lesson
An operation and a number's sign are different
1 · Learn
A negative sign can belong to a number; subtraction is an operation. Adding a negative value moves left on a number line. Subtracting a negative reverses that change. Keep brackets around a negative input when they make the distinction clearer.
Check direction and size before using a rule mechanically. From -4, adding -3 gives -7, while subtracting -3 gives -1.
2 · Worked example
For 5 - (-2), undo a decrease of 2, giving 7. For -5 - 2, decrease -5 by 2, giving -7.
3 · Your turn
Calculate -6 + 9, 3 - 8 and -4 - (-7).
Check your answer
3, -5 and 3.
4 · Apply your learning
Draw all three calculations on a number line and explain why the two minus signs in the last calculation have different jobs.
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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