GRAPHING
AND WRITING LINEAR EQUATIONS
Relating to the Real World
Algebra provedes a shorthand way to
look at a whole class of relatioships. Many cause-and-effect relationships in
everyday life, especially those involving time and money, use lnear equations
and graphs as models by understanding properties of linear models, both
economists and home budget makers can plan wisely.
Objectives
What students will learn:
Slope
** Counting Units to find Slope
** Using Coordinates to Find Slope
** Graphing a Line Given a Point and Its
Slope
Key Terms: slope
Rates
of Change
** Finding Rate of Change
** Using a Table
** Linear Functions
Key Terms: rate of change, linear
function
Direct
Variation
** Direct Variation
** Using the Constant of Variation to
Write Equations
** Using Proportions
Key Terms: constant of variation,
direct vations, linear equation
Slope_Intercept
Form
** Defining the Slope-Intercept Form
** Writing Equations
Key Terms: y-intercept, slope-intercet
form
Scatter
Plots and Equations of lines
** Trend Line
** Line of Best Fit
Key Terms: line of best fit,
corrrelation coefficent
Ax
+ By = C Form
** Graphing Equations
** Writing Equations
Key Terms: x-intercept, Ax + By = C form
Parallel
and Perpendicular Lines
** Slopes of Parallel Lines
** Slopes of Perpendicular Lines
Key Terms: parallel lines,
perpendicular lines
Lesson
Plan and Assessments:
Problem
of the Day, introduction, vocabulary, work examples together, self-assessment,
homework: "On Your Own" section from math textbook, handouts, pop quizzes,
quizzes, homework quizzes, pre-test assessment, and chapter assessment.
Resources:
Math Textbook, online research, real life
connections, powerpoint presentations for selected topics.
Equations and Inequalities
Relating to the Real World
you can use equations and formulas to
model a variety of real-world problems, business and industry, science,
sports, travel, architecture, banking-these are just some of the areas that
rely on equations and inequalities to find solutions to problems, often by
making comparisons and analyzing results.
Introduction
What students will learn and why: In
this chapter, students will build on their knowledge of algebraic concepts and
simple equations, learned in the previous Chapter, by learning to solve
equations and inequalities that involve proportions, variables on both sides,
absolute values, and formulas.
Objectives
1.Using
Proportions
-
Using Properties of Equality
-
Using Cross Products
-
Solving Percent Problems Using
Proportions
KEY TERMS: ratio, scale, proportion,
cross products, similar figures
2. Equations with Variables on Both
Side
-
Using Properties of Equality
-
Solving Special Types of Equations
KEY TERMS: no solutions, identity
3. Solving Absolute Value Equations
-
Solving Absolute Value Equations
-
Modeling by Writing Equations
4. Transforming Formulas
KEY TERMS: Literal equation
5. Solving Inequalities Using
Addition and Subtractions
-
Graphing and Writing Inequalities
-
Using Addition to Solve Inequalities
-
Using Subtraction to Solve Inequalities
KEY TERMS: solution of the Inequality,
equivalent inequalities
6. Solving Inequalities Using
Multiplication and Division
-
Solving Inequalities Using
Multiplication
-
Solving inequalities Using Division
7. Solving Multi-Step Inequalities
-
Solving with Variables on One Side
-
Solving with Variables on Both Sides
8. Compound Inequalities
-
Solving Compound Inequalities Joined by
And
-
Solving Compound Inequalities Joined by
Or
-
Solving Absolute Value Inequalities
KEY TERMS: compound Inequalities,
absolute value
9. Interpreting Solutions
-
Solving Inequalities Given a
Replacement Set
-
Determining a Reasonable Answer
KEY TERMS: replacement set
Assessment:
Homework assigned for each lesson from math
textbook/handouts, pop quizzes, quizzes, homework quizzes, warmups, pre-test
assessment, and chapter assessment.
Resources:
Math Textbook, online research, real life connections,
powerpoint presentations with hands-on activities.
