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Math lesson plan · 5th grade (Year 6 in England) · 45 minutes

Compare two number patterns and their rules

Algebra

CCSS 5.OA.B.3England: Y6 Algebra

Objective and success criteria

Students will: Compare two number patterns and their rules.

  • 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

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). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A pattern starts at 14 and the rule is "add 8". What is the 8th number in the pattern? → 70Prompt: From the 1st to the 8th number there are 7 jumps.
  2. Rule: start at 1, add 6. The pattern is 1, 7, 13, 19, 25, … 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 (6) do to an odd number?
  3. A pattern starts at 3 and adds 7 each time. Will 49 be in the pattern? (yes / no) → noPrompt: Subtract the start: is 49 − 3 a multiple of 7?

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Compare two number patterns and their rules. 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: Pattern A starts at 0 and adds 3: 0, 3, 6, 9, 12, 15. Pattern B starts at 0 and adds 12: 0, 12, 24, 36, 48, 60. Each term in B is how many times the matching term in A?
  • Step 1: 36 ÷ 9 = 4
  • Step 2: 4
  • Answer: 4
  • 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. Pattern A starts at 0 and adds 5: 0, 5, 10, 15, 20, 25. Pattern B starts at 0 and adds 15: 0, 15, 30, 45, 60, 75. Each term in B is how many times the matching term in A? → 3Prompt: Compare matching terms, e.g. the 2nd terms.
  2. Pattern A starts at 0 and adds 4: 0, 4, 8, 12, 16, 20. Pattern B starts at 0 and adds 8: 0, 8, 16, 24, 32, 40. Each term in B is how many times the matching term in A? → 2Prompt: Compare matching terms, e.g. the 2nd terms.

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. Pattern A starts at 0 and adds 2: 0, 2, 4, 6, 8, 10. Pattern B starts at 0 and adds 8: 0, 8, 16, 24, 32, 40. Each term in B is how many times the matching term in A? → 4Prompt: Compare matching terms, e.g. the 2nd terms.
  2. Pattern A starts at 0 and adds 5: 0, 5, 10, 15, 20, 25. Pattern B starts at 0 and adds 15: 0, 15, 30, 45, 60, 75. Each term in B is how many times the matching term in A? → 3Prompt: Compare matching terms, e.g. the 2nd terms.

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

eurekami

Compare two number patterns and their rules

Name

Date

Score/ 8

  1. Question 1

    Pattern X: start at 0, add 2. Pattern Y: start at 0, add 8. Make ordered pairs (X, Y) from matching terms. What is the 5th pair? Write it like (4, 12).

    xy61218243012243648607284961081200(0, 0)(2, 8)(4, 16)

    Answer

  2. Question 2

    Pattern A starts at 0 and adds 5: 0, 5, 10, 15, 20, 25. Pattern B starts at 0 and adds 20: 0, 20, 40, 60, 80, 100. Each term in B is how many times the matching term in A?

    Answer

  3. Question 3

    Pattern X: start at 0, add 5. Pattern Y: start at 0, add 15. Make ordered pairs (X, Y) from matching terms. What is the 6th pair? Write it like (4, 12).

    xy61218243012243648607284961081200(0, 0)(5, 15)(10, 30)

    Answer

  4. Question 4

    Pattern A starts at 0 and adds 3: 0, 3, 6, 9, 12, 15. Pattern B starts at 0 and adds 9: 0, 9, 18, 27, 36, 45. Each term in B is how many times the matching term in A?

    Answer

  5. Question 5

    Pattern X: start at 0, add 3. Pattern Y: start at 0, add 9. Make ordered pairs (X, Y) from matching terms. What is the 3rd pair? Write it like (4, 12).

    xy61218243012243648607284961081200(0, 0)(3, 9)(6, 18)

    Answer

  6. Question 6

    Pattern X: start at 0, add 2. Pattern Y: start at 0, add 4. Make ordered pairs (X, Y) from matching terms. What is the 6th pair? Write it like (4, 12).

    xy61218243012243648607284961081200(0, 0)(2, 4)(4, 8)

    Answer

  7. Question 7

    Pattern A starts at 0 and adds 5: 0, 5, 10, 15, 20, 25. Pattern B starts at 0 and adds 10: 0, 10, 20, 30, 40, 50. Each term in B is how many times the matching term in A?

    Answer

  8. Question 8

    Pattern X: start at 0, add 3. Pattern Y: start at 0, add 6. Make ordered pairs (X, Y) from matching terms. What is the 6th pair? Write it like (4, 12).

    xy61218243012243648607284961081200(0, 0)(3, 6)(6, 12)

    Answer

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Answer key: Compare two number patterns and their rules

  1. 1. (8, 32)

  2. 2. 4

  3. 3. (25, 75)

  4. 4. 3

  5. 5. (6, 18)

  6. 6. (10, 20)

  7. 7. 2

  8. 8. (15, 30)