Equation modelling

Objective. Create equations from constraints and evaluate solutions in context.

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Learn: the key idea

Equation modelling means translating a worded situation with given constraints into an algebraic equation, solving it, and interpreting the result in context. Begin by defining a letter for the unknown quantity clearly, then use the given relationships, such as equal perimeters or total costs, to build an equation step by step. After solving the equation algebraically, substitute the solution back into the original context to check it is sensible, such as giving a positive length or a whole number of items. Always state the final answer with correct units or in the form the question requires.

Worked example

A rectangle has length x + 3 cm and width x cm. Its perimeter is 26 cm. Form and solve an equation model to find x.

1 $Write the perimeter expression: 2((x + 3) + x) = 2(2x + 3).$
2 $Expand to give the equation: 4x + 6 = 26.$
3 $Subtract 6 from both sides: 4x = 20.$
4 $Divide by 4: x = 5 cm.$

Answer: x = 5 cm

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Common mistake. Pupils solve the equation correctly but forget to answer the original question in context, leaving the value of x rather than, for example, the length of a side. Always relate the algebraic answer back to what was asked.

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