Algebra 1

Jeff Caldwell, Jun 16, 2017

Table of Contents

  1. Slope
    1. Slope: Intuitive Introduction
    2. Slope: Intuitive Intro and Exploration
    3. Slope of a Line: Roller Coaster
    4. Rise & Run
    5. Rise & Run (Revamped)
    6. Slope (Quiz) I
    7. Slope (Quiz) II
    8. Finding Slope Given 2 Points: Question Generator
    9. Slope: Alternate Interpretation
    10. Parallel Consequence? (VA)
    11. Parallel Consequence? (VB)
    12. Perpendicular Lines Investigation (VA)
    13. Parallel & Perpendicular Consequence
    14. Perpendicular Lines Investigation (VB)
  2. Graphing Linear Equations
    1. Blueprint Equation of a Line (I)
    2. Blueprint Equation of a Line (II)
    3. Equation of a Line: Dynamic Illustrator
    4. Graphing Linear Equations: Question Generator (V1)
    5. Graphing Linear Equations: Question Generator (V3)
    6. Graphing Linear Equations: Question Generator (V2)
  3. Writing Linear Equations
    1. Writing the Equation of a Line (I-VA)
    2. Quiz: Modeling with Linear Functions
    3. Writing the Equation of a Line Given a Slope & Point (V1)
    4. Writing Linear Equations Given Slope & Point (V2)
    5. Writing Linear Equations Given 2 Points (y-int = integer)
    6. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
    7. Writing the Equation of a Line (I-VA)
    8. Writing Equations of Parallel and Perpendicular Lines
    9. Standard Form to Slope-Intercept Form (Rewriting Linear Equations)
    10. Writing the Equation of a Line Given Both Intercepts
  4. Solving Linear Systems Graphically
    1. Is P(x, y) a Solution?
    2. Solving Linear Systems Graphically
    3. Modeling Linear Growth (and Systems Introduction)
    4. Solving Linear Systems by Graphing: Quiz (V1)
    5. Solving Linear Systems by Graphing: REVAMPED
  5. Solving Linear Systems Algebraically
    1. Solving Linear Systems Algebraically: Quiz (V1)
    2. Solving Linear Systems Algebraically: Quiz (V2)
    3. Solving Linear Systems Algebraically: Quiz (V3)
  6. Parent Quadratic Function & Modifications
    1. Basic Quadratic Function (I)
    2. Basic Quadratic Function (II)
  7. Quadratic Expressions & Quadratic Equations
    1. Multiplying Binomials
    2. Solving Quadratic Equations Using Quadratic Formula (Quiz)
    3. Multiplying Binomials
  8. Locus Constructions
    1. Locus Problem (1)
    2. Locus Construction 1
    3. Locus Problem (2)
    4. Locus Construction 2
    5. Locus Problem (3)
    6. Locus Construction 3
    7. Locus Constructions (via Paper Folding)
  9. Parabola
    1. Locus Problem (1)
    2. Locus Construction 1
    3. Parabola as a Locus
    4. Parabola (Graph & Equation Anatomy)

1.

Slope

  • 1. Slope: Intuitive Introduction
  • 2. Slope: Intuitive Intro and Exploration
  • 3. Slope of a Line: Roller Coaster
  • 4. Rise & Run
  • 5. Rise & Run (Revamped)
  • 6. Slope (Quiz) I
  • 7. Slope (Quiz) II
  • 8. Finding Slope Given 2 Points: Question Generator
  • 9. Slope: Alternate Interpretation
  • 10. Parallel Consequence? (VA)
  • 11. Parallel Consequence? (VB)
  • 12. Perpendicular Lines Investigation (VA)
  • 13. Parallel & Perpendicular Consequence
  • 14. Perpendicular Lines Investigation (VB)

1.1.

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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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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2.

