MATH 099 (Elementary Algebra)

Tim Brzezinski, Oct 19, 2016

Contains interactive Elementary Algebra applets that can be used for discovery learning, meaningful remediation, differentiation, and formative assessment.

Table of Contents

  1. Geometry and Numbers
    1. Parallelogram: Area
    2. Area of a Triangle (Discovery)
    3. Trapezoid: Area (I)
    4. TRUE MEANING of π
    5. Circumference = ? (Animation)
    6. Circumference = ? (Animation II)
    7. Circle Area (by Peeling)
    8. Circle Area (By Peeling!)
  2. Algebraic Expressions
    1. Substitution & Evaluating Expressions
    2. Simplifying Linear Expressions
    3. Proof Without Words
    4. Plotting Points (x,y): Dynamic Illustration
    5. Plotting Points (x,y): Quiz
    6. Rant Rant Rant Rant!
    7. Quadrant Identification
    8. Rise & Run
    9. Distance in the Coordinate Plane (With Hints)
    10. Distance in the Coordinate Plane (II)
    11. Quiz: Distance in the Coordinate Plane (V1)
    12. Quiz: Distance in the Coordinate Plane (V2)
  3. Linear Equations
    1. Linear Equation Generator
    2. Verbal to Algebraic: Translating
    3. Matching Verbal Statements to Algebraic Statements (V1)
    4. Matching Verbal Statements to Algebraic Statements (V2)
    5. Triangle Angle Theorems
    6. Triangle Angle Theorems (V2)
    7. Triangle Angle Sum Theorem
    8. Application Problems: Solving Linear Equations (1)
    9. Perimeter of a Rectangle: Solving Linear Equations
    10. Friends and Money: Solving Linear Equations
    11. Application Problems: Solving Linear Equations (3)
    12. Application Problems: Solving Linear Equations (5)
  4. Systems of Linear Equations
    1. Slope: Intuitive Introduction
    2. Slope (Quiz) I
    3. Slope (Quiz) II
    4. Finding Slope Given 2 Points: Question Generator
    5. Blueprint Equation of a Line (I)
    6. Blueprint Equation of a Line (II)
    7. Equation of a Line: Dynamic Illustrator
    8. Graphing Linear Equations: Question Generator (V2)
    9. Writing the Equation of a Line (I-VA)
    10. Writing the Equation of a Line Given a Slope & Point (V1)
    11. Writing Linear Equations Given Slope & Point (V2)
    12. Writing Linear Equations Given 2 Points (y-int = integer)
    13. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
    14. Quiz: Application Problems - Writing Linear Equations Given 2 Points
    15. Writing the Equation of a Line Given Both Intercepts
    16. Solving Linear Systems Graphically
    17. Parallel Consequence? (VB)
    18. Slope Triangle Rotation (VB)
    19. Perpendicular Lines Investigation (VA)
    20. Perpendicular Lines Investigation (VB)
    21. Parallel & Perpendicular Consequence
    22. Writing Equations of Parallel and Perpendicular Lines
  5. More Applications of Linear Equations
    1. Working With Percents
    2. Working with Percent Change
    3. Solving Linear Systems Graphically
  6. Exponents and Factoring
    1. Multiplying Binomials
    2. Multiplying Binomials

1.

Geometry and Numbers

  • 1. Parallelogram: Area
  • 2. Area of a Triangle (Discovery)
  • 3. Trapezoid: Area (I)
  • 4. TRUE MEANING of π
  • 5. Circumference = ? (Animation)
  • 6. Circumference = ? (Animation II)
  • 7. Circle Area (by Peeling)
  • 8. Circle Area (By Peeling!)

1.1.

Parallelogram: Area

Directions:
In the app below, use the [b]filling[/b] slider to make the parallelogram light enough so that you can see the white gridlines through it. [b]But don't touch anything else yet! [/b][br][br]After you set the [b]filling[/b] slider, try to count the number of squares inside this parallelogram. [br]Be sure to include partial squares! Provide a good estimate in the question box below.
Try to count the number of squares inside this parallelogram. How many squares (i.e. square units) do you estimate to be inside this parallelogram?
Slide the "[b]Slide Me" [/b]slider now. Carefully observe what happens. What shape do you see now?
How does the area of this new shape compare with the area of the original parallelogram? How do you know this?
How many squares do you now count in the newer shape that was formed? How many squares were in the original parallelogram?
Without looking it up on another tab in your browser, describe how we can find the area of ANY PARALLELOGRAM.
– Tim Brzezinski

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1.8.

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2.

