Math lesson plan · 11th grade (Year 12 in England) · 60 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 · 6 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 20, 25, 30, … Find the 26th term. → 145Prompt: Find the common difference d.
- In an arithmetic sequence, a₂ = −9 and a₁₂ = 51. Find the first term a₁. → -15Prompt: From term 2 to term 12 there are 10 steps of d.
- The sequence 8, 7, 6, … continues with the same difference. Which term is equal to −43? → 52Prompt: Write the nth term formula.
Hook · 6 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 · 12 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 · 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.
- An arithmetic series has 12 terms. The first term is 22 and the last term is 0. Find the sum. → 132Prompt: Sₙ = n(first + last)/2.
- A theatre's first row has 13 seats and each row has 1 more than the row in front. There are 14 rows. How many seats are there altogether? → 273Prompt: Sₙ = n/2 × (2a + (n − 1)d).
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.
- The series 3 + 8 + 13 + … has a sum of 207. How many terms are there? → 9Prompt: Set n/2 × (2a + (n − 1)d) equal to the sum.
- A theatre's first row has 25 seats and each row has 3 more than the row in front. There are 22 rows. How many seats are there altogether? → 1243Prompt: Sₙ = n/2 × (2a + (n − 1)d).
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