Graphing Linear Equations

  • 1. Blueprint Equation of a Line (I)
  • 2. Blueprint Equation of a Line (II)
  • 3. Equation of a Line: Dynamic Illustrator
  • 4. Graphing Linear Equations: Question Generator (V1)
  • 5. Graphing Linear Equations: Question Generator (V3)
  • 6. Graphing Linear Equations: Question Generator (V2)

2.1.

Blueprint Equation of a Line (I)

[color=#000000]This applet accompanies the [/color][i][color=#0000ff][b]Blueprint Equation of a Line[/b] [/color][/i][i][color=#0000ff]lesson activity[/color][/i][color=#000000] given to you in class. [br]Please use this applet to help you complete this activity.[br]If, at any time, you need to reference the [/color][i][color=#0000ff]Slope: Intuitive Introduction [/color][/i][color=#000000]applet, it can be found [/color][url=https://tube.geogebra.org/m/Xutr9rPj]here[/url][color=#000000]. [br][br][/color][color=#000000][b]Teachers:[/b] [/color][color=#cc0000][b]A pdf copy of this[/b] [/color][color=#0000ff][b]lesson activity [/b][/color][color=#cc0000][b]can be found below this applet.[/b][/color]
Blueprint Equation of a Nonvertical Line (Investigation)
– Tim Brzezinski

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3.

Writing Linear Equations

  • 1. Writing the Equation of a Line (I-VA)
  • 2. Quiz: Modeling with Linear Functions
  • 3. Writing the Equation of a Line Given a Slope & Point (V1)
  • 4. Writing Linear Equations Given Slope & Point (V2)
  • 5. Writing Linear Equations Given 2 Points (y-int = integer)
  • 6. Writing Linear Equations Given 2 Points (y-int not necessarily an integer)
  • 7. Writing the Equation of a Line (I-VA)
  • 8. Writing Equations of Parallel and Perpendicular Lines
  • 9. Standard Form to Slope-Intercept Form (Rewriting Linear Equations)
  • 10. Writing the Equation of a Line Given Both Intercepts

3.1.

Writing the Equation of a Line (I-VA)

[color=#cc0000][b]Teachers:[/b][/color][br][br]This applet generates examples where the y-intercept is an integer. The purpose of this applet is to formatively test students' knowledge of writing the equation of a line by mere observation. [br][br][color=#cc0000][b]Students:[/b][/color][br][br]For the line displayed, write the slope-intercept form of its equation in the input box below. [br][color=#3c78d8][b]For some problems, you may need to ZOOM OUT in order to see the black point on the line. [/b][/color][br][color=#ff00ff][b]If you enter this equation correctly, you'll see a big "CORRECT"! text appear. [/b][/color] [br][br][color=#0000ff][i]Repeat this exercise as many times as you need in order to master this concept! [/i][/color]
– Tim Brzezinski

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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4.

Solving Linear Systems Graphically

  • 1. Is P(x, y) a Solution?
  • 2. Solving Linear Systems Graphically
  • 3. Modeling Linear Growth (and Systems Introduction)
  • 4. Solving Linear Systems by Graphing: Quiz (V1)
  • 5. Solving Linear Systems by Graphing: REVAMPED

4.1.

Is P(x, y) a Solution?

Drag the point to various positions (both ON and OFF the line). Pay attention to what you see here. Then, answer the questions that follow.
If a point [math]\left(x,y\right)[/math] LIES on a line with a given equation, what can we conclude?
If a point [math]\left(x,y\right)[/math] DOES NOT LIE on a line with a given equation, what can we conclude?
If we wanted to see whether [math]\left(4,-3\right)[/math] was a solution to the equation [math]3x-5y=27[/math], what would we need to do first?
Is [math]\left(4,-3\right)[/math] a solution to the equation [math]3x-5y=27[/math]?
If we wanted to see whether [math]\left(-3,4\right)[/math] was a solution to the equation [math]3x-5y=-30[/math], what would we need to do first?
Is [math]\left(-3,4\right)[/math] a solution to the equation [math]3x-5y=-30[/math]?
– Tim Brzezinski

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5.

