Use the same pair of simultaneous linear equations for substitution and elimination. Align corresponding transformations, ask pupils what remains invariant, then change the equations and require a justified method choice.
The aim is not to declare a winner. A method may be convenient because of the structure of a particular pair or useful because it makes a mathematical relationship visible. Ask pupils to analyse solved problems, compare strategies and connect the worked examples to a new problem.
Use equation pairs for which both methods are valid, and define the accepted notation before the lesson.
[1]Two valid methods expose the same structure
Solve y = x + 2 and 2x + y = 11. Neither method is universally best.
Substitution
- 1Replace y with x + 2
2x + (x + 2) = 11
- 2Combine equivalent terms
3x + 2 = 11
- 3Preserve equality and solve
3x = 9 → x = 3
- Check both equations
y = 5; 5 = 3 + 2; 6 + 5 = 11
Elimination
- 1Write both equations for combining
−x + y = 2; 2x + y = 11
- 2Subtract the first from the second
3x = 9
- 3Solve, then substitute
x = 3 → y = 5
- Check both equations
5 = 3 + 2; 6 + 5 = 11
Build two aligned worked methods
Choose one equation pair for which both substitution and elimination are valid and age-appropriate. In Praktikal, use formula content to present the equations and maths fill-in, ordering or closed numeric questions for carefully selected missing steps.
Do not turn every line into a blank. Leave enough of each solution visible for pupils to inspect the strategy, while making them supply a transformation that matters.
- Teacher decision
- decide whether an incorrect response reflects notation, arithmetic or the selected transformation before choosing the next example.
- Pupil action
- complete or order the steps, then identify where each method first uses one equation to rewrite or combine the other.
Match what stays the same
Place the two solutions side by side. Ask pupils to pair corresponding mathematical moves: preserving equality, replacing an expression with an equivalent one, removing a variable and checking the solution.
Praktikal contains formula, pairing, grouping and ordering blocks. Define the matching choices so equivalent forms are not rejected merely because they are written differently.
Ask two questions:
- What is invariant across both methods?
- What does this representation make easier to see?
Comparing alternative strategies is supported within algebra guidance, but the comparison has to be prompted; two columns alone are not enough.
[1]Compare explanations, not only answers
Collect one short explanation after the matching task. During live delivery, Praktikal shows answers and progress. Paraphrase or anonymise two contrasting explanations for discussion.
The platform can bring responses together. It does not label the method, infer the reasoning or decide which explanation the class needs. A pupil with the correct solution may still be imitating a surface pattern.
- Teacher decision
- model a transformation if explanations confuse equality; compare the two accounts if they reach the same answer for different reasons; continue only when pupils can name a structural feature.
Change the equations before asking for a method
Present a new pair with different structural features. Ask pupils to choose substitution or elimination and justify the choice from what they can see in the equations.
Use a closed item for the choice and a separate short response for the reason. Automatic scoring applies to the closed component only; review the written reasoning yourself. Praktikal does not automatically grade mathematical reasoning or proof.
Avoid “Which is best?” Ask instead:
- Which method would you start with here?
- What feature of the pair supports your choice?
- What would make the other method reasonable?
Method choice depends on the problem. This evidence applies to algebra and does not establish a rule for all mathematics.
[1]Solve again and use the work
Ask pupils to carry out the chosen method on a further pair. Use structured closed steps for the automatically scored part and a short explanation of one key transformation.
Review the work, give feedback and decide whether the next lesson should revisit equivalence, elimination, substitution or checking.
One successful solution is evidence for that task. It does not prove durable transfer.
[1] [2]Source notes
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students A systematic practice guide for middle- and high-school algebra. It supports analysing solved problems, comparing valid strategies and connecting worked examples to new problems; it does not establish automatic transfer or a universally best method.
Improving Mathematics in Key Stages 2 and 3 A public guidance summary used here only for the cautious formative-assessment framing. A method choice and reason can inform the next teaching decision, but one response does not reveal complete reasoning or durable transfer.