Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Find the rate of change from a table
Algebra
CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Find the rate of change from a table.
- 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: Slope (gradient) of a line
Leads to: Write a linear function rule from a table; Compare two functions given in different ways
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 (Slope (gradient) of a line). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the rate of change from a table. 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: x: 2, 5, 8, 11. y: −7, −16, −25, −34. What is the rate of change (slope)?
- Step 1: Δy = −9, Δx = 3
- Step 2: m = −9 ÷ 3 = −3
- Answer: -3
- 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.
- x: −1, 2, 5, 8. y: 6, −12, −30, −48. What is the rate of change (slope)? → -6Prompt: How much does y change each time x changes?
- x: 0, 2, 4, 6. y: 3, 8, 13, 18. Find the slope. Give a fraction in simplest form. → 5/2 (2 1/2)Prompt: Slope = change in y ÷ change in x.
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.
- x: −2, 1, 4, 7. y: −22, −1, 20, 41. What is the rate of change (slope)? → 7Prompt: How much does y change each time x changes?
- A phone's battery charge (%) is measured while charging. After 1, 2, 4 and 5 ten-minute periods it reads 53, 56, 62, 65%. By how many percentage points does it rise per ten-minute period? → 3Prompt: Compare two readings and the number of periods between them.
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: Slope (gradient) of a line.
- 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: Write a linear function rule from a table; Compare two functions given in different ways.
- 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