The 11+ syllabus now includes basic algebra, and children who have never met a letter standing in for a number can freeze the first time they see one. The good news is that 11+ algebra is narrow, predictable and genuinely quick to teach. Once a child understands that a letter is simply a mystery number, most of the fear disappears. This guide sets out exactly what is tested, shows a worked example for every core method, flags the marks children lose most often, and points you to free practice so your child can build fluency without any paywall.
Where algebra sits in the current 11+ landscape
Algebra appears across the modern 11+, but how much of it you meet depends on the paper. GL Assessment papers now dominate most grammar-school regions since the separate CEM tests were phased out around 2022-2023, and GL maths keeps algebra light: substitution, one and two-step equations, function machines and forming short expressions. CSSE (the Essex consortium) and independent-school ISEB-style papers tend to push a little further, with more equation-solving and worded algebra. Whatever the target school, the foundation is the same, so it is worth teaching properly. Use our 11+ process guide to confirm which board your target centres use.
What "algebra" actually means at 11+ level
It is not simultaneous equations or factorising quadratics. In an 11+ paper, algebra almost always comes down to a handful of skills:
- Substitution — if a = 3, work out 2a + 5.
- One-step equations — 3x = 12, find x.
- Two-step equations — 2x + 3 = 11, find x.
- Combining like terms — 3a + 2a simplifies to 5a.
- Function machines — a number goes in, a rule is applied, a number comes out (and sometimes you work backwards).
- Forming expressions — turning a sentence into algebra, such as "5 more than n" becoming n + 5.
- Simple sequences — spotting a term-to-term or position-to-term rule and predicting a later term.
Worked examples for every core method
Read these aloud with your child. The golden rule sits underneath all of them: whatever you do to one side of an equation, you must do to the other.
Substitution
If x = 5, find 2x² - 3. Deal with the power first: 5² = 25. Then multiply: 2 × 25 = 50. Finally subtract: 50 - 3 = 47. Order of operations matters here, so a quick refresher on BIDMAS in our revision hub pays off.
One-step equation
4y = 28. The 4 is multiplying y, so do the opposite and divide both sides by 4: y = 28 ÷ 4 = 7. Check by substituting back: 4 × 7 = 28. Correct.
Two-step equation
5x + 2 = 17. Undo the parts in reverse order. First subtract 2 from both sides: 5x = 15. Then divide both sides by 5: x = 3. Check: 5 × 3 + 2 = 17. Correct. Teaching children to always check by substituting their answer back turns a guess into a proof.
Combining like terms
3a + 2b - a + 5b. Group the a-terms and the b-terms separately: (3a - a) + (2b + 5b) = 2a + 7b. You can only add terms that share the same letter; a and b never combine.
Function machine (forwards and backwards)
A machine does "× 3 then + 4". Put in 5: 5 × 3 = 15, then 15 + 4 = 19. Now work backwards: the output is 25, what went in? Reverse the steps and reverse the operations: 25 - 4 = 21, then 21 ÷ 3 = 7.
Sentence to expression
"A pencil costs y pence. A pen costs 5p more than a pencil." A pen costs y + 5. If instead a pen costs three times as much, it is 3y. Reading the sentence slowly is the whole skill.
A quick-reference method table
When a child is stuck, the fix is almost always "do the opposite operation to both sides". This table is worth pinning above a desk.
| You see | To undo it, do |
|---|---|
| + a number | Subtract that number from both sides |
| - a number | Add that number to both sides |
| × a number | Divide both sides by that number |
| ÷ a number | Multiply both sides by that number |
| A power (x²) | Work it out during substitution, before × or + |
Difficulty progression: Year 4 to Year 6
Algebra usually lands in the Year 6 curriculum, but 11+ testing happens in Year 6 September, so the skill is really a late Year 5 job. Build it in stages:
- Year 4 (gentle start) — missing-number sums with a box: 7 + □ = 12. This is algebra in disguise and needs no new notation.
- Year 5 (core work) — replace the box with a letter, then master substitution and one and two-step equations.
- Year 6 (exam level) — worded problems, function machines run backwards, and forming an equation from a real situation before solving it.
How algebra appears in the exam
In a GL maths paper of roughly 50 questions in 50 minutes, you get about a minute per question, answers are multiple-choice A to E marked on a separate OMR answer sheet, and no calculator is allowed. That format shapes strategy: because the options are given, a child who is unsure can substitute each option back into the equation and see which one fits, which is often faster than solving from scratch. Every raw mark eventually feeds into a Standard Age Score (SAS, roughly 69-141, with 100 average and many grammar schools looking for around 111+), and the score is age-adjusted so younger children in the year are not penalised. Master a topic like algebra and you protect several near-certain marks. Time yourself against our free mock papers to make that minute-per-question pace feel normal.
Exam traps: where children lose the marks
- Only undoing one step. In 5x + 2 = 17 they divide by 5 too early, before subtracting the 2. Always clear the add or subtract first, then the multiply or divide.
- Combining unlike terms. Writing 3a + 2b = 5ab. You cannot merge different letters.
- Ignoring the power. Reading 2x² as (2x)². The square applies only to the x unless brackets say otherwise.
- Misreading the sentence. "5 less than n" is n - 5, not 5 - n. Word order flips it.
- Not checking. A ten-second substitution back into the equation catches most slips.
A four-week practice plan
Fifteen focused minutes a day for four weeks is enough for most Year 5 children. Week one: substitution. Week two: one and two-step equations. Week three: function machines and forming expressions. Week four: mixed, timed practice under exam pressure. Quest Arena's free maths worksheets include algebra sheets graded from foundation to top-tier 11+, all downloadable with no sign-up wall, so you can slot a sheet into each day and track coverage across the whole syllabus.
Frequently asked questions
Is a calculator allowed for algebra questions?
No. GL 11+ maths is a no-calculator paper, so children must be secure with mental and written arithmetic as well as the algebra method itself.
How hard is 11+ algebra really?
It stays basic: substitution, simple equations, combining like terms and forming short expressions. There are no quadratics or simultaneous equations. Most children reach comfort within a few weeks of short daily practice.
Which papers include the most algebra?
GL papers keep it light. CSSE (Essex) and independent-school ISEB-style papers tend to include a little more equation-solving and worded algebra, so check your target centre's board before deciding how far to push.