Growing Patterns
Growing patterns appear everywhere in mathematics, from the 2, 4, 6, 8 sequence students learn in grade 2 to the complex square number patterns like 1, 4, 9, 16, 25 they encounter later. Norwegian curriculum standard LK20 for grade 4 emphasizes pattern recognition as a foundation for algebraic thinking.
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Why it matters
Growing patterns prepare students for algebra by teaching them to recognize relationships between numbers and predict future values. In real life, students use pattern thinking to calculate savings growth (saving $5 weekly creates the pattern 5, 10, 15, 20), understand seating arrangements at events (tables for 4 create the pattern 4, 8, 12, 16 for multiple tables), and solve scheduling problems. Construction workers use patterns when calculating materials needed for steps or terraced gardens. Even simple chores like stacking dishes follow patterns where each shelf holds 6 plates, creating 6, 12, 18, 24. These mathematical thinking skills transfer to science concepts like plant growth rates and physics formulas, making pattern recognition essential for STEM success.
How to solve growing patterns
Pattern Structures
- A pattern has a rule. Find what stays the same and what changes.
- Describe the rule in words first, then in symbols or numbers.
- Test the rule on the next term: does it predict correctly?
- Extend the pattern both forwards and backwards to check.
Example: 1, 4, 9, 16, ... The rule is square the position: 1², 2², 3², 4². Next: 5² = 25.
Worked examples
What comes next? 2, 4, 6, 8, ?
Answer: 10
- Find the difference between consecutive terms → 4 - 2 = 2 — Each number increases by 2.
- Add the difference to the last term → 8 + 2 = 10 — The next number is 8 + 2 = 10.
What comes next? 4, 9, 16, 25, ?
Answer: 36
- Check if these are perfect squares → 2²=4, 3²=9, 4²=16, 5²=25 — Each number is a perfect square: 2², 3², 4², 5².
- Find the next square → 6² = 36 — The next square is 6² = 36.
What comes next? 4, 8, 6, 10, 8, 12, ?
Answer: 10
- Look at the pattern of changes → +4, -2, +4, -2, ... — The pattern alternates: add 4, subtract 2, add 4, subtract 2, ...
- Apply the next operation → 12 -2 = 10 — The next step is -2, so 12 -2 = 10.
Common mistakes
- ✗Students assume all patterns increase by the same amount, writing 2, 4, 8, 16 continues as 32 when it should be 20 (mistaking doubling for adding 4)
- ✗They confuse position with value in square patterns, writing 1, 4, 9, 16 continues as 20 instead of 25 (adding 4 instead of calculating 5²)
- ✗Students miss alternating operations, continuing 5, 8, 6, 9, 7 as 10 instead of 12 (not recognizing the +3, -2 pattern)
- ✗They apply rules incorrectly backward, writing that 3, 6, 9 starts with 1 instead of 0 when extending left
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