Algebraic Concepts
and Simple Equations
CHAPTER
PROJECT
The
Project gives students an opportunity to learn how to use equations to model a
personal budget. In the Find Out questions, students write an equation to
model a budget plan. They develop a budget plan and a spreadsheet to analyze
their spending and saving habits. Students will display and present their
budgets using a circle graph.
>>Students
are to keep all project-related materials in a separate folder. Segments of
the project will be due when homework for the related lesson is due. The
complete project is due at END of the CHAPTER.
>>Students
are to visit Finishing the Chapter Project on page 150 for an overview of the
project. Rubric will be posted on students' ENGRADE site.
******************************************************************************************
Examine the
expression below.
6(2+4x)
"The two terms
inside the parentheses cannot be added because they are not like terms.
Therefore, 2 + 4x, the expression inside the parentheses, cannot be simplified
any further. To simplify this multiplication, another method will be needed.
This is where the Distributive Property comes in ..."
**********************************************************************************
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Relating to the real World:
** How do you solve a problem? Do you first decide what the problem really
is, and then take a series of steps to improve the situation? In Algebra,
that's exactly what happens. To solve problems, many people, including
pharmacists, marine biologists, and money managers, all us simple equations
and step-by-step methods.
Objectives:
Students will build on their knowledge of functions learned in the previous
chapter, by learning :
1. Modeling and
Solving Equations
* Solving Addition and Subtraction Equations
* Sloving Multiplication and Division Equations
* Modeling by Writing Equations
Key Terms:
solutions, inverse operations, equivalent equations, properites of equality
2. Modeling and
Solving Two-Step Equations
* Using Properties
Key Terms: two-step
equation, calculator-ready form
3. Combining Like
Terms
* Combining Like Terms
* Solving Equations
Key Terms:
coefficient, like terms, constant term
4. Using The
Distributive Property
* Simplifying Variable Expressions
* Solving and Modeling Equations
Key Terms:
distributive property
5. Rational Numbers
and Equations
* Multiplying by a Reciprocal
* Multiplying by a Common Denominator
6. Using Probability
* Finding the Probability of Independent Events
* Finding the Probability of Dependent Events
* Finding Probability Using an Equation
Key Terms:
independent events, depenent events
7. Percent Equations
* Solving Percent Equations
* Writing Equations to Solve Percent Problems
* Simple Interest
Key Terms: simple
interest
8. Percent of Change
* Percent Change
Key Terms: percent of change, percent of increase, percent
of decrease
Assessment:
Homework assigned
for each lesson from math textbook/handouts, pop quizzes, quizzes, homework
quizzes, warmups, pre-test assessment, and chapter assessment.
Resources:
Math Textbook,
online research, real life connections, powerpoint presentations, and chapter
project.
Functions and Their
Graphs
Introduction
Functions are key concept in algebra. A function describes a relationship
and allows you to predict future outcomes. Most of the technology we take for
granted, from automobiles and CD players to medical procedures and microchips,
has been made been possible because some one first used functions to make
predictions.
Objectives
Students will build on their knowledge of algebra skills in
learned in the previous chapter, by:
1. Analyzing Data
Using Scatter Plots
- Drawing and Interpreting Scatter Plots
- Analyzing Trends in Data
Key Terms: scatter
plot, trend line, positive correlation, negative correlation, no correlation
2. Relating Graphs
to Events
- Interpreting Graphs
- Sketching Graphs
- Classifying Data
Key Terms: continuous
data, discrete data
3. Linking Graphs to
Tables
Key Terms: dependent
variable, independent variable
4. Functions
- Identifying Relations and Functions
- Evaluating Functions
- Analyzing Graphs
Key Terms: relation,
function, function rule, domain, range, vertical-line test
5. Writing a
function Rule
- understanding Function Notation
- using a Table of Values
- Using words to Write a Rule
Key Terms: function
notation
6. The Three Views
of a Function
7. Families of
Functions
