🔵Growing Patterns
A pattern is a sequence that follows a rule. In a growing pattern, each term is larger than the one before it.
- Add patterns: 5, 10, 15, 20, 25 — Rule: +5 each time
- Multiply patterns: 2, 4, 8, 16, 32 — Rule: ×2 each time
To find the rule: check what you add or multiply to get from one term to the next. Then use that rule to find the missing term.
Steps to extend a growing pattern:
- Look at two consecutive terms
- Find the difference (for add) or ratio (for multiply)
- Check it works for the next pair too
- Apply the rule to find the next term
👀 See a worked example
🤖 Vidi's Key Points
- A growing pattern gets larger with each term
- Add patterns: find the difference between consecutive terms
- Multiply patterns: find what you multiply each term by
- Always check your rule works for at least two pairs of terms
🟢Shrinking Patterns
In a shrinking pattern, each term is smaller than the one before it. The sequence is going down.
- Subtract patterns: 40, 35, 30, 25 — Rule: -5 each time
- Divide patterns: 64, 32, 16, 8 — Rule: ÷2 each time
Some patterns have a changing difference — this makes them trickier.
Example: 55, 50, 44, 37, 29 — differences are -5, -6, -7, -8 — so the next difference is -9, making the next term 29 - 9 = 20.
Always check if the difference is constant (same) or changing (increasing or decreasing).
👀 See a worked example
🤖 Vidi's Key Points
- A shrinking pattern gets smaller with each term
- Subtract patterns: find the constant difference being subtracted
- Divide patterns: find what you divide each term by
- Some patterns have a changing difference — check if the gap increases or decreases
🟣Input-Output Tables and Rules
An input-output table shows pairs of numbers connected by a rule — like a machine that transforms the input into the output.
The rule can be:
- Add or subtract: Input 3 → Output 8 (Rule: +5)
- Multiply or divide: Input 4 → Output 12 (Rule: ×3)
- Two-step rule: Input 2 → Output 5 (Rule: ×2+1)
How to find the rule:
- Look at the first input-output pair
- Try simple operations (+, -, ×, ÷)
- Test your rule on at least two more pairs
- If it works for all pairs, you have the rule
Once you know the rule, you can find any output for any input.
👀 See a worked example
🤖 Vidi's Key Points
- An input-output table shows how inputs are transformed by a rule
- Test your rule on ALL given pairs before finalising it
- Rules can be one-step (x3) or two-step (x2+1)
- Squaring means multiplying a number by itself: 4x4=16
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