1. Introduction Algebraic Reasoning

2. Life is about change. Introduction Life can seem chaotic.Sharpen your algebraic skills.Work with patterns of change.

3. There are four components to this course. 1234 Linear Algebra Rules of Algebra Using Technology Patterns of Change

4. Component 1 Patterns in Linear Algebra

5. Component 1 Patterns in Linear Algebra Linear Algebra is used in these fields to show trends and make decisions. 1 Linear Algebra EconomicsSociologyPolitical Science Medicine Multiple Representatio ns

10. Stage Stage NumberNumber of Counters Used 01 13 25 37 49 511 Independent Dependent IndependentDependent Stage NumberNumber of Counters Used 01 13 25 37 49 511 1 Linear Algebra

11. Stage 1 Linear Algebra IndependentDependent Stage NumberNumber of Counters Used 01 13 25 37 49 511 = x = y

12. Stage IndependentDependent Stage NumberNumber of Counters Used 01 13 25 37 49 511 = x = y (x, y) (0, 1) (x, y) (0, 1) Independent = xDependent = y Stage Number Number of Counters Used 01 13 25 37 49 511 0 1 1 Linear Algebra

13. Stage (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) IndependentDependent Stage Number Number of Counters Used 01 13 25 37 49 511 1 Linear Algebra Did you write the ordered pairs like this?

14. Stage (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) IndependentDependent Stage Number Number of Counters Used 01 13 25 37 49 511 1 Linear Algebra Did you write the ordered pairs like this? (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11)

15. (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) 1 Linear Algebra What trend do you see?

18. Independent = xDependent = y Stage NumberNumber of Counters Used 01 13 25 37 49 511 6 7 13 15 1 Linear Algebra

19. Independent = xDependent = y Stage NumberNumber of Counters Used 01 13 25 37 49 511 6 7 13 15 1 Linear Algebra Independent = xDependent = y Stage Number Number of Counters Used 01 13 25 37 49 511 613 715 Your Verbal Description Your Verbal Description Complete the mathematical sentence below. y = ______ Hint Box Y (number of counters used) = ______ Y (number of counters used) = 1 + _______ Y (number of counters used) = 1 + the Stage Number times 2 Hint Box Y (number of counters used) = ______ Y (number of counters used) = 1 + _______ Y (number of counters used) = 1 + the Stage Number times 2 Check your work Check your work

20. Independent = xDependent = y Stage Number Number of Counters Used 01 13 25 37 49 511 613 715 Complete the mathematical sentence below. y = ______ Hint Box Y (number of counters used) = ______ Y (number of counters used) = 1 + _______ Y (number of counters used) = 1 + the Stage Number times 2 Hint Box Y (number of counters used) = ______ Y (number of counters used) = 1 + _______ Y (number of counters used) = 1 + the Stage Number times 2 1 Linear Algebra Your Verbal Description Your Verbal Description y = 1 + 2x

21. Slope Intercept Form The slope will describe the rate of change. The intercept will describe the data when x = 0. The equation that describes the work we have done in this component, written in slope intercept form, is y = 2x + 1. y = 1 + 2x 1 Linear Algebra

22. 1 Relationship between the stage number Number of counters in equation form 1 Linear Algebra A function, like an equation, describes a relationships between sets of data. A function assigns each value of the independent variable (x) to only one value of the dependent variable (y). The function that describes Maria’s work would be f(x) = 2x + 1. If the value of x is 3, the function tells us that f(3) = 2 3 + 1 = 7. Function notation Slope Intercept Form The slope will describe the rate of change The intercept will describe the data when x = 0. The equation that describes the work we have done in this component, written in slope intercept form, is y = 2x + 1.

23. Independent = xDependent = y Stage Number Number of Counters Used 01 13 25 37 49 511 613 715 1 Linear Algebra 1 Your Verbal Description Your Verbal Description f(x) = 2x + 1 Geometric Pattern Table Graph Verbal Descriptio n Algebraic Equation

25. Component 1 This concludes Component 1. 1234 Linear Algebra Rules of Algebra Using Technology Patterns of Change