lesson
Use a pattern to explain the sign
1 · Learn
Multiplication by a negative can be understood through consistent number patterns. As the first factor decreases by one in n × (-3), the product increases by 3. The pattern passes through 0 × (-3) = 0 to (-1) × (-3) = 3.
This supports the rule that two negative factors have a positive product. Division is checked through multiplication. A positive result is not justified merely because a story feels favourable.
2 · Worked example
(-4) × 6 = -24, so -24 ÷ 6 = -4. Also (-4) × (-6) = 24.
3 · Your turn
Calculate (-7) × 3, (-7) × (-3) and 24 ÷ (-6).
Check your answer
-21, 21 and -4.
4 · Apply your learning
Extend a product table through zero and explain the pattern without relying only on a memorised slogan.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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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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