Solving Linear Systems Algebraically

  • 1. Solving Linear Systems Algebraically: Quiz (V1)
  • 2. Solving Linear Systems Algebraically: Quiz (V2)
  • 3. Solving Linear Systems Algebraically: Quiz (V3)

5.1.

Solving Linear Systems Algebraically: Quiz (V1)

[b]Directions:[/b][br][br]On a separate sheet of paper, solve the system of linear equations shown in the upper right hand corner of the applet. Once you obtain your solution, move the BIG WHITE POINT (shown in the coordinate plane on the left) to the location of the solution of this system. [br][br][color=#ff7700][b]If you solve this system correctly, the applet will automatically notify you. [/b][/color][br][br][color=#0000ff][i]Generate as many practice problems as you need in order to master this concept! [/i][/color]
– Tim Brzezinski

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6.

Parent Quadratic Function & Modifications

  • 1. Basic Quadratic Function (I)
  • 2. Basic Quadratic Function (II)

6.1.

Basic Quadratic Function (I)

[color=#000000]Interact with the applet below for a minute. [br]Then, answer the question that follows. [/color]
[color=#000000]How does the parameter "a" affect the graph of this quadratic function? [br]Explain. [/color]
– Tim Brzezinski

6.2.

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7.

Quadratic Expressions & Quadratic Equations

  • 1. Multiplying Binomials
  • 2. Solving Quadratic Equations Using Quadratic Formula (Quiz)
  • 3. Multiplying Binomials

7.1.

Multiplying Binomials

In the following applet, you will use algebra tiles to multiply 2 binomials.
1) What is the formula for the area of a rectangle? [br]2) If a farmer partitioned his/her field into 4 separate regions, how could he/she find the area of this field? (Explain 2 methods of calculating the total area.)
– Tim Brzezinski, garnettn

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8.

Locus Constructions

Locus Constructions: Parabola, Ellipse, Hyperbola, others

  • 1. Locus Problem (1)
  • 2. Locus Construction 1
  • 3. Locus Problem (2)
  • 4. Locus Construction 2
  • 5. Locus Problem (3)
  • 6. Locus Construction 3
  • 7. Locus Constructions (via Paper Folding)

8.1.

Locus Problem (1)

In the applet below, [br][br][i][color=#1e84cc][b]F[/b][/color][/i][color=#1e84cc][b] is a point[/b] [/color]that is not on line [i]d[/i]. [br][b]Point [i]D[/i] is a point that lies ON [color=#666666]the line that passes through [i]A [/i]and [i]B[/i][/color]. [br][/b]The [color=#ff00ff][b]pink line[/b][/color] is the [color=#ff00ff][b]perpendicular bisector[/b][/color] of the segment with endpoints [i][color=#1e84cc][b]F[/b][/color][/i] and [i][b]D[/b][/i]. [br][br]Drag [b]point [i]D[/i][/b] along the line. What do you see? Describe in detail! [br] [br]Feel free to alter the locations of [color=#666666][i][b]A,[/b][/i][/color] [i][color=#666666][b]B[/b][/color], [/i]and/or [i][color=#1e84cc][b]F[/b][/color][/i][color=#666666]. [br][/color]Then [color=#38761d][b]clear the trace[/b][/color] and drag [b]point [i]D[/i][/b] along [color=#666666][b]the line[/b][/color] again. [br][br]Why does this occur?
Please go to the [url=https://www.geogebra.org/m/sduBXC6P]Locus Construction 1 Task[/url] and begin!
– Tim Brzezinski

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8.5.

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8.7.

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9.

Parabola

  • 1. Locus Problem (1)
  • 2. Locus Construction 1
  • 3. Parabola as a Locus
  • 4. Parabola (Graph & Equation Anatomy)

9.1.

– Tim Brzezinski

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Information