Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Arithmetic and geometric sequences and series
Algebra
CCSS HSF.BF.A.2CCSS HSA.SSE.B.4CCSS HSF.LE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Arithmetic and geometric sequences and series.
- 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: Linear sequences: the nth term; Exponential growth and decay
Leads to: Sigma notation and infinite geometric series
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 (Linear sequences: the nth term; Exponential growth and decay). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the nth term of the sequence −5, 1, 7, 13, … → 6n-11Prompt: The common difference tells you the number in front of n.
- y = 40 × 1.5ˣ. Find y when x = 3. Round to 2 decimal places if needed. → 135Prompt: Work out the power first.
- The nth term of a sequence is −3n − 10. What is the 10th term? → -40Prompt: Substitute n = 10.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Arithmetic and geometric sequences and series. 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 sum of the first 28 terms of the arithmetic series −7 + (−11) + (−15) + …
- Step 1: S = 28/2 × (2 × (−7) + 27 × (−4))
- Step 2: = 14 × (−122) = −1708
- Answer: -1708
- 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 sum of the first 37 terms of the arithmetic series 3 + 9 + 15 + … → 4107Prompt: Sₙ = n/2 × (2a + (n − 1)d).
- A geometric sequence starts 1, 3, 9, … What is the 7th term? → 729Prompt: Find the common ratio r by dividing consecutive terms.
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 sum of the first 7 terms of the geometric series 4 + 12 + 36 + … → 4372Prompt: Sₙ = a(rⁿ − 1)/(r − 1).
- A geometric sequence starts 5, 10, 20, … What is the 4th term? → 40Prompt: Find the common ratio r by dividing consecutive terms.
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: Linear sequences: the nth term.
- 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: Sigma notation and infinite geometric series.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder