Rearranging Formulae Lessons

Rearranging Formulae: Clear Methods, Formulae and Worked Exercises

Rearranging Formulae provides a useful bridge between basic fluency and multi-step mathematical problem solving. This online lesson is written for KS3, GCSE, IGCSE, A-Level students working at Foundation, Higher, A-Level level and covers changing the subject, inverse operations, formulae with fractions and powers. This creates confidence gradually and helps the learner explain the method in their own words. The central skill is to identify the required subject, undo operations in reverse order, preserve equality and handle brackets, fractions and powers. Students identify the important information, choose a suitable representation and set out each calculation logically. These habits reduce guesswork, protect method marks and make checking easier. During tutoring, examples are selected so that one idea changes at a time before several skills are combined. The learner describes what each symbol, number, diagram or condition means before calculating, because accurate interpretation is often the difference between a secure answer and an avoidable mistake.

In the UK curriculum, Rearranging Formulae can appear in KS3, KS4, KS5 work for Year 8, Year 9, Year 10, Year 11, Year 12, with wording that varies across AQA, Edexcel, OCR, WJEC, Cambridge IGCSE. The underlying reasoning remains consistent. Key formulae and relationships include v=u+at ⇒ a=(v-u)/t; A=πr² ⇒ r=√(A/π). Every symbol is matched to the correct value, unit, coordinate, event or algebraic term. A reliable routine is to read the full question, underline quantities and conditions, draw a diagram or table when useful, write the rule, substitute carefully, calculate and interpret the answer. Interpretation may require units, an inequality, a restriction, a degree symbol, a probability between 0 and 1, an exact value or a conclusion in context. Students also learn when calculator use is helpful and when simplification should be completed by hand.

Common errors include moving terms without applying the same operation to both sides, changing signs incorrectly, dividing only one term and forgetting positive roots in a physical context. The lesson identifies the first incorrect decision and explains why it changes everything that follows. The student corrects that line, repeats a nearby example and then returns to the original question. Exam technique is included throughout: working is spaced clearly, brackets and negative signs are checked, exact answers are retained when requested, intermediate values are kept before final rounding and the result is compared with the question. The topic connects with science equations, geometry, finance, mechanics and modelling, helping learners recognise rearranging formulae when it is hidden inside a multi-step problem rather than announced by a heading.

Independent practice should mix familiar and unfamiliar forms. Start with two direct questions, continue with two that require a choice of method and finish with a longer exam-style problem. After marking, record the first successful step, the first error and one efficient improvement. Explain a Rearranging Formulae solution aloud without the model answer, naming the rule, justifying the substitution or transformation and showing why the result is reasonable. Progress is measured through accuracy, independence and flexibility: obtaining the correct result, starting without a prompt and adapting when the numbers, diagram or wording changes. This creates durable understanding rather than short-term familiarity.

Five Worked Exercises with Formulae and Results

Exercise 1: Make x the subject of y=3x+5. Formula, method and result: Subtract 5 and divide by 3: x=(y-5)/3. Check the answer against the original conditions and present it with the required notation or units. Exercise 2: Make h the subject of A=bh/2. Formula, method and result: Multiply by 2: 2A=bh. Divide by b: h=2A/b. Check the answer against the original conditions and present it with the required notation or units. Exercise 3: Make t the subject of v=u+at. Formula, method and result: Subtract u: v-u=at. Divide by a: t=(v-u)/a. Check the answer against the original conditions and present it with the required notation or units. Exercise 4: Make r the subject of C=2πr. Formula, method and result: Divide by 2π: r=C/(2π). Check the answer against the original conditions and present it with the required notation or units. Exercise 5: Make x the subject of y=(x+4)/3. Formula, method and result: Multiply by 3: 3y=x+4. Subtract 4: x=3y-4. Check the answer against the original conditions and present it with the required notation or units.

During a focused lesson, the tutor varies one feature at a time so the student can see which part of the method changes and which part remains fixed. This comparison is especially useful for exam questions that look unfamiliar but use the same underlying structure. The learner then completes a parallel question independently and checks the answer against the original information.

Continue learning through: Linear Equations and Algebra Basics; Year 10 GCSE Maths Support; GCSE Maths Calculator Exam Practice; Can tutoring help with worded maths questions?; Rearranging Formulae.

This Rearranging Formulae lesson builds a method that remains clear when the question changes form. By combining explanation, formulae, five complete worked exercises and selected follow-up pages, students can build confidence, communicate their reasoning and approach beginner, intermediate, advanced questions more independently.