Algebra for Applications and Problem Solving

Teacher: Michael
Customers Who Have Viewed This Course: 317

What is Algebra for Applications?

1 How is the course organized? 10:10

Modeling Data with Functions

2 Lesson #1 - Defining Data 10:22

3 Lesson #1 - Model Online Student 16:00

4 Lesson #2 - Building the Number System is not so Complex 18:23

5 Lesson #2 - Model Online Student 12:34

6 Lesson #3 - Variables on the Real Number Line 09:03

7 Lesson #3 - Model Online Student 08:41

8 Lesson #4 - Tables and The Coordinate Plane 12:42

9 Lesson #4 -Model Online Student 13:01

10 Lesson #5 - The Algebra of Language or The Language of Algebra 13:08

11 Lesson #5 - Model Online Student 11:45

12 Lesson #6 - How Functions Work 08:18

13 Lesson #6 - Model Online Student 13:22

14 Lesson #7 - Satisfying Relationships 07:58

15 Lesson #7 - Model Online Student 14:09

16 Lesson #8 - Functions are Equations, but Not All Equations are Functional 25:43

17 Lesson #8 - Model Online Student 19:19

18 Lesson #9 - Making Predictions 09:07

19 Lesson #9 - Model Online Student 17:06

20 Lesson #10 - Restrictions Upon Functions 11:37

21 Lesson #10 - Model Online Student 06:13

22 Lesson #11 - Rationalizing the Irrational 18:12

23 Lesson #11 - Model Online Student 13:39

24 Lesson #12 - Manipulating Forms and Formulas 07:54

25 Lesson #12 - Model Online Student 13:37

26 Modeling Data and Functions Exam 00:00

Building Linear Equation Models

27 Lesson #13 - Linearity 09:26

28 Lesson #13 - Model Online Student 15:37

29 Lesson #14 - Linear Changes and Exchanges: Rates, Ratios, and Proportionality 07:52

30 Lesson #14 - Model Online Student 16:33

31 Lesson #15 - A Slippery Slope 07:57

32 Lesson #15 - Model Online Student 08:34

33 Lesson #16 - Slope Analysis 09:12

34 Lesson #16 - Model Online Student 06:22

35 Lesson #17 - A Formula for Slope 10:55

36 Lesson #17 - Model Online Student 09:19

37 Lesson #18 - Intercepts In Sequences: A Good Place to Start 15:23

38 Lesson #18 - Model Online Student 23:52

39 Lesson #19 -Slope-Intercept Form: Linear Fun with Functions 13:01

40 Lesson #19 - Model Online Student 09:07

41 Lesson #20 - Problems with Points and Slopes 12:32

42 Lesson #20 - Model Online Student 24:32

43 Lesson #21 - Farm Animals and Systems of Equations 10:54

44 Lesson #21 - Model Online Student 15:16

45 Lesson #22 - Systems of Linear Equations and The Transitive Property 10:09

46 Lesson #22 Model Online Student 12:43

47 Lesson #23 - Row Operations and Elimintation 14:49

48 Lesson #23 Model Online Student 12:48

49 Lesson #24 - Step Inside the Matrix 16:41

50 Lesson #24 Model Online Student Pt1 16:17

51 Lesson #24 Model Online Student Pt2 09:41

53 Building Linear Equation Models Exam 00:00

Algebra of Geometry: Linear Transformations on a Coordinate Plane

52 Lesson #25 Model Online Student 20:43

54 Lesson #25 - Matrix/Vector Multiplication 17:29

55 Lesson #26 - Distance on the Coordinate Plane 16:14

56 Lesson #26 Model Online Student 19:09

57 Lesson #27 - Lost and Found in Translation 11:12

58 Lesson #27 Model Online Student 11:09

59 Lesson #28 - Reflections upon Reflections 16:01

60 Lesson #28 - Model Online Student 17:34

61 Lesson #29 - Rotations got me Spinning 09:38

62 Lesson #29 - Model Online Student 20:10

63 Lesson #30 - Scaling and Dilation 15:04

64 Lesson #30 - Model Online Student 17:17

65 Lesson #31 - Sequences of Transformations 10:42

66 Lesson #31 - Model Online Student 13:57

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.

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