Patterns

2, 4, 6, 8, … 1, 3, 5, 7, 9, … • Geometrical • Numerical

Where can you find patterns? music investments sleep habits nature

From pictures or physical models we can sometimes find both numerical and geometrical patterns.

Understanding a pattern can help us: • extend the pattern • create new patterns

MODELS Numerical Algebraic Graphical Mathematicians … look for patterns find patterns in physical or pictorial models look for ways to create different models for patterns use mathematical models to solve problems Numerical Algebraic Graphical

Number Patterns 2 2 + 2 2 + 2 + 2 2 + 2 + 2 + 2 1 2 3 4 n? 2 1(2) 4 Term Number Term Expression 2 2 + 2 2 + 2 + 2 2 + 2 + 2 + 2 1 2 3 4 n? 2 1(2) 4 2(2) 6 3(2) 8 4(2) __(2) n

Number Patterns 1 2 3 4 n? 3(5) + 4 19 4(5) + 4 24 5(5) + 4 29 34 Term Number Term Expression How does the different part relate to the term number? What’s the same? What’s different? 1 2 3 4 n? 3(5) + 4 19 4(5) + 4 24 5(5) + 4 29 34 6(5) + 4 (n + 2) _____(5) + 4

Number Patterns 3 - 2(0) 1 2 3 4 n? 3 3 - 2(1) 1 3 - 2(2) -1 3 - 2(3) Term Number Term Expression How does the different part relate to the term number? What’s the same? What’s different? 3 - 2(0) 1 2 3 4 n? 3 3 - 2(1) 1 3 - 2(2) -1 3 - 2(3) -3 3 - 2(____) n - 1

Number Patterns 1 2 3 4 n? 4 22 16 42 36 62 64 82 (___)2 2n Term Number Term Expression How does the different part relate to the term number? What’s the same? What’s different? 1 2 3 4 n? 4 22 16 42 36 62 64 82 (___)2 2n