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Algebra I

Miscellaneous Topics

1.  Operations with Integers - Addition

 

 

2.  Operations with Integers - Subtraction

 

 

3.  Operations with Integers - Multiplication and Division

 

 

     
4.  One Period Lesson on Using Algebra Tiles to Develop the Concept of Addition of Integers

Activity Sheet
5.  One Period Lesson on Subtraction of Signed Numbers

Activity Sheet
6.  One Period Lesson on Multiplication and Division of Integers

Student Activity Sheet
     
7.  Writing Sequences Recursively

Recursive Toothpick Chart
8.  Reasoning with Proportions

9.  Building a Visual Model for (a+b)2 and a+b)3


     
10.  Secret Code


Alphabetic Coding Grid
11.  Loosing Area in a Fractal

12.  Compound Interest


     
13.  Composition of Functions


14.  Developing the Concept of a Function

function
15.  Changing Perimeter
     
16.  Working with Algebraic Fractions


17.  Understanding the Relationship of Parallel and Perpendicular Lines

Grid Paper
18.  Capture-Recapture Lesson on Ratios

Student Recording Sheet
     
19.  The Wheels Go Round and Round

Communicator Template
20.  Painted Cube Problem
21.  Looking at Patterns in More than One Way

Student Handout

Additional Patterns
     
22.  Analyzing the Bounce Height of a Racketball

23.  The Balancing Game
(Solving Equations)
24.  Developing Rules for Exponents

Do Now

Transparency Masters

Assignment
     
  25.  Thinking About Keeping a Scale Balanced

Solutions
 
     
26.  Visualizing the Quadratic Formula with the Area Model



27.  Using Tables to Collect Data

Do Now

Questions
28.  What Does It Mean to Solve a System of Equations?


     
     


Absolute Value
1.  How Does the Absolute Value Change the Graph of a Function?


2.  Eight Activities for Deeper Understanding of Graphing of Absolute Value


3.  Four Investigations to Explore Absolute Value Graphically and Numerically


     
4.  Lesson on Graphing Absolute Value Graphs


Do Now
Grid Sheet for Communicators
xy table
Transformations
Transformation Activity Sheet
  5.  Developing an Understanding for the Absolute Value Function


 

Mathematical Patterns
1.  Patterns and Algebraic Expressions
2.  Writing Equations to Fit a Number Pattern

Student Activity Sheet
3.  Working with Patterns

Do Now

Do Now Transparency Master

Do Now Answers

Pattern Chart

Garden Path Pattern

Different ways to Think of the Garden Path

Additional Patterns

Assignment

Assignment Answers

   
4.  Four Geometric Patterns to Study Algebraically

Student Handout
5.  Additional Geometric Patterns to Explore 6.  Communicator Template for Patterns
     
7.  Linear Patterns

Copies of Linear Patterns

Charts for Students
8.  Setting Up equations with Tables and Pictures
9.  Can You See the Patterns in More than One Way?

Questions to Ask

Follow Up Activity
     
  10.  Algebraic Patterns with Squares and Cubes
 
     

Inequalities
1.  Introduction to Graphing Inequalities in Two Variables


2.  Building Understanding for Graphing Inequalities


     

Simultaneous Equations
1.  Do These Equations Share a Pair of Coordinates?
2.  Using Tables to Find the Solution to a System of Equations
3.  Solving a System of Equations Graphically and Numerically

Student Activity Sheet
     
4.  Solving a System of Linear Equations

Do Now

Assignment

5.  Solving a System of Linear Equations with Matrices

Student Activity Sheet
6.  Solving a System of Linear Equations using the Inverse Matrix

Student Activity Sheet
     
7.   What Does it Mean to Solve a System of Equations?

Time-Position Chart

Position of Two Walkers

Assignment
8.  Building Understanding for Solving a System of Equations by Substitution

All Tied Up Template
9.  Developing an Understanding for the Elimination Method for Solving a System of Equations
     

10.  Developing an Understanding for Solving a System of Equations Using Matrices  

Linear Functions
1.  Wind Chill

linear
2.  Direct Variation with Common Canned Goods


3.  Life-Expectancy

linear
     
4.  Building an Understanding for Graphing Linear Functions

Lesson
Function Machine with Chart Template
Function Machine with Graph Paper
Quiz 1
Quiz 2
 Quiz 3
5.  Is there a Relationship between the Radius and the Circumference of a circle?
6.  What's My Line?
     
7.  How Fast Did He Run?
8.  Studying the  Effects of m
9.  Studying the  Effects of b
10.  What's the Same, What's Different
11.  Match Graph, Tables, and Equations
12.  Using Linear Functions in Analyzing Data
     
13.  Tied Up in Knots
14.  Developing an Understanding for the Direct Variation
15.  Building a Connection between Rate of Change and Straight Lines

     
16.  Build Understanding for Slope and Y-Intercepts
17.  Match the Graph with the Equation

Large copy of graphs and Equations
18.  Building Understanding for the Equation
 y = b+ mx
     
19.  Studying Constant Rate of Change with Recursive Sequences

One Additional Pattern

Recursive Toothpick Pattern
20.  All Tied Up

linear
Chart
linear
21.  Is this Point a Solution to the Equation?

     
22. Constant Rate of Change

Answers
23.  What is the Y-Value when x is a certain number - Using Graphing Calculator Home Screen
24.  What is the Y-Value when x is a certain number - Using Graphing Calculator Table Feature
     
25.  Understanding Patterns from Initial Values and Rate of Change
Student Graphs and Chart
26.  Walk the Line

Walker Program
27.  Which Way Do I Walk?
     
