lesson
List every possibility once
1 · Learn
Systematic listing means choosing an order that includes every permitted outcome once and only once. A two-way table or ordered pairs can make the structure visible. Randomly writing examples makes omissions and repeats hard to detect.
If there are 3 starters and 4 mains, there are 3 rows of 4 choices, so 12 meals. This multiplication describes independent choices. If a restriction removes combinations, first list the complete grid and then cross out only the forbidden cells.
The multiplication rule for counting is useful enrichment, but the core skill is the justified complete list. State what each position in an ordered pair means: (S2,M3) differs from (M3,S2) because the roles differ.
2 · Worked example
Shirts A,B,C and trousers 1,2 give (A,1),(A,2),(B,1),(B,2),(C,1),(C,2): six outfits. If (B,2) is unavailable, five remain.
3 · Your turn
List all outcomes for two drinks P,Q and three snacks 1,2,3. Then remove (Q,2).
Check your answer
(P,1),(P,2),(P,3),(Q,1),(Q,2),(Q,3); five permitted outcomes after removing (Q,2).
4 · Apply your learning
Build a table on the working pad. Mark each cell as permitted or forbidden, then explain why the rows prove completeness.
Adult guidance and safety
This is England national-curriculum core teaching, not an exam-board specification. Check prerequisite understanding, require clear working and use additional varied practice before judging fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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