Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Linear sequences: the nth term
Algebra
CCSS HSF.BF.A.2CCSS HSF.LE.A.2England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Linear sequences: the nth term.
- 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: Number patterns; Evaluate expressions
Leads to: Arithmetic and geometric sequences and series; Use aₙ = a₁ + (n − 1)d for arithmetic sequences; Find the ratio and terms of a geometric sequence
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 (Number patterns; Evaluate expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What comes next? 35, 46, 57, 68, __ → 79Prompt: How much does the pattern go up each time?
- Find the value of 6x + 14 when x = 7. → 56Prompt: Replace x with 7.
- Find the missing number: 117, 111, 105, __, 93 → 99Prompt: Is the pattern going up or down? By how much?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Linear sequences: the nth term. 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: Find the nth term of the sequence 15, 13, 11, 9, …
- Step 1: Difference = −2
- Step 2: −2n + 17
- Answer: -2n+17
- 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.
- Find the nth term of the sequence −10, −16, −22, −28, … → -6n-4Prompt: The common difference tells you the number in front of n.
- The nth term of a sequence is 2n − 1. What is the 20th term? → 39Prompt: Substitute n = 20.
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.
- Find the nth term of the sequence −8, −9, −10, −11, … → -n-7Prompt: The common difference tells you the number in front of n.
- Is 75 a term in the sequence with nth term 3n + 1? (Yes / No) → NoPrompt: Solve 3n + 1 = 75.
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: Number patterns.
- 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: Arithmetic and geometric sequences and series; Use aₙ = a₁ + (n − 1)d for arithmetic sequences; Find the ratio and terms of a geometric sequence.
- 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