Mathematicians look for patterns in various contexts such as music, investments, nature, and physical models. They analyze patterns to extend them, create new patterns, and use mathematical models to solve problems. The document then provides examples of number patterns and questions to help understand the relationship between the term number and term expression in different patterns.

1. Patterns

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

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

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

8. Number Patterns 4(5) + 14 3(5) + 14 2(5) + 14 1(5) + 14 1 2 3 4 n? ____X_(5) + 14 (n) How does the different part relate to the term number? What’s the same? What’s different? 19 24 29 34 Term Number Term Expression

9. Number Patterns -2(4)+5 -2(3)+5 -2(2)+5 -2(1)+5 1 2 3 4 n? (____)+5 How does the different part relate to the term number? What’s the same? What’s different? 3 1 -1 -3 Term Number Term Expression

10. Number Patterns 8 2 6 2 4 2 2 2 1 2 3 4 n? (___) 2 2n How does the different part relate to the term number? What’s the same? What’s different? 4 16 36 64 Term Number Term Expression