Math lesson plan · 5th grade (Year 6 in England) · 45 minutes
Describe linear sequences with a rule for the nth term
Algebra
CCSS 6.EE.A.2England: Y6 Algebra
Objective and success criteria
Students will: Describe linear sequences with a rule for 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: Generate a pattern from a rule and predict later terms; Use simple formulas written in words and letters
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 · 5 min
- Quick retrieval from earlier learning (Generate a pattern from a rule and predict later terms; Use simple formulas written in words and letters). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A pattern starts at 11 and the rule is "add 3". What is the 9th number in the pattern? → 35Prompt: From the 1st to the 9th number there are 8 jumps.
- Bike hire costs C = 6h + 20, where h is the number of hours. What is C when h = 8? → 68Prompt: 6h means 6 × h.
- Rule: start at 5, add 2. The pattern is 5, 7, 9, 11, 13, … Will the numbers always be odd, always even, or alternate? (always odd / always even / alternate) → always oddPrompt: The start is odd. What does adding an even number (2) do to an odd number?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Describe linear sequences with a rule for 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: The nth term of a sequence is 2n − 3. What is the 43rd term?
- Step 1: 2 × 43 − 3 = 83
- Answer: 83
- 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.
- The nth term of a sequence is 7n + 1. What is the 10th term? → 71Prompt: Replace n with 10.
- Which rule gives the sequence 7, 11, 15, 19, 23, …? (5n + 3 / n + 4 / 4n + 3 / 5n + 2) → 4n + 3Prompt: The difference between terms tells you the number in front of n.
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.
- Which rule gives the sequence 4, 7, 10, 13, 16, …? (4n + 1 / n + 3 / 3n + 1 / 4n) → 3n + 1Prompt: The difference between terms tells you the number in front of n.
- The nth term of a sequence is 4n + 9. What is the 19th term? → 85Prompt: Replace n with 19.
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: Generate a pattern from a rule and predict later terms.
- 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-5.
Free lesson plan from eurekami.com/lesson-plan-builder