lesson
A term's variable part matters
1 · Learn
An expression represents a calculation without necessarily asserting equality. Like terms have the same variable part, so 3x + 5x = 8x. But 3x + 5y cannot be combined into 8x or 8xy.
Substitution replaces letters with values. Keep brackets around negative substituted values and follow operation order. Different values may make two expressions equal once without making them identical for every input.
2 · Worked example
For x = -2, 4x + 7 = 4 × (-2) + 7 = -1. I do not interpret 4x as a two-digit number.
3 · Your turn
Simplify 6a + 3b - 2a + b. Evaluate the result for a = 2 and b = -1.
Check your answer
4a + 4b; the value is 8 - 4 = 4.
4 · Apply your learning
Use labelled counters to represent unlike terms and explain why their labels cannot be ignored.
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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