# Algebra For Problem Solving

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Teacher: Michael
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#### 67 Linear Transformations Exam 00:00

Algebra for Applications and Problem Solving

Course Overview:  Often the Algebra we learn is devoid of context. We will look at Algebra through the lens of how we apply it in the real world.  We will explore pure elementary algebra in the context of its practice.  At the end of this course students should have an inventory of problem solving strategies.  This course covers and goes beyond standards from the Common Core Integrated Math pathway.

Target Audience:

This course is primarily intended for students curious about for what they are ever going to use high school Algebra.  The course is intended for both students whose strengths and interests are in STEM fields or students whose strengths are in verbal reasoning.  Any student looking for relevance in many of the topics of a traditional Algebra 1 course should take Algebra for Applications and Problem Solving.

This course includes:

• 3 Major Units - Modeling Data and Functions, Building Linear Equation Models, The Algebra of Geometry: Linear Transformations
• 31 Lessons
• 31 Assignments - including Guided Notes and Exercises/Problems
• 31 Model Student Videos - including step-by-step answers to exercises, additional web resources (manipulatives, instructions for how to use free graphing software, additional challenges, etc.)
• 31 Lesson Quizzes
• 3 Unit Exams
• Important Course Terminology
• Approximately 15 hours of Instructional and Support Videos

Course Goals:

Upon completion of this course, students should be able to-

• Use Venn diagrams to analyze concepts
• Visualize data from patterns
• Solve real world problems involving rates, ratios, and proportions - food, money, travel, etc.
• Model numerical data with linear equations and functions
• Solve systems of equations with 2 variables and 2 unknowns
• Scale and transform geometric objects using matrix operations
• Give examples of where they can apply math to their current lives and future career paths

Course Requirements/Prerequisite Skills:

Students taking this course will need to be able to do -

• Use Order of Operations
• Use Operations upon + and - numbers
• Use Operations upon fractions (add, subtract, multiply, divide)
• Have had an introduction to equation solving strategies
• Have knowledge of how to evaluate exponents computationally- e.g. 23 =2*2*2
• Be ready to learn some of the most interesting and thought provoking applications of Algebraic Thinking they've ever seen

Learning Outcomes:

 Unit 1:  Modeling Data and Functions To differentiate between quantitative and qualitative data sets To analyze qualitative data sets using Venn diagrams To analyze univariate quantitative data sets To analyze bivariate quantitative data sets using a table and a coordinate plane To write relations in mathematical notation or to put patterns into mathematical notation To identify when tables of data from a pattern or relation are functions To determine if a data point satisfies an equation or inequality in the context of a relation To compare relations that are functions to those that are not functions To make a prediction using a function generated by data To understand how restricting the from which subset of the real numbers our data comes can produce a function To determine if a solving for parameter of a formula produces a function of another parameter. Unit 2:  Building Linear Equation Models To use the data collecting methods to compare linear data to non-linear data To define rates as linear relationships To define an algebraic sequence as a linear function with a domain restricted to the natural numbers To define the slope as ratio of the change in dependent variable to the change in independent variable To analyze the slope as a ratio of two mutually exclusive parameters To derive a formula for determining the slope between any two points on a coordinate plane To discuss the significance of the point a function intercepts an axis on a coordinate plane in the context of a problem To discuss the significance of a the slope between any two points in the context of the problem To analyze the slope intercept form of a linear function as an abstract object To derive slope intercept form a line, when you are given the rate of change and a point on the line To define a linear equation as an abstract object To define a 2x2 system of equations and its solution To solve a 2x2 system of equations using the transitive property To solve a 2x2 system of equations using row operations To define a 2x2 system of equations a matrix equation Unit 3:  The Algebra of Geometry: Linear Transformations To define two types of metrics on the coordinate plane To define matrix vector multiplication To define a translation on a coordinate plane To define a reflection on a coordinate plane To define similarity on a coordinate plane To define matrix matrix multiplication To define matrix transformations as functions To define scaling To define a sequence of transformations as a composition of linear transformations

• Teacher: Michael
• Areas of expertise: Differentiated Education, Special Education, Developmental Mathematics, Application and Problem Solving
• Education: BA - German Culture and Langauge: The Ohio State University BA - Mathematics Education: Otterbein University State of California Teaching Credential MS - Applied Mathematics: Califonria State University, Los Angeles
• Interests: Algebraic Graph Theory, Social Networks, Cooking, Hiking, Travel, Photography, Video Editing, Television and Film, Exercise, Fitness, and Nutrition
• Skills: Logic and Empathy
• Associations: NCTM Member AMATYC Member
• Issues I care about: Health, Fitness, and Nutrition Mental Health

I care about my students' education. I believe that learning should make your brain hurt. I believe that all students can learn. I believe that a quality mathematics education is enriching for all students.