Algebra I: Lesson Plan * 11/17/2006

Quickstart
Mini - BAT Assessment
Strand E, Standard 3, Form A
Experiments
MA.E.3.4.1, MA.E.3.4.2

Reteaching
Strand E, Standard 1
Data Analysis
A useful website about reading Venn Diagrams.


Strand E, Standard 2
Combinations and Permutations
Watch a video tutorial about finding the probability of independent events.

Lesson
7-1 Solving Systems by Graphing
Objective
(MA.C.3.4.2) To graph, apply, and verify properties of two-and three-dimensional figures.
(MA.C.3.4.2, MA.D.2.4.2) To use systems of equations to solve real-world problems.

Circulatory system...

Lots of arteries and veins working together.
Skeletal system...

Not just one bone, many bones
Muscular system...

Many, many muscles

A system of linear equations is two or more linear equations together.
Any ordered pair that makes all the equations true is a solution of the system of linear equations.

There are many ways to solve a system of equations.
We will discuss three of them in Chapter 7: Systems of Equations and Inequalities
1. Graphing
2. Substitution
3. Elimination

**Collected all Quickstarts, Homework, etc. from beginning of term**

PreCalculus: Lesson Plan * 11/17/2006

Quickstart
p.524 #127 - 133 odd

Lesson
7.4 Systems of Inequalities
Objectives: Students will know how to sketch the graphs of inequalities in two variables and how to solve systems of inequalities.

I. The graph of an inequality (pp.525 - 526)
Example 1 - Sketching the graph of an inequality
Example 2 - Sketching the graphs of linear inequalities
Example 3 - Sketching the graph of a linear inequality
Watch a video tutorial about graphing linear inequalities.

II. Systems of Inequalities (pp. 527 - 529)
To graph a system of inequalities we graph eah inequality in the system, and where the shaded regions all overlap is the solution region.
Example 4 - Solving a system of inequalities
Example 5 - Solving a system of inequalities

Assignment
Writing about Math - Creating a system of inequalities p.531

Algebra I: Lesson Plan * 11/16/2006

Quickstart
FCAT Practice
p.317 #73 - 79

Lesson
7-5 Linear Inequalities pp.370 - 372
Objectives
(MA.D.1.4.1) To describe inequalities using variables and graphs

Investigation: Graphing Inequalities p.370

Example 1 - Graphing an inequality

Helpful Website

Homework
p.373 #3, 6, 7 - 10ALL, 15 - 36 x 3's

PreCalculus: Lesson Plan * 11/16/2006

High School Reform Day

Quickstart
p.508 #110 & 111

Lesson
7.3 Multivariable Linear Systems
Objective: Students will know how to solve nonsquare systems of equations

III. Nonsquare systems (p.513)
Example 5 - A system with fewer equations than variables

IV. Graphical Interpretations of Three -Variable System p.514
Homework
p.519 #3 - 39 x 3's

Algebra I: Lesson Plan * 11/15/2006

Lesson
6-6 Scatter Plots and Equations of Lines pp.318 - 324
Objectives
(MA.D.1.4.1, MA.E.1.4.1) To write an equation for a trend line and use it to make predictions.

I. Writing an equation for a trend line
Example 1 - Trend line
Watch a video tutorial of this example.
Check Understanding #1

Homework
p.320 #1 - 5

PreCalculus: Lesson Plan * 11/15/2006

Quickstart
Real Life Applications of Solving Linear Equations
p. 507 #69, 71, 72


Assignment
7.1 & 7.2 Quiz - 10 points
Solving systems of equations by substitution, by graphing, and by elimination.

Lesson
7.3 Multivariable Linear Systems
Objective: Students will know how to solve nonsquare systems of equations, recognize linear systems in row-echelon form and use back-substitution to solve the system.

I. Row-Echelon Form and Back-Substitution p.509 -
A system of equations in row-echelon form will have a "stair-step" pattern with leading coefficients of 1.
Example 1 - Solve the system of equations that is in row-echelon form.

II. Gaussian elimination
Solving a system of equations by transforming it into row-echelon form is Gaussian elimination.
We use the Elementary Row Operations (p.510) to transform a system of equations into row-echelon form.
Example 2 - using Gaussian Elimination to Solve a System

Algebra I: Lesson Plan * 11/14/2006

Quickstart
MiniBAT Practice MA.E.3.4.1

Lesson
6-5: Parallel and Perpendicular Lines Objectives: (MA.C.2.4.1, MA.C.3.4.2) To determine whether lines are parallel. (MA.C.3.4.2, MA.D.1.4.2) To determine whether lines are perpendicular with different parameters of a graph.

Parallel lines are lines in the same plane that never intersect.
Perpendicular lines are lines that intersect to form right angles.

Small Groups Activity: Modeling Math - Slope of Parallel and Perpendicular Lines

Key Concepts
Slopes of parallel lines
Nonvertical lines are parallel if they have the same slope and different y-intercepts. Any two vertical lines are parallel.

Slopes of perpendicular lines
Two lines are perpendicular if the product of their slopes is -1. A vertical and horizontal line are also perpendicular.


Watch a video about
determining whether lines are parallel
writing equations of parallel lines
determining whether lines are perpendicular
writing equations of perpendicular lines


Homework
p.314 - 315
#3 - 48 x 3's

PreCalculus: Lesson Plan * 11/14/2006

Quickstart
Review Section 7.1
1. Solve a system by substitution
3x + 2y = 14
x - 2y = 10
2. Find all points of intersection
4x - y - 5 = 0
4x² - 8x + y + 5 = 0
3. Solve the system graphically
3x + 2y = 6
y = ln(x - 1)

Lesson
7.2 Systems of Linear Equations in Two Variables Objectives: Students will know how to solve systems of equations by elimination.
I. Method of Elimination p. 500
This method works on systems of linear equations and a few systems that include nonlinear equations. In general, substitution is a better method for solving systems involving nonlinear equations.
Example 1 - Eliminate by adding
Example 2 - Obtain opposite signs by multiplying, then eliminate by adding

Guided practice
p. 505 #14, 16, 20

II Graphical Interpretation of Solutions p.501
Example 3 Recognizing Graphs of Linear Systems

III Applications p.504
Example 7 - Airplane Speed

Homework
p. 505 - 507
# 3 - 30 x 3's, #66

PreCalculus: Lesson Plan * 11/13/2006

Quickstart
Classify Conics in the General Equation
p.719

Lesson
Chapter 7 - Systems of Equations and Inequalities
Essential Question
How can systems of equations model and solve real-life problems?
7.1: Solving Systems of Equations
Objective: Students will know how to solve systems of equations by substitution and by graphing.

I. The method of substitution p. 489 - 492
Example 1 - Solve a system of equations using substitution
Two linear Equations, one solution
Example 3 - Two solutions
Example 4 - No solution

II. The method of graphing
The solution(s) to a system of equations is the point of intersection of the graphs of the equations.
Explore the graphical representations of systems in Example 1, 3, 4

Example 5 - Solving system of Equations Graphically

III. Applications
Example 6 - Break-even point

Assignment
(Block I)
Writing About Math p. 494
Points of Intersection

Homework
p. 495 -496
# 3 - 36 x 3's, #69

Algebra I: Lesson Plan * 11/13/2006

Quickstart
Graph an equation in slope-intercept form.
Graph an equation in standard form.

Project
Gallery Walk
Objective: Students will be able to graph equations in slope-intercept and standard form as well as identify the equation of a graph.
In small groups students graph two equations assigned by the teacher.
Then graphs are posted and the groups "critique" each group of "artists" by matching each graph with a list of equations in slope-intercept and standard form.