explanation is structural, and the fix is earlier than the topic it was found in.
Write down what you confirm, with the year group attached, and order the list oldest first. Gaps compound in sequence, so the earliest unresolved skill is almost always the one to address first, even when it feels far below where your child is meant to be working.
7. Look Across Year Groups, Not Just the Current One
The most common mistake at this stage is searching only within the topic the child is on now. A Year 8 student stuck on solving equations may have an intact grasp of algebra and an unresolved problem with negative numbers from Years 4 to 6. A Year 6 pupil struggling with ratio may be missing nothing about ratio at all.
This is why a wide-ranging assessment is more informative than a topic test. A topic test tells you whether this fortnight’s teaching landed. An assessment that samples across several year groups tells you where the foundation actually stops being solid. Ivy Maths Full Assessments are built to do exactly that, and the resulting Instant Report lists confirmed gaps by strand rather than giving a single mark.
8. What the School’s Data Does and Does Not Tell You
School reporting gives you a level, not a list. At the end of key stage 2, results are reported as a scaled score from 80 to 120, where 100 is the expected standard and a score below it means the child may need more support to reach it. That is a summary judgement across the whole subject. A score of 97 does not tell you whether the problem is fractions, division or reading the question.
The Year 4 multiplication tables check is narrower and therefore more useful diagnostically. It is an onscreen check of 25 times table questions with 6 seconds allowed for each, and it assesses instant recall only, with no expected standard or pass mark attached, so a higher score simply indicates greater fluency. A low score points specifically at retrieval speed rather than at understanding of multiplication.
When you speak to the teacher, ask a narrow question. “How is she doing in maths” produces a reassuring answer almost every time. “Which strands is she insecure in, and what would you want her to consolidate” produces something you can act on.
9. What to Do Once You Have Found a Gap
Start with the earliest skill on your list, not the most recent. Give it a short, regular slot rather than a long session, and stop as soon as the child can explain a right answer in their own words and get it right when the question changes form. Then move to the next skill on the list. A gap that has been closed properly rarely needs revisiting; one that was patched with more of the same practice usually does.
If you want a reference point for what should be secure at each stage, the Ivy Maths curriculum checklists set out each year group in plain language, so you can check a suspected gap against what the year actually requires. And if the marked work is thin or the pattern will not settle, an Ivy Maths Assessment does the tracing for you: it samples across year groups and reports the confirmed gaps by strand.
Questions Parents Ask
How do I know if my child has gaps in maths?
Look for the same error in the same place across several weeks of marked work, blank answers rather than wrong ones, slow recall of number facts, and right answers the child cannot explain. One wrong answer is not a gap. A pattern that survives being retaught is.
What is the difference between a careless mistake and a maths gap?
A careless mistake disappears when the child slows down and does not recur. A gap persists after a clear explanation, appears in more than one form of question, and shows up when the topic is not the current unit.
Which year group should I look at when my child struggles with a topic?
Usually an earlier one. The skill underneath a Year 6 difficulty is often introduced in Year 3 or 4. Trace the error back to the skill it depends on and check that year first, then work forwards.
Does a low SATs score mean my child has gaps in maths?
It means the child was below the expected standard across the whole subject on that day. A scaled score does not say which strands are insecure, so use it as a prompt to look at the work, not as a diagnosis.
What does the Year 4 multiplication tables check tell me?
Only how quickly your child recalls times table facts, since it allows six seconds a question and has no pass mark. A low score points at retrieval speed, not at understanding of multiplication.
How can I find out exactly which maths skills my child is missing?
Collect marked work, trace repeated errors back to the earlier skill, and confirm each with short questions that change one thing at a time. An assessment that samples across year groups, such as an Ivy Maths Full Assessment, does the same tracing and reports the confirmed gaps by strand.