Download More Possible Mathematical Models

How do you analyze
and figure out what
does not fit?
Apply the Design Process
• 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
How does
ACE-M
support your
problem
solving?
C. Process Re-visited:
ACE-M
Questions
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
throughout
E: ExecuteSolve/Build.
C: Planconnections between given, want, know &
figure out questions that need to be answered and
constraints that might apply
Write convincing justification using logical mathematical
reasoning that answers the “want” question/prompt
POST IT
What is your favorite sport?
Why?
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.
What question comes to mind?
The Infamous El Segundo
Baseball problem
Approach
Approach
Independently
Create 2 Plans that
might work
Compare plans by
communicating with
partner
The Longest Home Runs in the History
of Major League Baseball
How does the information inform your plan?
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
B. Visual
Multiplication can only occur if
the number of columns in the first
matrix equals the number of rows
in the second matrix
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
Matrix Multiplication
Inverse Matrices
Identity Matrix
ScalarofMultiplication
Addition or Subtraction
Multiply each entry in the matrix
matrices is only defined when
by the scalar value outside of the
Matrix Addition
both matrices have the same
dimensions.
Add or Subtract values in
corresponding positions
matrix
B. Visual
Matrix Multiplication
Inverse Matrices
Identity Matrix
Scalar Multiplication
Matrix Addition
B. Visual
B. Visual
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
C. Process
Solve the Matrix Equation
1 2   x  4
3  5   y   1

    
C. Process
Solve the Matrix Equation
1 2   x  4
3  5   y   1

    
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
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
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
• 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
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.
Goals
Recall & Reproduction
Routine
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?
D. Purpose
1. Solving Systems of Equations
How can matrices find the path of
Pagan’s ball?
D. Our purpose: Solve ESHS Infamous
Baseball Problem
Show how to use matrices to find equation of a
quadratic
Find the equation that
models the path of the
diver.
Why care?
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.
II. Solving Quadratic Functions