Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Rearrange formulas (change the subject)
Algebra
CCSS HSA.CED.A.4England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Rearrange formulas (change the subject).
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Two-step equations
Leads to: Composite and inverse functions; Make a chosen letter the subject of a literal equation; Read the slope and intercept from Ax + By = C
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Two-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: −9x + 3 = −42 → x = 5Prompt: Subtract 3 from both sides.
- Solve: x/3 − 12 = −5 → x = 21Prompt: Add 12 to both sides first.
- Solve: −3x − 16 = −40 → x = 8Prompt: Add 16 to both sides.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Rearrange formulas (change the subject). Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Make x the subject of y = 9x − 2. Type the expression for x.
- Step 1: y + 2 = 9x
- Step 2: x = (y + 2)/9
- Answer: (y+2)/9
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Make x the subject of y = 7x − 4. Type the expression for x. → (y+4)/7Prompt: Undo the operations on x in reverse order.
- Rearrange y = mx + c to make x the subject. Type the expression for x. → (y-c)/mPrompt: Subtract c, then divide by m.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Make x the subject of y = 8x + 9. Type the expression for x. → (y-9)/8Prompt: Undo the operations on x in reverse order.
- Rearrange v = u + at to make u the subject. Type the expression for u. → v-a*tPrompt: Subtract at from both sides.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Two-step equations.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Composite and inverse functions; Make a chosen letter the subject of a literal equation; Read the slope and intercept from Ax + By = C.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-9.
Free lesson plan from eurekami.com/lesson-plan-builder