S2 Maths | Changing the Subject of a Formula Lesson Prep Guide (for tutors)

S2 Maths | Changing the Subject of a Formula Lesson Prep Guide (for tutors) | Four steps, denominators and roots

2026-11-09

Tutor lesson-prep guides · Secondary Maths (DSE)

Rearranging a formula is solving an equation where the answer happens to be a letter rather than a number.

Objectives — Students can: (1) use a four-step routine to make a named letter the subject; (2) handle letters in denominators and cases that need a square root; (3) verify a rearrangement by substituting a set of numbers, and state which quantity must not be zero, scoring at least 9 of 12 in the diagnostic.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Solving equations	If 3x plus 4 equals 19, what is x?	5
Substitution	When u is 4, a is 3 and t is 5, what is u plus at?	19
Fractions	What is 36 times 2 divided by 12?	6

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Same process as solving	v equals u plus at, make t the subject: subtract u, then divide by a	Name the two moves
6-18 min	The four steps	P equals 2(l plus w), make w the subject: divide by 2 then subtract l, giving 7	Write out every step
18-30 min	Letters in the denominator	1 over R equals 1 over R1 plus 1 over R2; combine then invert to get R equals R1R2 over R1 plus R2, which is 2	Derive it yourself
30-42 min	Squares and roots	From y equals (3x minus 1) over 4, x equals (4y plus 1) over 3, so y equals 2 gives x equals 3	Handle the sign of the root
42-56 min	12-question diagnostic	Four question types marked on the spot: 9 right, 3 wrong	Independent work
56-60 min	Exit check	Three oral questions; any miss points to the stage to reteach	Oral answers

03 Teaching script (read it out)

Scene 1: Rearranging is solving, with a letter as the answer

Solving finds a number; rearranging finds a letter. To make t the subject of v equals u plus at, subtract u from both sides for v minus u equals at, then divide both sides by a for t equals (v minus u) over a. Substituting u equals 4, a equals 3 and v equals 19 gives t equals 5, which matches the original.
Teaching move: every chapter starts with the question “what is currently wrapped around the target letter”, then unwrap from the outside in.

Students do: make u the subject of v equals u plus at (u equals v minus at) and check with the same numbers.

Scene 2: Four steps: unwrap, move, divide, write

P equals 2(l plus w), make w the subject. The target sits inside a bracket multiplied by 2, so divide both sides by 2 to get P over 2 equals l plus w, then subtract l for w equals P over 2 minus l, and finally write it as a single fraction and check. With P equals 30 and l equals 8, w equals 7, and 2 times (8 plus 7) is 30.
Teaching move: keep the four steps as a written checklist at the side of the page and never combine two steps into one.

Students do: make h the subject of A equals (a plus b)h over 2, then substitute A equals 36, a equals 5 and b equals 7 to get h equals 6.

Scene 3: Letters in denominators: combine, then invert

From 1 over R equals 1 over R1 plus 1 over R2, combining the right side gives (R1 plus R2) over (R1R2); inverting both sides gives R equals R1R2 over (R1 plus R2). With R1 equals 6 and R2 equals 3, R equals 2, and 1 over 6 plus 1 over 3 equals 1 over 2.
Teaching move: insist that the right side is a single fraction before inverting; otherwise students invert term by term and write R equals R1 plus R2.

Students do: make F the subject of C equals 5(F minus 32) over 9, then substitute C equals 100 to get F equals 212.

Scene 4: Squares and roots come last, and carry a sign

From y equals (3x minus 1) over 4: multiply both sides by 4 for 4y equals 3x minus 1, add 1 for 4y plus 1 equals 3x, divide by 3 for x equals (4y plus 1) over 3. With y equals 2, x equals 3, which matches the original. When the formula contains a square, the final step is a square root and the question decides whether one root, or both, are wanted.
Teaching move: after taking a root, require one written line stating which root is taken and why; that line is usually where the mark sits.

Students do: make x the subject of y equals (3x minus 1) over 4, then check with y equals 5 (x equals 7).

04 Question types and worked steps

Type	Example	Steps	Answer
Additive	v equals u plus at, make t the subject	Subtract u from both sides, then divide by a	t equals (v minus u) over a, giving 5
With brackets	P equals 2(l plus w), make w the subject	Divide by the outside number, then move the constant	w equals P over 2 minus l, giving 7
Letters in denominators	1 over R equals 1 over R1 plus 1 over R2, make R the subject	Combine into one fraction, then invert	R equals R1R2 over (R1 plus R2), giving 2
Fractional	y equals (3x minus 1) over 4, make x the subject	Clear the denominator, move, then divide by the coefficient	x equals (4y plus 1) over 3, giving 3

Sanity check (teach this): Sanity checks: substitute numbers into the new formula and compare with the original; the divisor must not be zero (a, R1 plus R2 and 3 all matter here); the right side must be one fraction before inverting; roots carry a plus or minus; one move per line, because skipped lines are where errors hide; 9 out of 12 is 75 percent, not 9 percent.

05 Independent practice (3 questions)

Question	Answer	What to watch
Three basic rearrangements	One additive, one multiplicative, one bracketed	Is every move written down
Two with letters in denominators	Resistors in parallel and an average formula	Was the right side combined before inverting
Two substitution checks	One number set through both formulas	Do both sides agree

06 Common mistakes and what to say

Mistake	Student writes	Say this
Inverting term by term	Turning 1 over R equals 1 over R1 plus 1 over R2 into R equals R1 plus R2	Inverting applies to the whole fraction, not to each term; combine first, then invert, never the other way round.
Dividing only the first term	Turning P equals 2(l plus w) into P over 2 equals l plus 2w	Dividing both sides by 2 divides every term on the right; expand once afterwards to check.
Skipping steps	Jumping from v equals u plus at straight to t equals v minus u over a	One move per line shows which side was missed; thirty seconds saved now costs three minutes in marking.
Forgetting the negative root	Writing only x equals 3 from x squared equals 9	A square root has two signs unless the quantity cannot be negative, such as a length or a time; state which you keep.

07 Homework (paper, section and question numbers)

Secondary maths chapter index — See the other chapters in this subject
Lesson prep guides home — Compare related chapters
Redo this chapter — Redo diagnostic questions 1 to 6, writing all four steps

08 Exit check (last 5 minutes)

Question	Answer	Decision
t in v equals u plus at	t equals (v minus u) over a	Writing t equals v minus u over a means brackets were dropped; reteach stage one
w in P equals 2(l plus w)	w equals P over 2 minus l, giving 7	Writing w equals P minus 2l means only one term was divided; reteach stage two
R in 1 over R equals 1 over R1 plus 1 over R2	R equals R1R2 over (R1 plus R2), giving 2	Writing R equals R1 plus R2 means term-by-term inversion; reteach stage three

09 Tutor FAQ

Must the answer be simplified?

Yes, especially with letters in the denominator; a single fraction is easier to substitute into and usually earns full marks.

How do I know the rearrangement is right?

Substitute one set of numbers into both versions; equal results mean it is right, and it is faster than rereading the steps.

How is the sign of a root decided?

From what the letter means: lengths, times and counts take the positive root; pure algebra usually keeps both and writes plus or minus.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.