Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Tell linear from exponential patterns in a table
Algebra
CCSS HSF.LE.A.1CCSS HSF.LE.A.1.AEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Tell linear from exponential patterns in 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: Exponential growth and decay; Graphs of linear equations y = mx + b
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 · 5 min
- Quick retrieval from earlier learning (Exponential growth and decay; Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- y = 11 × 1.1ˣ. Find y when x = 2. Round to 2 decimal places if needed. → 13.31Prompt: Work out the power first.
- Does y = 21(0.8)ˣ show exponential growth or decay? (Growth / Decay) → DecayPrompt: Look at the base b being raised to the power x.
- y = 36 × 2ˣ. Find y when x = 3. Round to 2 decimal places if needed. → 288Prompt: Work out the power first.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Tell linear from exponential patterns in 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: 0, 1, 2, 3, 4 y: 1, 3, 9, 27, 81 Is the relationship linear, exponential or neither?
- Step 1: Constant ratio: exponential.
- Step 2: Exponential
- Answer: Exponential
- 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: 0, 1, 2, 3, 4 y: 64, 32, 16, 8, 4 Is the relationship linear, exponential or neither? (Linear / Exponential / Neither) → ExponentialPrompt: Check the differences between consecutive y-values.
- x: 0, 1, 2, 3 y: 128, 64, 32, 16 What is the constant ratio (growth factor)? → 0.5Prompt: Divide each y-value by the one before it.
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: 0, 1, 2, 3, 4 y: −3, 2, 7, 12, 17 Is the relationship linear, exponential or neither? (Linear / Exponential / Neither) → LinearPrompt: Check the differences between consecutive y-values.
- x: 0, 1, 2, 3 y: 5, 20, 80, 320 What is the constant ratio (growth factor)? → 4Prompt: Divide each y-value by the one before it.
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: Exponential growth and decay.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder