Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Sum an arithmetic series and find its length
Algebra
CCSS HSA.SSE.B.4England: A-level Pure Mathematics
Objective and success criteria
Students will: Sum an arithmetic series and find its length.
- 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: Use aₙ = a₁ + (n − 1)d for arithmetic sequences
Leads to: Evaluate sums written in sigma notation
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 (Use aₙ = a₁ + (n − 1)d for arithmetic sequences). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- An arithmetic sequence starts −6, 0, 6, … Find the 78th term. → 456Prompt: Find the common difference d.
- In an arithmetic sequence, a₃ = 9 and a₁₂ = −27. Find the common difference d. → -4Prompt: From term 3 to term 12 there are 9 steps of d.
- The sequence 18, 23, 28, … continues with the same difference. Which term is equal to 88? → 15Prompt: Write the nth term formula.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Sum an arithmetic series and find its length. 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: An arithmetic series has 15 terms. The first term is 8 and the last term is 92. Find the sum.
- Step 1: 15 × (8 + 92) ÷ 2 = 750
- Answer: 750
- 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.
- An arithmetic series has 23 terms. The first term is 23 and the last term is −43. Find the sum. → -230Prompt: Sₙ = n(first + last)/2.
- A theatre's first row has 24 seats and each row has 2 more than the row in front. There are 21 rows. How many seats are there altogether? → 924Prompt: Sₙ = n/2 × (2a + (n − 1)d).
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.
- A theatre's first row has 12 seats and each row has 1 more than the row in front. There are 23 rows. How many seats are there altogether? → 529Prompt: Sₙ = n/2 × (2a + (n − 1)d).
- The series 1 + 6 + 11 + … has a sum of 1071. How many terms are there? → 21Prompt: Set n/2 × (2a + (n − 1)d) equal to the sum.
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: Use aₙ = a₁ + (n − 1)d for arithmetic sequences.
- 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: Evaluate sums written in sigma notation.
- 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