Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Interpret rate of change and initial value in context
Algebra
CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Interpret rate of change and initial value in context.
- 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: Write y = mx + b from a slope and intercept, or from a graph
Leads to: Compare two functions given in different ways; Interpret the slope and intercept of a line of best fit
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Write y = mx + b from a slope and intercept, or from a graph). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write the equation of the line with slope 4 and y-intercept −7. Type the right-hand side (y = …). → 4x-7Prompt: Use y = mx + b.
- Diego says the line through (0, −1) with slope 4 is y = −x + 4. Write the correct equation. Type the right-hand side. → 4x-1Prompt: Diego swapped the slope and the intercept.
- Write the equation of the line with slope −2 and y-intercept −5. Type the right-hand side (y = …). → -2x-5Prompt: Use y = mx + b.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Interpret rate of change and initial value in context. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A bamboo shoot is 10 cm tall and grows 10 cm per day. In y = mx + b, what is b?
- Step 1: b = 10
- Step 2: y = 10x + 10
- Answer: 10
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A bamboo shoot is 35 cm tall and grows 7 cm per day. In y = mx + b, what is b? → 35Prompt: m is the rate of change: how much per unit of time.
- A water tank holds 61 litres and drains at 6 litres per minute. Write the amount left after t minutes and find how much is left after 2 minutes. → 49Prompt: The rate of change is −6 (it goes down).
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A water tank holds 69 litres and drains at 2 litres per minute. Write the amount left after t minutes and find how much is left after 12 minutes. → 45Prompt: The rate of change is −2 (it goes down).
- A savings jar has 28 coins and 5 coins are added each week. In y = mx + b, what is m? → 5Prompt: m is the rate of change: how much per unit of time.
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: Write y = mx + b from a slope and intercept, or from a graph.
- 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: Compare two functions given in different ways; Interpret the slope and intercept of a line of best fit.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder