lesson
Keep both sides equal
1 · Learn
An equation states that two expressions have equal value. To solve x + 7 = 19, subtract 7 from both sides. Check by substituting the answer into the original equation.
With two unknowns, a single equation can have several solutions. If a + b = 8 and both are non-negative whole numbers, list possibilities systematically; a restriction such as a > b reduces the list.
2 · Worked example
3x + 2 = 20 gives 3x = 18 and x = 6. For a + b = 5 with non-negative whole numbers, (0,5) through (5,0) are ordered pairs.
3 · Your turn
Solve 4x - 3 = 25. List ordered non-negative whole-number pairs (a,b) with a + b = 4 and a > b.
Check your answer
x = 7. The pairs are (3,1) and (4,0). (2,2) fails a > b.
4 · Apply your learning
Use counters to enumerate pairs without missing or repeating one, then add a new restriction.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish 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.
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