Learning Objectives
- Identify and extend number patterns
- Recognize patterns in shapes and designs
- Discover patterns in multiplication tables
- Create your own patterns using rules
Key Concepts
Number Patterns
Number patterns follow a rule that tells you what comes next. In the pattern 3, 6, 9, 12, the rule is "add 3". In the pattern 64, 32, 16, 8, the rule is "divide by 2" or "halve". To find the next number, first figure out the rule, then apply it. Sometimes the rule involves two steps, like "add 2, then multiply by 3".
Growing and Shrinking Patterns
A growing pattern gets bigger each time: 1, 3, 5, 7, 9 (add 2 each time). A shrinking pattern gets smaller: 100, 90, 80, 70 (subtract 10 each time). Some patterns grow very fast by multiplying: 2, 4, 8, 16, 32 (multiply by 2 each time). These are called doubling patterns.
Shape Patterns
Shape patterns use a repeating group. For example: star, heart, diamond, star, heart, diamond. The repeating group is "star, heart, diamond", which has 3 shapes. To find the 10th shape, divide 10 by 3. You get 3 groups with 1 left over. The 1st shape in the group is "star", so the 10th shape is a star!
Patterns in Multiplication
Multiplication tables are full of patterns. The 9 times table has a digit-sum pattern: 9, 18, 27, 36 (digits add up to 9). The 11 times table has a double-digit pattern: 11, 22, 33, 44, 55. Even-number tables always give even answers. Odd times odd always gives an odd answer. Finding patterns makes math more fun!
Important Terms
- Pattern: A sequence that follows a fixed rule
- Rule: The instruction that describes how a pattern changes
- Growing Pattern: A pattern where numbers get larger
- Shrinking Pattern: A pattern where numbers get smaller
- Repeating Group: A set of items that repeats in a shape pattern
Quick Revision
- Every pattern follows a rule
- Find the rule first, then predict the next number or shape
- Growing patterns: numbers increase (add or multiply)
- Shrinking patterns: numbers decrease (subtract or divide)
- Multiplication tables contain many useful patterns
- Shape patterns repeat a fixed group of shapes