1. How do you analyze and figure out what does not fit?

2. Apply the Design Process How does ACE-M support your problem solving? Build the tallest tower possible that will support the weight of a tennis ball. Write a justification for why a company should purchase your tower

3. C. Process Re-visited: ACE-M A: Approach  diagram the givens, define the unknowns/variables, define the “want”, jot down what I know (3 pieces of information) and what I want to know C: Plan  connections between given, want, know & figure out questions that need to be answered and constraints that might apply E: Execute  Solve/Build. Write convincing justification using logical mathematical reasoning that answers the “want” question/prompt A: Approach  diagram the givens, define the unknowns/variables, define the “want”, jot down what I know (3 pieces of information) and what I want to know C: Plan  connections between given, want, know & figure out questions that need to be answered and constraints that might apply E: Execute  Solve/Build. Write convincing justification using logical mathematical reasoning that answers the “want” question/prompt Questions throughout

4. POST IT What is your favorite sport? Why?

5. Unit 3: Mathematical Modeling Concept Category: Matrices LT 3A I can use matrices to represent a quadratic. I can use inverse matrices to solve a system of linear equations. I can find solutions to quadratic equations and explain the relevance of the solutions both in a context (applied) and out of a context (theoretical). LT 3B I can multiply matrices by scalars to produce new matrices. I can add, subtract, and multiply matrices of appropriate dimensions. I can explain why matrix multiplication for square matrices is not commutative but is associative and distributive. I can explain the role of a zero matrix and identity matrix in matrix addition and multiplication and how each is similar to the role of one in the real numbers.

6. What question comes to mind?

7. The Infamous El Segundo Baseball problem Approach Independently Create 2 Plans that might work Compare plans by communicating with partner Approach Create Plans

8. The Longest Home Runs in the History of Major League Baseball How does the information inform your plan?

9. I Matrices A.Definition: A matrix is a two dimensional array of numbers or expressions arranged in a set of rows and columns Dimensions are stated m x n

10. B. Visual Matrix Multiplication Inverse Matrices Identity Matrix Scalar Multiplication Matrix Addition Multiplication can only occur if the number of columns in the first matrix equals the number of rows in the second matrix Multiply each entry in the matrix by the scalar value outside of the matrix Addition or Subtraction of matrices is only defined when both matrices have the same dimensions. Add or Subtract values in corresponding positions Addition or Subtraction of matrices is only defined when both matrices have the same dimensions. Add or Subtract values in corresponding positions Multiplying a matrix by it’s inverse gives you the Identity Matrix. To find the inverse of a matrix you need to find the Determinant…if the Determinant is 0 then the matrix has no inverse Multiplying a matrix by it’s inverse gives you the Identity Matrix. To find the inverse of a matrix you need to find the Determinant…if the Determinant is 0 then the matrix has no inverse

11. B. Visual Matrix Multiplication Inverse Matrices Identity Matrix Scalar Multiplication Matrix Addition

12. B. Visual

14. C. Elementary Matrix Arithmetic 1.Matrix addition: operation of addition of 2 matrices is only defined when both have the same dimension 2.Multiplication by a scalar 3.Matrix Multiplication (not commutative) 4.Inverse Matrix

15. C. Process Solve the Matrix Equation

16. C. Process Solve the Matrix Equation

18. C. Elementary Matrix Arithmetic 1.Matrix addition: operation of addition of 2 matrices is only defined when both have the same dimension 2.Multiplication by a scalar 3.Matrix Multiplication (not commutative) 4.Inverse Matrix

19. Concept Check Supplies needed: Something to write with Paper to write on (and keep) Purpose: to check our understanding of the concepts surrounding the procedures

20. Concept Check Describe in detail the restrictions related to each of the following operations. 1.Matrix addition 2.Multiplication by a scalar 3.Matrix Multiplication 4.Inverse Matrix

21. Matrix addition (Commutative) – Matrices must have the exact same dimensions Multiplication by a scalar (Commutative) – No restrictions. Commutative Matrix Multiplication (not commutative) – Columns of left matrix must match rows of right matrix. Inverse Matrix – Determinant must exists – Inverse Matrix must multiply from the left

22. Goals Recall & Reproduction A. B. Use the given matrices to find -8C + 3A C. Find the product of the given matrices D. Solve for the unknown variables.

23. Goals Recall & Reproduction Routine

24. Active Practice Insights 1.Do I know the purpose for learning this information? 2.Do I know anything about this topic? 3.Do I know strategies that will help me learn? 4.Am I understanding as I proceed? 5.How should I correct errors? 6.Have I accomplished the goals I set myself? How do I know?

25. D. Purpose 1. Solving Systems of Equations

26. How can matrices find the path of Pagan’s ball?

27. D. Our purpose: Solve ESHS Infamous Baseball Problem Show how to use matrices to find equation of a quadratic

28. Find the equation that models the path of the diver. Why care?

29. Concept Category: Matrices LT 3C Categorize problems as quadratic-type and then apply tools to solve quadratic equations. I can solve applications involving linear and non-linear systems and explain the constraints LT 3D I can find the mathematical model that describes the vertical displacement for projectile motion.

30. II. Solving Quadratic Functions