11+ algebra is gentler than it sounds: substitute values into an expression, solve a two-step equation like 2x + 3 = 11, and turn a sentence such as "a pencil costs p pence" into a piece of maths. It is really a tidy set of habits, and four weeks of short daily practice with our free graded worksheets covers the whole basics list comfortably.
What 11+ algebra basics actually cover
At 11+ level, "algebra" does not mean anything frightening. It means using a letter to stand for an unknown or changing number, and working with it in a few predictable ways. The current syllabus, tested most heavily by GL Assessment papers and the Essex CSSE exam, breaks into five sub-skills:
- Substitution: replacing a letter with a number, e.g. if a = 4, find 3a + 2.
- Forming expressions: writing a rule in symbols, e.g. "3 more than n" becomes n + 3.
- Function machines: a number goes in, an operation happens, a number comes out, and children often work backwards to find the input.
- Simplifying: collecting like terms, so 2a + 3a + 4 becomes 5a + 4.
- Solving equations: one-step (x + 7 = 12) and two-step (2x + 3 = 11) equations, plus simple worded problems.
Our free worksheet library grades every one of these across four tiers — Foundation, Developing, Secure and Greater Depth — so a child can enter at their level and climb. Algebra sits in the Year 6 national-curriculum programme, but 11+ papers test it in the autumn of Year 5 or 6, so most families start earlier than school does.
Substitution: the core skill, worked step by step
Substitution is the foundation, so master it first. The golden rule is BIDMAS: do the multiplication before the addition. Take this typical question — If a = 5 and b = 2, find the value of 3a - 4b.
- Replace each letter with its number: 3 × 5 - 4 × 2.
- Do the multiplications first: 15 - 8.
- Now subtract: 15 - 8 = 7.
The classic trap is writing 3a as "3 then 5" and reading 35, or doing the subtraction before the multiplication and getting (15 - 4) × 2. Remind your child that a letter written next to a number always means "multiply", and that the order of operations never sleeps. If BIDMAS is shaky, pair this with our revision hub order-of-operations refresher before pushing on.
Solving two-step equations: keep it balanced
A two-step equation is solved by undoing operations in reverse, keeping both sides equal like a set of scales. Here is 2x + 3 = 11 in full:
- Subtract 3 from both sides to undo the +3: 2x = 8.
- Divide both sides by 2 to undo the ×2: x = 4.
- Check by substituting back: 2 × 4 + 3 = 11. Correct.
That final check is the single most valuable habit in 11+ algebra, and it costs about five seconds. Children who check catch the commonest error — undoing in the wrong order, e.g. dividing by 2 before subtracting the 3. The named method to drill is "reverse the order, balance both sides, then check".
Function machines and forming expressions
Function machines are algebra in disguise and appear often in GL papers. A machine that does "×3 then +1" turns 4 into 13. Working forwards is easy; the exam usually asks children to work backwards. If the output is 13, reverse each step in reverse order: undo +1 to get 12, then undo ×3 to get 4. This is the same balancing logic as solving an equation, which is worth pointing out so the two topics reinforce each other.
Forming expressions rewards careful reading. "Sam has n stickers. Ben has 5 more, and Cara has twice as many as Ben." Ben = n + 5; Cara = 2(n + 5). Encourage the child to define the letter, then build each phrase one clause at a time.
Quick-reference: algebra language and key facts
| Phrase in words | In algebra |
|---|---|
| 5 more than a number | n + 5 |
| 7 less than a number | n - 7 |
| Three times a number | 3n |
| A number divided by 4 | n ÷ 4 or n/4 |
| Double a number, then add 1 | 2n + 1 |
| The next even number after 2n | 2n + 2 |
Two facts save marks: a term like 3a means 3 × a (never 30-something), and only like terms combine — 2a + 3a = 5a, but 2a + 3b cannot be simplified further.
How algebra appears in a real GL 11+ paper
In a standard GL maths paper of roughly 50 questions in 50 minutes — about a minute per question, no calculator — algebra usually accounts for a small handful of items rather than a whole section. Answers are multiple-choice, marked A to E on a separate OMR sheet, so a child who reaches x = 4 simply finds "4" among the options and shades the bubble. That format is a gift: children can substitute each option back into the equation if they are unsure, which turns a solving question into a quick checking exercise. The raw score is later converted to a Standardised Age Score (roughly 69-141, with 100 average and many grammar schools looking for about 111 or higher), and because the score is age-adjusted, a younger child is not disadvantaged. Practise under the clock with our free timed mock papers and the free papers hub so the timing feels normal on the day.
Common mistakes and exam traps
- Ignoring BIDMAS in substitution — doing addition before multiplication.
- Reading 3a as the number 35 when a = 5, instead of 3 × 5.
- Undoing operations in the wrong order in two-step equations.
- Dropping a minus sign when moving terms across the equals sign.
- Combining unlike terms, e.g. writing 2a + 3b as 5ab.
- Not re-reading the last line of a worded problem, which often switches what is asked.
Difficulty progression: Year 5 versus Year 6
The same skill scales neatly. An easier Year 5 version: If y = 6, find y + 4 (answer 10) — a single substitution with one operation. An exam-level Year 6 version: If y = 6, find (2y - 3) ÷ 3 — substitute to get (12 - 3) ÷ 3 = 9 ÷ 3 = 3, blending substitution, BIDMAS and division. Our worksheets step through exactly this gradient, so a child builds confidence at Foundation before meeting the multi-step Greater Depth items that separate strong candidates.
How to use the worksheets
- Diagnose: one Secure-tier sheet, unaided. Score under 70%? Drop a tier. Over 90%? Climb one.
- Little and often: 15-20 minutes daily beats a weekend marathon — retention lives in the gaps between sessions.
- Review errors out loud: the child explains what went wrong; you resist explaining first. Self-diagnosis sticks.
- Fold into mocks: once a topic hits Greater Depth, let full timed mock papers keep it warm rather than more isolated drilling.
Frequently asked questions
Is a calculator allowed for 11+ algebra?
No. GL and CSSE maths papers are non-calculator, so all substitution and equation work must be done by hand. That is another reason to practise the balancing method until it is automatic.
How much algebra is on the 11+?
Only a few questions in a typical GL paper, but they are quick marks once the method is secure, and independent-school and CSSE papers can ask slightly more. It is high-value practice for the time invested.
When should my child start algebra practice?
Most families begin in Year 5, since 11+ papers test it before schools teach it fully in Year 6. Short, regular sessions with our graded worksheets close that gap without pressure.