- Identifying the Family of an Equation
- Identifying the Family of a Graph
Key Terms: f amilies
of functions, linear functions, quadratic functions, absolute value functions
8. The Probability
Formula
- Finding Theoretical Probability
- Using a Tree Diagram to Find a Sample Space
Key Terms: outcomes,
theoretical probability, impossible event, certain event, complement of an
event, sample space, tree diagram
Assessment:
homework is assigned daily from the textbook, quizzes, pop quizzes, powerpoint
presentations, handson activities, chapter pre-test assessment, and chapter
assessment
Tools of Algebra
The BIG DIG
Chapter Project (due at the end of this chapter). Please refer to the
opening of chapter 1 "TOOLS OF ALGEBRA"
In
this chapter students will:
-
build on their knowledge of interpreting
data
-
learn to analyze real-world data to find
the mean, median, and mode
Prerequisite
Skills
-
Interpreting data
-
Performing operations with integers
-
Finding number patterns
-
Simplifying expressions
-
Substituting numbers for variables in
equations
-
Using algebra tiles
-
Finding distance on a number line
-
Using the order of operations
-
Adding and subtracting fractions
-
Reducing fractions
-
Converting fractions to percents
-
Adding and subtracting integers
-
Understanding the terms row and column
-
Evaluating formulas
Key
Terms
|
-
absolute value
-
bar graph
-
base
-
cell
-
entry
-
equation
-
evaluate
-
event
-
experimental probability
-
exponent
-
integers
-
irrational numbers
-
line graph
-
line plot
|
-
matrix
-
mean
-
median
-
mode
-
opposite
-
order of operations
-
rational numbers
-
real numbers
-
reciprocal
-
simulation
-
spreadsheet
-
term
-
variable
-
variable expression
|
|
Review
** Inclass assignment
** Homework
** Chapter Wrap Up
** Project
Assessment
** Prior Knowledge assessments in form of
QOD (question of the day) or POD (problem of the day)
** Homework
** Inclass assignment
** Chapter Wrap Up
** Oral Participation
** Quizzes and Chapter Test
Geometry Overview
Homework:
Complete the chapter 10 packet: 1-9
lessons- Cumulative Reviews (originally assigned on Frid 10 lesson 1-5 was due
on Mon. 14 & 6-9 was due on Wed. 15)
Complete the in-class activity- How
much rapping paper do you need to envelope your object?
Work odd problems on page 556- Cumulative
Review.
all the obove assignement is due Friday
17, 08
In this chapter students will:
-
learn
how to find the areas of figures
-
learn
how to find the surface areas of space figures
-
learn
how to find the volumes of space figures
-
learn
how to solve a problem by making a model
|
Prerequisite Skills
-
find
the area of squares and rectangles
-
find
the product of a fraction and an integer or variable expression
-
simplify
the product of a number and a number squared
-
find
the circumference of a circle
|
Key Terms
|
-
altitude
-
altitude
of a triangle
-
area
-
cone
-
cubic
unit
-
cylinder
-
lateral
area
-
net
|
-
prism
-
pyramid
-
slant
height
-
space
figure
-
sphere
-
surface
area
-
volume
|
|
REVIEW (homework/inclass)
Chapter Wrap Up
Cumulative Review
Mixed Review in every Lesson
Assessment
Quizzes and Chapter Test
Spatial Thinking
This year we are commencing with an extensive review of geometric figures
and space and such properties of figures as size and shape.
Students will:
-
learn how to use properties of figures to solve problems
-
learn how to classify geometric figures
-
learn how to construct figures
-
learn how to solve a problem by drawing a diagram
Prerequisite Skills:
-
classify polygons by the number of sides
-
identify the radius of a circle
-
identify the diameter of a circle
-
graph points on a coordinate plane
Key Terms:
adjacent angles,
points, alternate interior angles, polygon, angle bisector, reflection, angle
of rotation, reflectional symmetry, center of rotation, regular polygon,
central angle, rotation, complementary angles,rotational symmetry, congruent
angles, segment, corresponding angles, segment bisector, image, skew, line,
supplementary angles, line of reflection, transformation, line of symmetry,
translation, parallel, transversal, perpendicular bisector, vertical angles,
perpendicular lines, plane
Project #1
To help students apply the math to real-life
applications;
** The first activity, students will build a
prism and a cylinder. They will calculate their volumes by using both formulas
and water displacement.
** For the second activity, students will
redesign packaging for their favorite cereal to contain the same volume.