Patterns and Inverse

Overview

In this lesson (15 of 20) students build on earlier number and pattern work to recognise simple number patterns and describe the pattern rule using addition and subtraction as inverse operations. Students then apply the inverse relationship to complete and check number sentences.

Learning intentions

• WALT identify simple number patterns.
• WALT describe pattern rules using addition and subtraction.
• WALT use inverse operations (addition/subtraction) to find unknown values in number sentences.
• WALT explain how I know my answer fits the pattern.

Success criteria

• I can continue a number pattern by using a consistent rule.
• I can describe the pattern rule using words (e.g. “add 3”, “subtract 2”).
• I can write and solve a related number sentence using inverse operations.
• I can justify my answer by referring to how it matches the pattern.

Curriculum links

• Algebra — connection between addition and subtraction as inverse operations; apply to find unknown values in number sentences.
• Algebra — partition numbers and use inverse reasoning to support finding unknowns.
• Number — represent and solve using models/strategies that support understanding (counting on, partitioning, diagrams).
• Learning-to-investigate patterns through structured reasoning (recognise and describe patterns as rules).

Lesson structure (60 minutes)

1. 0–5 min · Warm-up (pattern quick start). Teacher displays a 4-term pattern: 6, 9, 12, 15 and asks, “What is changing every time?” Students turn-and-talk, then share the change (add 3).

2. 5–15 min · Direct teaching (inverse pattern thinking). Teacher models two linked patterns on the board:

• Pattern A: 10, 13, 16, 19 (add 3)
• Pattern B: 19, 16, 13, 10 (subtract 3) Teacher says: “If we add 3 to get the next number, we can subtract 3 to get back—addition and subtraction undo each other.” Students copy a simple “undo” statement into books: “+3 and −3 are inverse.”

3. 15–25 min · Guided practice (complete the pattern). Teacher gives three patterns with blanks: a) 7, 10, __, 16, 19 b) 20, __, 16, 13 c) 5, 8, 11, __, 17 Students work in pairs to choose the rule and fill blanks; teacher circulates, prompting: “How do you know this is the next number?” and “Does subtracting undo your adding?”

4. 25–40 min · Main task (number sentences from patterns). Teacher introduces a “pattern to equations” routine:

• Show: Pattern A rule is “add 4”.
• Ask: “If the next term is 15, what was the previous term?” Students complete a worksheet page with three items:
• i) 9, 13, 17, __ → write a matching number sentence (e.g. __ + 4 = 17 or 17 − 4 = __).
• ii) 24, 21, __, 15 → write a number sentence using inverse (subtract 3).
• iii) “Rule: add 2” starting at 14 → fill the missing term and write the related inverse sentence to check it (e.g. 16 − 2 = 14). Teacher expects students to show the connection: pattern rule ↔ an addition/subtraction inverse sentence. (Students may use counting on/back or number lines if needed.)

5. 40–50 min · Share and clarify (explain reasoning). Teacher selects 3–4 student strategies (one correct using addition, one using subtraction/back-check, one with a near miss). Class discusses: “Which inverse sentence proves it?” Teacher records “Good explanations include: rule + inverse check.”

6. 50–58 min · Independent check (teacher-led choice of support). Students complete a short teacher-collected set (on half-sheets):

• Continue: 12, 15, __, 21
• Solve: 18 − __ = 12 (write the subtraction inverse that matches the pattern)
• Write: “To get the next number, I ___ (add/subtract) __.” Teacher uses quick conferencing to verify understanding of inverse relationships.

7. 58–60 min · Exit ticket (1-minute reasoning). Students answer: “My pattern rule is: add 5. The number sentence that checks the inverse is: ___ − 5 = ___.”

Resources

• Pattern cards or slides (with blanks and term lengths of 4–6)
• Worksheet: “Pattern to Equations” (3–4 items)
• Whiteboards or mini slates for pair checking
• Number lines (printed or on board) for counting on/back
• Base-10 materials or counters (optional for students needing concrete support)
• Exit ticket slips
• Pencils, erasers, highlighters

Assessment

• Formative: teacher observes pair work, listens for language that links “add” with “subtract” as undoing.
• Formative: review completed pattern blanks and matching number sentences for correct inverse reasoning.
• Exit ticket: check that students can write an inverse number sentence that matches the stated pattern rule.

Differentiation

• Support:
• Sentence starters: “My pattern rule is ___.” “To check, I do ___ because it is the inverse of ___.”
• Provide a partially completed number sentence template with the operation sign and one number missing.
• Offer a number line for counting on/back for students who struggle with quick recall.
• All students: require both the pattern continuation and an inverse check sentence (not just one).
• Extension (advanced learners):
• Create their own pattern using “add/subtract ___” and include one matching inverse equation to verify (e.g. pattern starts at 9, add 6; include equation “next − 6 = start”).
• Challenge: given a number sentence, generate the pattern (e.g. “13 = 9 + 4” → write the next three terms and the inverse check).
• EAL/SEN considerations:
• Keep pattern lengths consistent (4–5 terms) to reduce working memory load.
• Use clear visual cues (arrows for “next term”) and consistent wording (“undo”, “back”, “inverse”).

Extension (optional)

• SKIP (not requested).