Math lesson plan · 12th grade (Year 13 in England) · 30 minutes
Evaluate sums written in sigma notation
Algebra
CCSS HSA.SSE.B.4England: A-level Pure Mathematics
Objective and success criteria
Students will: Evaluate sums written in sigma notation.
- 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: Sum an arithmetic series and find its length; Sum a finite geometric series
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 · 4 min
- Quick retrieval from earlier learning (Sum an arithmetic series and find its length; Sum a finite geometric series). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- An arithmetic series has 38 terms. The first term is 14 and the last term is −23. Find the sum. → -171Prompt: Sₙ = n(first + last)/2.
- Find the sum of the first 5 terms of 2 + 4 + 8 + … → 62Prompt: Sₙ = a(rⁿ − 1)/(r − 1).
- A theatre's first row has 17 seats and each row has 4 more than the row in front. There are 10 rows. How many seats are there altogether? → 350Prompt: Sₙ = n/2 × (2a + (n − 1)d).
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Evaluate sums written in sigma notation. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Evaluate Σ (from r = 1 to 11) of (−2r + 2).
- Step 1: first = 0, last = −20
- Step 2: 11(0 + (−20))/2 = −110
- Answer: -110
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Evaluate Σ (from r = 1 to 8) of (3r + 5). → 148Prompt: Write out the first few terms: it's an arithmetic series.
- Evaluate Σ (from r = 1 to 6) of 3^r. → 1092Prompt: The terms are 3, 9, 27, …: geometric.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Evaluate Σ (from r = 1 to 6) of 3^r. → 1092Prompt: The terms are 3, 9, 27, …: geometric.
- Evaluate Σ (from r = 1 to 7) of r². → 140Prompt: Write out each square and add them.
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: Sum an arithmetic series and find its length.
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder