This worksheet builds mathematical reasoning, teaching students to test conjectures about linear functions and generalise the patterns they discover. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- In y = ax + b, "a" controls the steepness and direction (positive a → y increases as x increases; negative a → y decreases).
- In y = ax + b, "b" is the value of y when x = 0 — changing b shifts every y-value by the same fixed amount without changing the steepness.
- A conjecture is a mathematical claim that needs to be tested with evidence before it can be trusted.
- A two-variable linear equation like 2x + 3y = 18 can have multiple whole-number (integer) solution pairs.
- Testing a conjecture with one example supports it but doesn't prove it for every case — but a single counterexample disproves it.
What your child will practise:
- Generating a table of values for a linear rule to test how changing a or b affects the pattern.
- Comparing two related rules (e.g. same a, different b) to see the effect of changing one parameter.
- Systematicallying search for integer solutions to a two-variable linear equation.
- Using a table of values to confirm whether a rule is genuinely linear (constant first difference).
- Stating a conjecture clearly, then test it against specific numeric evidence.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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