A grade-by-grade math checklist for Grades 1 to 10, the one skill that matters most at each stage, and how US grades map to UK school years.
Quick answer
Grades 1–3 build number sense and fact fluency. Grades 4–6 are dominated by fractions, decimals and ratio — the stage where most lasting gaps form. Grades 7–8 convert arithmetic into algebra. Grades 9–10 move into functions, quadratics and geometry with proof. If a child is struggling in any grade, the cause is usually one grade band earlier, and fractions is the single most common culprit.
How to use this page
Curricula differ between US states, between exam boards, and between countries. Treat what follows as the common core of what is taught at each stage, not as any one syllabus. The useful part is not the topic list — it is the "must hold before moving on" column. That is the idea which, if missing, causes trouble later.
One note on terminology for families in the UK: US Grade + 1 = UK Year. A US Grade 6 student is in UK Year 7.
Grades 1–3 · Number sense
| Grade | Core topics | Must hold before moving on |
|---|---|---|
| 1 | Counting to 100, addition and subtraction within 20, place value to tens, shapes, simple measurement | Numbers represent quantities, and the order of counting is fixed |
| 2 | Addition and subtraction within 100, introduction to multiplication, place value to hundreds, time, money | Regrouping — why you "carry" and "borrow" |
| 3 | Multiplication and division facts, fractions as parts of a whole, area and perimeter, rounding | Multiplication is repeated addition, and division is its reverse |
The thing that matters most here is fact fluency. A child who still calculates 7 × 8 rather than recalling it will spend the rest of their math education using working memory on arithmetic instead of on the actual problem. It is the quietest and most expensive gap there is.
Tables should be automatic by the end of Grade 3 or early Grade 4. If they are not, fix that before anything else — it is worth more than any amount of work on the current topic.
Grades 4–6 · Where most gaps form
| Grade | Core topics | Must hold before moving on |
|---|---|---|
| 4 | Multi-digit multiplication and division, equivalent fractions, decimals, angles, factors and multiples | Equivalent fractions — that ½ and 3/6 are the same number |
| 5 | Adding and subtracting fractions, multiplying and dividing decimals, volume, coordinate plane | Why you need a common denominator |
| 6 | Ratio and proportion, percentages, negative numbers, expressions, dividing fractions, basic statistics | Negative numbers as positions, not just "minus something" |
If you read one section of this page, read this one. Grades 4 to 6 are where the majority of lasting math difficulties begin. Fractions, decimals, percentages, ratio and negative numbers are all the same underlying idea — proportional reasoning — and every one of them reappears inside algebra two years later. A child who leaves Grade 6 shaky on fractions will appear to "suddenly struggle" in Grade 8 algebra. Nothing sudden has happened.
Grades 7–8 · Arithmetic becomes algebra
| Grade | Core topics | Must hold before moving on |
|---|---|---|
| 7 | Linear equations, proportional relationships, integers and rational numbers, circles, probability | A letter stands for a number, and both sides of an equation stay balanced |
| 8 | Linear functions, systems of equations, exponents, Pythagoras, transformations, scatter plots | A function as a relationship between two quantities, readable as a graph |
This is the transition that decides how a child feels about math for the rest of school. The shift is from calculating an answer to describing a relationship, and it is genuinely abstract for the first time.
Children who struggle here almost always struggle for one of two reasons, and both are fixable: they are still weak on fractions and negative numbers, so the algebra is buried under arithmetic errors; or nobody explained what the letter is actually for, so they are manipulating symbols without meaning.
Grades 9–10 · Formal mathematics
| Grade | Core topics | Must hold before moving on |
|---|---|---|
| 9 | Quadratics, factoring, inequalities, functions and notation, geometry with proof, surds and indices | Factoring, and what the solutions of a quadratic mean on a graph |
| 10 | Trigonometry, simultaneous and quadratic equations, sequences, circle theorems, statistics and probability | Trigonometric ratios as relationships, not three formulas to memorise |
By this stage the pace assumes everything before it is secure. There is little room in the school year to revisit Grade 5, which is precisely why a student with an old gap finds these two years brutal — and why tutoring that goes backwards works when more homework does not.
US grade to UK year, at a glance
| US grade | UK year | Typical age | Stage |
|---|---|---|---|
| Grade 1 | Year 2 | 6–7 | Number sense |
| Grade 2 | Year 3 | 7–8 | Number sense |
| Grade 3 | Year 4 | 8–9 | Number sense |
| Grade 4 | Year 5 | 9–10 | Proportional reasoning |
| Grade 5 | Year 6 | 10–11 | Proportional reasoning |
| Grade 6 | Year 7 | 11–12 | Proportional reasoning |
| Grade 7 | Year 8 | 12–13 | Early algebra |
| Grade 8 | Year 9 | 13–14 | Early algebra |
| Grade 9 | Year 10 | 14–15 | GCSE course begins |
| Grade 10 | Year 11 | 15–16 | GCSE examinations |
How to check whether your child is actually on track
School reports tell you how a child performs relative to their class, which is not the same as whether the foundations are secure. These four checks are more informative and take ten minutes.
- The explain test. Ask them to explain why a method works, not to perform it. "Why do you flip the second fraction when you divide?" A child who can only perform it has memorised, not understood.
- The speed test. Times tables and number bonds should be recalled, not computed. Watch for a pause and a look upward.
- The backwards test. Give them a problem from two grades below. It should be effortless. If it is not, you have found the gap.
- The word-problem test. Many children can solve 3x + 7 = 22 but cannot turn a sentence into that equation. The gap there is translation, not math.
What to do if you find a gap
- Go back to where it is secure, even if that is three grades down. This feels wrong to most parents and it is the step that works.
- Teach the idea, not the procedure. A procedure learned twice is forgotten twice.
- Rebuild forward quickly. Once the foundation is in, later topics arrive far faster than the first time.
- Keep up with current schoolwork in parallel, so the child does not fall behind the class while catching up on the past.
That parallel track is the part a group class cannot do, and it is covered in more detail in our guide to online math tutoring.
How 2ndRank handles grade levels
We do not place children by their school grade. Every student takes a free assessment first, and we place them by what they can actually do — which is frequently one or two years below where the report card suggests, and occasionally above it.
Our math programme by grade runs two parallel tracks for every student when needed: the current grade's work, so school does not slip, and the underlying gap, so it stops recurring. One teacher, one child, the same teacher throughout, with written progress reporting each month.
If the assessment shows your child is on track and does not need us, we will tell you that too.
Next step
Find out which grade your child is actually working at. Book a free assessment — thirty minutes with a teacher, and a straight answer, whether or not you enrol.
Frequently Asked Questions
Written by
2ndRank Editorial Team
Written by the 2ndRank math mentors who teach one-to-one math from Grade 1 to SAT and GCSE.