Algebraic Expressions

  • 1. Substitution & Evaluating Expressions
  • 2. Simplifying Linear Expressions
  • 3. Proof Without Words
  • 4. Plotting Points (x,y): Dynamic Illustration
  • 5. Plotting Points (x,y): Quiz
  • 6. Rant Rant Rant Rant!
  • 7. Quadrant Identification
  • 8. Rise & Run
  • 9. Distance in the Coordinate Plane (With Hints)
  • 10. Distance in the Coordinate Plane (II)
  • 11. Quiz: Distance in the Coordinate Plane (V1)
  • 12. Quiz: Distance in the Coordinate Plane (V2)

2.1.

Substitution & Evaluating Expressions

– Tim Brzezinski

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2.7.

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2.10.

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2.11.

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2.12.

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3.

Linear Equations

  • 1. Linear Equation Generator
  • 2. Verbal to Algebraic: Translating
  • 3. Matching Verbal Statements to Algebraic Statements (V1)
  • 4. Matching Verbal Statements to Algebraic Statements (V2)
  • 5. Triangle Angle Theorems
  • 6. Triangle Angle Theorems (V2)
  • 7. Triangle Angle Sum Theorem
  • 8. Application Problems: Solving Linear Equations (1)
  • 9. Perimeter of a Rectangle: Solving Linear Equations
  • 10. Friends and Money: Solving Linear Equations
  • 11. Application Problems: Solving Linear Equations (3)
  • 12. Application Problems: Solving Linear Equations (5)

3.1.

Linear Equation Generator

[color=#000000]Solve each linear equation that appears on the screen. [br]You can show your work to solve any equation in any workspace below.[br][/color][color=#000000][br]There are 4 difficulty levels here (see slider at bottom.) [/color]
You can use this space to show your work below.
You can use this space to show your work below.
You can use this space to show your work below.
You can use this space to show your work below.
– Steve Phelps, Tim Brzezinski

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3.9.

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3.10.

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3.11.

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3.12.

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4.

Systems of Linear Equations

  • 1. Slope: Intuitive Introduction
  • 2. Slope (Quiz) I
  • 3. Slope (Quiz) II
  • 4. Finding Slope Given 2 Points: Question Generator
  • 5. Blueprint Equation of a Line (I)
  • 6. Blueprint Equation of a Line (II)
  • 7. Equation of a Line: Dynamic Illustrator
  • 8. Graphing Linear Equations: Question Generator (V2)
  • 9. Writing the Equation of a Line (I-VA)
  • 10. Writing the Equation of a Line Given a Slope & Point (V1)
  • 11. Writing Linear Equations Given Slope & Point (V2)
  • 12. Writing Linear Equations Given 2 Points (y-int = integer)
  • 13. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
  • 14. Quiz: Application Problems - Writing Linear Equations Given 2 Points
  • 15. Writing the Equation of a Line Given Both Intercepts
  • 16. Solving Linear Systems Graphically
  • 17. Parallel Consequence? (VB)
  • 18. Slope Triangle Rotation (VB)
  • 19. Perpendicular Lines Investigation (VA)
  • 20. Perpendicular Lines Investigation (VB)
  • 21. Parallel & Perpendicular Consequence
  • 22. Writing Equations of Parallel and Perpendicular Lines

4.1.

Slope: Intuitive Introduction

[color=#000000]Discovery Lesson Activity: [br][/color][color=#980000][br][/color][b][color=#0000ff][url=https://docs.google.com/document/d/1W5fggl-QmnwOoT1Yjs2MfZnwVzIF49pflGX33xe0PN0/edit?usp=sharing]Slope: Intuitive Introduction Investigation [/url][/color][/b]
– Tim Brzezinski

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4.17.

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4.19.

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4.21.

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4.22.

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5.

More Applications of Linear Equations

  • 1. Working With Percents
  • 2. Working with Percent Change
  • 3. Solving Linear Systems Graphically

5.1.

Working With Percents

Use this template to help you model & solve any problem above.
– Tim Brzezinski

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6.

Exponents and Factoring

  • 1. Multiplying Binomials
  • 2. Multiplying Binomials

6.1.

Multiplying Binomials

[color=#cc0000][b]Students:[/b][/color][br][br]On a separate sheet of paper, multiply the binomials you see on the screen.[br]Be sure to simplify your expression afterwards. [br][br]After doing so, enter this expression into the input box provided. (Enter "x^2" to show [math]x^2[/math]). [br][color=#ff00ff][b]If you enter in a correct expression, you'll see a big "[i]CORRECT !!![/i]" sign appear. [/b][/color][br][br][i][color=#0000ff]Generate new problems and work through them as many times as you need in order to master this concept! [/color][/i]
– Tim Brzezinski

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