Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Compare two functions given in different ways
Algebra
CCSS 8.F.A.2England: KS3 Algebra
Objective and success criteria
Students will: Compare two functions given in different ways.
- 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: Find the rate of change from a table; Interpret rate of change and initial value in context
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Find the rate of change from a table; Interpret rate of change and initial value in context). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- x: 3, 6, 9, 12. y: −12, −24, −36, −48. What is the rate of change (slope)? → -4Prompt: How much does y change each time x changes?
- A bamboo shoot is 40 cm tall and grows 10 cm per day. In y = mx + b, what is b? → 40Prompt: m is the rate of change: how much per unit of time.
- x: 0, 2, 4, 6. y: 0, −1, −2, −3. Find the slope. Give a fraction in simplest form. → -1/2Prompt: Slope = change in y ÷ change in x.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Compare two functions given in different ways. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Liam's savings: y = 4x + 7. Zoe's savings (x = weeks): weeks 0, 1, 2, 3 → 4, 7, 10, 13. Who saves more per week?
- Step 1: Liam: 4 per week; Zoe: 3 per week
- Step 2: Liam
- Answer: Liam
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Kwame's savings: y = 4x + 4. Ines's savings (x = weeks): weeks 0, 1, 2, 3 → 5, 14, 23, 32. Who saves more per week? (Kwame / Ines) → InesPrompt: Compare the rates of change (slopes).
- Function A: y = −2x. Function B is a line through (1, −6) and (2, −7). Which has the greater initial value (y-intercept)? (A / B) → APrompt: A's initial value is its constant term.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Function A: y = 3x + 9. Function B is a line through (1, 14) and (2, 18). Which has the greater initial value (y-intercept)? (A / B) → BPrompt: A's initial value is its constant term.
- Sofia's savings: y = 4x + 0. Jamal's savings (x = weeks): weeks 0, 1, 2, 3 → 6, 11, 16, 21. Who saves more per week? (Sofia / Jamal) → JamalPrompt: Compare the rates of change (slopes).
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: Find the rate of change from a table.
- 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
- 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