Start with the meaning
Begin with addition, subtraction, multiplication and division of small whole numbers. Use positive values first. The examples here introduce notation; they do not cover the whole algebra curriculum.
Explain what the letter is doing
In x + 4 = 11, x represents a number that makes the statement true. In the expression n + 4, n can take different values and the expression changes with it.
A letter is not automatically a hidden answer in every context. Start with a missing-number box, then replace the box with a letter while keeping the same quantities.
Read notation out loud
3x means three times x. If x = 5, then 3x = 15. It does not mean 35, and it does not mean 3 + x. Write the multiplication sign explicitly until the shorthand is familiar.
By contrast, the two-digit numeral 35 means three tens and five ones. Comparing these two kinds of notation helps explain why joining a digit and a letter has a different meaning.
Separate expressions from equations
An expression such as 2x + 3 names a quantity. You can evaluate it when x is given. An equation such as 2x + 3 = 13 states that two quantities are equal; solving asks which value makes that true.
Ask your child what the question requires before calculating. “Evaluate when x = 4” and “solve for x” are not interchangeable instructions.
Keep equality visible
Use a balance drawing for x + 4 = 11. Remove four units from both sides to leave x = 7. Write the same operation beneath each side.
Then substitute seven into the original: 7 + 4 = 11. This independent check catches an operation performed on only one side. Avoid beginning with “move it across and change the sign” before equality makes sense.
Worked examples, step by step
Example 1: Evaluate 4n when n = 6
- 4n means 4 × n.
- Replace n with six: 4 × 6 = 24.
- The answer is 24, not 46 or 10.
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Example 2: Solve x + 8 = 19
- Subtract eight from both sides.
- x = 19 − 8 = 11.
- Check in the original equation: 11 + 8 = 19.
Example 3: Evaluate 2x + 3 when x = 4
- Replace x with four: 2 × 4 + 3.
- Do the multiplication first: 8 + 3 = 11.
- This evaluates an expression; there was no equation to solve.
Common mistakes and useful repairs
Changing the value of the letter within one expression
In x + x, both occurrences of x represent the same value in that expression. If x = 6, the result is 12.
Treating equals as a one-way instruction
Show 8 = 3 + 5 as well as 3 + 5 = 8. Both state equality. This supports equations with the unknown on either side.
Try before revealing
Quick understanding check
Read the check answers
6 × x. A number written next to a letter represents multiplication.
7. Subtract five from both sides; 7 + 5 = 12.
How to help your child with algebra: letters, expressions and equations — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
Evaluate 5a when a = 3.
Show answer and reasoning
15. 5 × 3 = 15.
Evaluate b + 7 when b = 9.
Show answer and reasoning
16. Substitute nine, then add seven.
Solve y + 6 = 14 and check.
Show answer and reasoning
y = 8. Subtract six from both sides; 8 + 6 = 14.
Solve 4m = 28.
Show answer and reasoning
m = 7. Divide both sides by four; 4 × 7 = 28.
Is 3p + 2 an expression or an equation?
Show answer and reasoning
Expression. It has no equality statement. It can be evaluated if p is supplied.
Explain why x = 5 does not solve x + 4 = 12.
Show answer and reasoning
5 + 4 = 9, not 12. Substituting into the original tests the proposed value. The solution is x = 8.
How to help your child with algebra: letters, expressions and equations — worked answer key
15. 5 × 3 = 15.
16. Substitute nine, then add seven.
y = 8. Subtract six from both sides; 8 + 6 = 14.
m = 7. Divide both sides by four; 4 × 7 = 28.
Expression. It has no equality statement. It can be evaluated if p is supplied.
5 + 4 = 9, not 12. Substituting into the original tests the proposed value. The solution is x = 8.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, return to One-step equations: keep both sides equal before trying a fresh problem.
Help at home: Use a covered quantity
Put a hidden number of counters in a cup and four loose counters beside it. Say the total is eleven. Ask your child to find the cup’s amount, then write x + 4 = 11.
If the objects are easy but the symbols are difficult, keep switching between the drawing, words and equation. If inverse operations are difficult too, practise missing-number arithmetic before longer algebra.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Should I teach my own shortcut?
Ask how the teacher represents the method, then use language that preserves equality. A shortcut is useful only when the child can explain why it works and check it.
When is extra help useful?
Bring a specific piece of work if confusion persists across fresh examples. A teacher can distinguish notation, arithmetic and equation reasoning rather than treating all errors as the same problem.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
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