Extending Number Patterns

Grade: 5

Duration: 45 minutes

Class Size: 6 students

Unit: Patterns in Numbers

Lesson 2 of 5

Topic: Extending Patterns: Finding the Next Terms

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Learning Standards

This lesson aligns with the Common Core State Standards (CCSS) for Mathematics:

• CCSS.MATH.CONTENT.5.OA.B.3
  Identify patterns in arithmetic sequences and explain them using properties of operations (addition and subtraction).

• CCSS.MATH.PRACTICE.MP1
  Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP3
  Construct viable arguments and critique the reasoning of others.

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Learning Objectives ("I can" statements)

• I can identify a number pattern and find the next terms using addition or subtraction.
• I can explain how I extended the pattern using math words.
• I can create a number pattern for my classmates to solve.

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Success Criteria

• I correctly extend number patterns by finding the next 2–3 terms.
• I use addition or subtraction accurately to find missing numbers.
• I communicate my thinking clearly to my partner.
• I design a number pattern that follows a rule for others to solve.

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Materials Needed

• Whiteboard and markers
• Pattern cards (pre-prepared sequences missing last terms)
• Individual student whiteboards or notebooks
• Pencil and eraser
• Pair worksheet for creating and solving patterns
• Visual aids showing number patterns (sequence charts)

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Lesson Sequence

1. Introduction (5 minutes)

• Engage students with a quick warm-up: display a simple pattern on the board (e.g., 2, 4, 6, __, __).
• Ask: "What comes next? How did you find your answer?"
• State today’s goal using "I can" statements on the board.

2. Direct Instruction (10 minutes)

• Review the concept of patterns and sequences from the previous lesson.
• Show examples of extending addition and subtraction patterns:
  • Addition example: 3, 6, 9, __, __ (adding 3 each time)
  • Subtraction example: 20, 18, 16, __, __ (subtracting 2 each time)
• Use clear vocabulary: term, rule, sequence, extend.
• Model step-by-step how to find the next terms by adding or subtracting the same number. Write process out loud.
• Introduce the idea of “rule” as what happens between terms.

3. Guided Practice (10 minutes)

• Hand out pattern cards with sequences missing last terms to each student (one per student).
• In pairs, students take turns finding missing terms.
• Encourage them to say their thinking aloud and write it on their whiteboards.
• Teacher circulates, asking questions:
  • “What is the rule of this pattern?”
  • “How do you know what number to add or subtract?”
• Use positive reinforcement for clear reasoning and correct computation.

4. Independent Practice: Creating Patterns (10 minutes)

• Each pair creates their own number pattern with a clear addition or subtraction rule.
• Students write the first several terms and leave the last two blank for classmates to solve.
• Pairs swap their patterns with another pair and try to extend the sequence accurately.
• Encourage pairs to explain their reasoning to each other after solving.

5. Reflection and Assessment (8 minutes)

• Whole group discussion: each pair shares one pattern they made and how others solved it.
• Ask: "How did knowing the rule help you find the next terms?"
• Confirm learning with a quick verbal quiz: ask students to extend a pattern shown on the board.

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Differentiation Strategies

• For students needing support:

  • Provide patterned number lines or visual aids to help “see” the patterns.
  • Offer patterns with smaller differences (e.g., +1, -1) and fewer missing terms.
  • Pair with a peer tutor or guided support during practice.

• For advanced learners:

  • Challenge to create more complex patterns with different operations (e.g., alternating addition and subtraction).
  • Introduce doubling or halving sequences or repetition patterns (skip counting).
  • Ask them to create word problems based on their patterns.

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Extension Activity (Optional)

• Introduce a pattern with a missing operation, e.g., 2, 4, 8, 16, __, __.
• Ask students to hypothesize the rule (multiplying by 2), then predict the next terms.
• Discuss how patterns can involve different operations, encouraging curiosity about future lessons.

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Teacher Reflection Notes

• Observe if students can articulate the "rule" of the pattern in their own words.
• Take note of pairs that excel or struggle to plan targeted support next lesson.
• Adjust extension tasks depending on student interest and capability.

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This detailed, engaging lesson plan meets the Common Core framework by promoting understanding and application of patterns in arithmetic sequences through collaboration, reasoning, and hands-on practice tailored to 5th grade students’ readiness.