Maths
Find the error: expand and solve
For Years 8 to 12 Mathematics pupils, find an incorrect expansion, correct the equation and verify the solution by substitution.
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For Years 8 to 12 Mathematics pupils, find an incorrect expansion, correct the equation and verify the solution by substitution.
Pupil worksheet. Use the preview for diagrams and layout.
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Find the error: expand and solve Pupil activity Audience: Years 8 to 12 Mathematics pupils Find an incorrect expansion, correct the equation and verify the solution by substitution. Student work Solve 2(x + 5) = 18. Working: 2(x + 5) = 18 2x + 5 = 18 2x = 13 x = 6.5 Find and fix 1. Circle the first incorrect line. 2. Write the full expansion. 3. Solve and check by substitution. 4. Explain the error in one sentence. Pupil activity Page 1 of 1
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Find the error: expand and solve Teacher key and guidance supporting this exact edition Teacher answer 2(x + 5) = 2x + 10. Then 2x + 10 = 18, 2x = 8 and x = 4. Substitution gives 2(4 + 5) = 18. Teacher companion Page 1 of 1
A teaching sequence
Find an incorrect expansion, correct the equation and verify the solution by substitution.
Expand and solve correctly
Expand 2(x + 5) correctly. Solve the corrected equation 2(x + 5) = 18.
Did 2 multiply both x and 5?
Check by substitution
Test the corrected value in the original bracketed equation. Show that both sides agree after substitution.
Does your corrected value satisfy 2(x + 5) = 18?
Explain why the original fails
Explain why the student's result does not satisfy both sides.
What happens when 6.5 is substituted into the original equation?
Before you teach
Look for the thinking behind an answer, choose the support your class needs and leave room for an independent response.
What to look for
The student missed the factor on 5. The correct solution is x = 4; 2(4 + 5) = 18. Ask, “What does the 2 multiply?”
Give a little support
Use two groups of (x + 5) to model the expansion.
Take the idea further
Create another incorrect expansion and ask a partner to find its first invalid line.
Things to keep in mind
Confirm that the class has met brackets and equations; select extensions to match the course.
Keep the idea. Make it yours.
Bring your topic, learning goal and class context to PLAI™, then review what you create.
Another starting point
Explore a different teaching task from this selection.
Solving equations: watch the move, then make your move
Review the worked examples and check the algebra, layout and answer guidance before use. Explain that the same operation must be applied to both sides, and that substitution can test whether a proposed value works.
Explore resource
Find the error: algebra and equations
Read the student's work and circle the first incorrect step.
Explore resourceIdeas to try with your class
Sample teaching perspectives on what to try, what to adapt and what to watch for.
Meet The Creators
Meet a creator whose teaching interests connect with this template.
Little Lightbulbs
The problem uses 2(x + 5) = 18 and shows the incorrect line 2x + 5 = 18. Pupils circle that first error, restore the full expansion, solve and verify by substitution.
Planning List
For Years 8 to 12, the single-page task isolates distribution before solving a linear equation. Requiring the first incorrect line helps pupils identify where equivalence was lost rather than only replacing the final value.
Margin Note
Use 2(x + 5) = 18 to model multiplying both bracket terms by two, then invite pupils to complete the remaining steps. Substitution into that equation checks the answer against the original relationship.
Bright Idea Break
This prompt addresses one particular expansion error, not every cause of incorrect algebra. Treat a pupil’s explanation as evidence to explore, and follow with a distinct expression to see whether the method transfers.