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Math lesson plan · 4th grade (Year 5 in England) · 45 minutes

Generate a pattern from a rule and predict later terms

Algebra

CCSS 4.OA.C.5England: Y5 Number and place value

Objective and success criteria

Students will: Generate a pattern from a rule and predict later terms.

  • 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: Find the rule of a number pattern

Leads to: Compare two number patterns and their rules; Describe linear sequences with a rule for the nth term

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 (Find the rule of a number pattern). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. What is the rule? 25, 50, 75, 100, 125, … (multiply by 25 / add 26 / add 25 / subtract 25) → add 25Prompt: Find the difference between neighbouring numbers.
  2. The rule is "add 9". One number is wrong: 3, 12, 21, 32, 39. What should it be? → 30Prompt: Check each jump: is it exactly 9?
  3. Look at the 4 times table: 4, 8, 12, 16, 20, … Are all the answers odd, all even, or a mix? (all even / all odd / a mix) → all evenPrompt: Is 4 odd or even?

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Generate a pattern from a rule and predict later terms. 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: A pattern starts at 18 and the rule is "add 9". What is the 7th number in the pattern?
  • Step 1: 18 + 6 × 9 = 72
  • Answer: 72
  • 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.
  1. A pattern starts at 10 and the rule is "add 10". What is the 9th number in the pattern? → 90Prompt: From the 1st to the 9th number there are 8 jumps.
  2. Rule: start at 7, add 2. The pattern is 7, 9, 11, 13, 15, … 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?

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.
  1. 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?
  2. A pattern starts at 15 and adds 8 each time. Will 71 be in the pattern? (yes / no) → yesPrompt: Subtract the start: is 71 − 15 a multiple of 8?

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: Find the rule of a number pattern.
  • 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: Compare two number patterns and their rules; Describe linear sequences with a rule for the nth term.
  • 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-4.

Free lesson plan from eurekami.com/lesson-plan-builder

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Generate a pattern from a rule and predict later terms

Name

Date

Score/ 8

  1. Question 1

    Rule: start at 1, add 10. The pattern is 1, 11, 21, 31, 41, … Will the numbers always be odd, always even, or alternate?

    • A. always odd
    • B. always even
    • C. alternate

  2. Question 2

    A pattern starts at 6 and adds 6 each time. Will 78 be in the pattern?

    • A. yes
    • B. no

  3. Question 3

    A pattern starts at 7 and the rule is "add 4". What is the 7th number in the pattern?

    Answer

  4. Question 4

    Rule: start at 3, add 6. The pattern is 3, 9, 15, 21, 27, … Will the numbers always be odd, always even, or alternate?

    • A. always odd
    • B. always even
    • C. alternate

  5. Question 5

    A pattern starts at 15 and adds 3 each time. Will 53 be in the pattern?

    • A. yes
    • B. no

  6. Question 6

    A pattern starts at 11 and the rule is "add 5". What is the 8th number in the pattern?

    Answer

  7. Question 7

    Rule: start at 1, add 6. The pattern is 1, 7, 13, 19, 25, … Will the numbers always be odd, always even, or alternate?

    • A. always odd
    • B. always even
    • C. alternate

  8. Question 8

    A pattern starts at 3 and adds 4 each time. Will 65 be in the pattern?

    • A. yes
    • B. no

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Answer key: Generate a pattern from a rule and predict later terms

  1. 1. A. always odd

  2. 2. A. yes

  3. 3. 31

  4. 4. A. always odd

  5. 5. B. no

  6. 6. 46

  7. 7. A. always odd

  8. 8. B. no