What does a child have to do to evaluate an algebraic expression in the 11+?

Substitute one supplied value and calculate the expression. It is one of 55 named maths skills in the 11+, in the algebra strand, and this page carries 2 interactive exercises that practise it.

What is the trap in an 11+ evaluate an algebraic expression question?

A number written next to a letter means multiply by it, not add it. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What can I say if my child is stuck on evaluate an algebraic expression?

Point at the next move rather than explaining the whole rule. Use the value stated for A, put it in place of the letter, and only then do the arithmetic.

What is not part of evaluate an algebraic expression in the 11+?

The skill map draws the line here: Excludes solving an equation. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside evaluate an algebraic expression?

The algebra strand holds 2 skills that are tested together, and the page next to evaluate an algebraic expression is use a term rule. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise evaluate an algebraic expression for free?

Use Balance Scale and Function Machine, embedded on this page. They are the exercises the skill map attaches to evaluate an algebraic expression, they run in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Maths · Algebra

Evaluate an algebraic expression

Substitute one supplied value and calculate the expression.

Watch the worked example

Open the video page

Swap the Letter, Find the Value

This video shows how to replace a letter with its given value and calculate the value of an algebraic expression. Watch an 11+ maths question solved step by step.

0:00 / 2:29

Turn on captions with the CC button. Jump to any part with the chapter buttons.

Read the transcript

Keep practising with Trace Learn. Find topics to practise next

Quick quiz: Evaluate an algebraic expression

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz

Question 1
Point Q marks 12 and point A marks 3 on the number line, so m = 12 and n = 3. What is 8m + 3n?
- A.165
- B.60
- C.113
- D.105
Question 2
Point T marks 13 and point P marks 4 on the number line, so m = 13 and n = 4. What is 8m + 7n?
- A.28
- B.132
- C.123
- D.255
Question 3
Point Q marks 9 and point T marks 11 on the number line, so m = 9 and n = 11. What is 4m + 3n?
- A.65
- B.47
- C.69
- D.42
Question 4
Point Q marks 9 and point B marks 7 on the number line, so m = 9 and n = 7. What is 5m + 8n?
- A.107
- B.132
- C.65
- D.101
Question 5
Point D marks 9 and point B marks 11 on the number line, so m = 9 and n = 11. What is 2m + 9n?
- A.117
- B.103
- C.220
- D.119
Question 6
Point D marks 4 and point T marks 12 on the number line, so m = 4 and n = 12. What is 2m + 9n?
- A.60
- B.132
- C.176
- D.116
Question 7
Point Q marks 3 and point A marks 9 on the number line, so m = 3 and n = 9. What is 5m + 6n?
- A.63
- B.132
- C.84
- D.69
Question 8
Point A marks 8 and point T marks 12 on the number line, so m = 8 and n = 12. What is 2m + 5n?
- A.88
- B.140
- C.64
- D.76
Question 9
Point D marks 12 and point C marks 2 on the number line, so m = 12 and n = 2. What is 7m + 3n?
- A.116
- B.90
- C.97
- D.140
Question 10
Point B marks 13 and point P marks 12 on the number line, so m = 13 and n = 12. What is 7m + 4n?
- A.139
- B.61
- C.275
- D.136

Practise it now

Get ONE mystery bag alone on a pan - keeping the scale level - and you have found x.

It covers most of this skill rather than all of it.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Putting a value in place of a letter

Point A marks 5 on the number line, so n = 5. What is 4n - 8?

Each small step on this line is worth 1, and every labelled tick is ten steps on.

Answer: 12

How you get there

Reading the line and substituting gives 4n - 8 = 12: substitute n = 5, so 4n means $4 \times 5 = 20$ , and taking 8 away gives 12. A letter written next to a number always means multiply, so the multiplication happens before the addition or subtraction unless a bracket says otherwise.

Why the other answers tempt

A number written next to a letter means multiply by it, not add it.

If they are stuck, say this

Use the value stated for A, put it in place of the letter, and only then do the arithmetic.

Now do it live in Balance Scale

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's have a go at Evaluate an algebraic expression together. Take a look at the picture. Here is what matters: Number line from 0 to 20 in steps of 1 with major steps of 10. Here comes the question: Point A marks 5 on the number line, so n = 5. What is 4n - 8? Before we race ahead, let us choose one good first step. Here is a helpful clue: Use the value stated for A, put it in place of the letter, and only then do the arithmetic. Nice work. Now let us follow the thinking: A letter written next to a number always means multiply, so the multiplication happens before the addition or subtraction unless a bracket says otherwise. So our answer is: 12. There is one sneaky trap to watch for: A number written next to a letter means multiply by it, not add it. Can you show me that first move again in your own words? Brilliant. No rush; we are practising a method you can reuse, not trying to win a speed contest.

How each of these 2 exercises teaches it

Balance Scale

Get ONE mystery bag alone on a pan - keeping the scale level - and you have found x.

A balanced scale is an equals sign made of metal. 2x + $3 = 11$ means the two pans genuinely weigh the same. Remove 3 from both pans and it is still level: 2x = 8. Halve both pans and it is still level: x = 4. Every step of algebra is just something you did to both sides at once.

What to say if they get stuck

Take a weight off one pan and watch what happens. The beam is telling you something.
Whatever you take from one side, take the SAME from the other. Then it stays level.
Once only bags are left on one side, split BOTH sides into that many equal groups.

Open Balance Scale on its own page to share it

Function Machine

Work out which two gears turn these numbers into those numbers.

This engine’s own main skill is Function Machines & Inverse. It practises evaluate an algebraic expression alongside it.

A function machine does the same thing to every number that enters it. You found the rule backwards - from the outputs - which is inverse thinking. And the order of the gears is part of the rule: ×3 then +1 turns 2 into 7, while +1 then ×3 turns the same 2 into 9. Same gears, different machine.

Step 1. Deduce the gears. Drag gears into the machine so every ticket comes out right.
Step 2. Run it. New number going in. Predict the output BEFORE you pull the lever.

What to say if they get stuck

Look at 2 → 7 and 4 → 13. When the input goes up by 2, the output jumps by 6. What multiplies by 3?
Try ×3 first: 2 becomes 6, but the ticket says 7. What tiny gear finishes the job?
The order of the gears changes the answer. ×3 then +1 gives 7; +1 then ×3 gives 9.

Open Function Machine on its own page to share it

How evaluate an algebraic expression differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: substitute one supplied value and calculate the expression, and it stops where excludes solving an equation.

Use a term rule
Use an algebraic rule to calculate a named sequence term. Rule is supplied.
Solve a one-step number problem
Choose and perform one operation in a short context. Exactly one operation is required.
Apply a number code rule
Apply one arithmetic mapping to a letter or number code. One invariant rule only.

Questions parents ask about evaluate an algebraic expression

What this skill involves, common mistakes and ways to practise it at home.

: Substitute one supplied value and calculate the expression. It is one of 55 named maths skills in the 11+, in the algebra strand, and this page carries 2 interactive exercises that practise it.
: A number written next to a letter means multiply by it, not add it. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Use the value stated for A, put it in place of the letter, and only then do the arithmetic.
: The skill map draws the line here: Excludes solving an equation. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The algebra strand holds 2 skills that are tested together, and the page next to evaluate an algebraic expression is use a term rule. Each has its own exercise and its own link, and none of them needs an account.
: Use Balance Scale and Function Machine, embedded on this page. They are the exercises the skill map attaches to evaluate an algebraic expression, they run in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. Each also has its own link, so you can send one to a child without sending them anywhere else first.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.