28.  Extending Student Understanding of Graphs
29.  Discovering the Effects of M
30.  Discovering the Liine of Best Fit with the Graphing Calculator
     
31.  Writing Stories to Match Graphs
32.  Building Understanding for the Line of Best Fit
33.  Pattern for Recursive Sequences
     
34.  Graphing a Way to See a Picture of an Equation Lesson

Do Now

Student Activity Sheet

Student Assignment
35.  Building Understanding for the Slope Intercept Form with a Beam Strength
36.  Guesstimating

Chart
     
37.  Building Understanding for Slope Through Distance Time Graphs and the CBR
38.  Building Understanding for Reading Graphs with the CBR Lesson

Student Copy
39.  Is there a Relationship between the Circumference and Radius of a Circle?
     
40.  Understanding Linear Equations and Intercept Form

41.  Making the Most of It

Chart
42.  Building Understanding for Slope-Intercept Form


     
43.  Creating Linear Plots

linear
44.  Working with Polynomials

Transparency 1

Transparency 2

Transparency 3

Assignment
45.  Follow Up Lesson on Combining Like Terms with Polynomials

Do Now

Transparency

Assignment
     
  46.  Visualizing Addition and Subtraction of Algebraic Expressions with Algebra Tiles
 

Non-Linear Functions
1.  Factoring a Trinomial

trinomial
2.  Make a Square - Factoring Quadratic Expressions  4 Puzzles


3.  Make a Square - Solving Quadratic Equations


     
4.  Graphing Quadratic Equations

Student Recording Sheet
5.  Sound Wave

Student Recording Sheet
6.  Different Types of Patterns
Charts and Graphs

Questions to be Considered

Follow Up Assignment
     
7.  Exploring Zeros of a Function on a Graphing Calculator
8.  4 part Exploration of Quadratic Functions with the Transformation APPS

Part I: How does A change the function y=Ax2 +Bx +C Part II: How does C change the function y=Ax2 +Bx +C
Part III: How does B change the function y=Ax2 +Bx +C
Part IV: More on How does C change the function y=Ax2 +Bx +C
9.  Introduction to the Graphs of Square and Square Root

Do Now
Four Quadrant Coordinate Labeled Graph Template

Function Machine with Chart Template

Closure Chart
     
10.  Developing an Understanding for Exponential Growth

Do Now
Student Activity Sheet
Student Activity Sheet Answers
Assignment
Assignment Answers

11.  Finding Zeros of a Quadratic Function

Student Activity Sheet
12.  Developing an Understanding for Inverse Functions

Inverse Program for the TI-84
     
13.  Introduction to Quadratics - Height of Hit Ball
14.  Model Rocket Science
15.  What's the Biggest Area?
     
16.  Making a Connection Between Zeros and the Verrtex of a Parabola
17.  Another Form for a Parabola
18.  Building Understanding for Rational Powers
     
19.  Performance Assessment on Quadratic Equations

Solutions
20.  4 Part Investigation on the Logarithms Function with the Graphing Calculator

Part I
Part II
Part III
Part IV
21.  Introducing Quadratic Functions
     
22.  Understanding the Meaning of a and b in the Exponential Function
23.  Bugs, Bugs, Everywhere Bugs

Student Chart

Answers
24.  Applying Trigonometric Functions to Distance Time Graphs

     
25.  Ratiuonal Functions - An Exploration with a TI84


26.  Rational Functions with Holes


27.  Rational Functions with Asymptot



     
28.  Simplifying Rational Expressions



29.  Performing Operations with Rational Expressions



Transformations
1.  Exploring Translations

Transformation Grid and Chart

Powerpoint Lesson

Sketchpad File
2.  Exploring Reflections

Transformation Grid and Chart

Powerpoint Lesson

Sketchpad File
3.  Exploring Rotations

Transformation Grid and Chart

Powerpoint Lesson

Sketchpad File
     
4.  Stretching and Shrinking
5.  Translating Functions
6.  Stretching Functions
     

Radicals and Irrational Numbers
 1.  Rational Exponents - An Exploration


2.  Modified Lesson on Square Root of 2 and its Multiples

Assignment

Assignment Answers
3.  Approximating Square Roots with a Geoboard

     
4.  Providing a Visual Model to Simplify Radicals

Do Now

These Squares are Really Radical Chart

Assignment


Assignment Answers

5.  Can the Area Model Help Me Solve Radical Expressions?

Communicator Template
6. Visualizing Simplifying Radical Expressions

 

Slope
1.  Understanding Slope or Steepness of a Line - 1

2.  Understand Slope or Steepness of a Liine - 2


3.  Understand Slope or Steepness of a Line - 3


     
4.  Looking for Relationships Between Slopes on Straight Lines


5.  Worksheet on Slope


6.  Understanding Slope Using Tables on the Graphing Calculator Discovering the Effects of M
     
7.  Investigating Slope on a Geoboard
8.  Discovering Properties of Slope


9.  Exploring the Concept of Slope of Parallel and Perpendicular Lines


     
10.  Exploring the Concept of Slope
11.  Match the Slopes
12.  Slope of a Straight Line

Lesson

Centimeter Grid Paper

Homework Assignment and Answers
     
13.  Building Understanding for Slope through Time-Distance Graphs with Assignment for Lesson


  14.  Building Understanding for Using Slope