Download Literacy Elements

Working Document Summer 2008
Concept: The Language of Algebra
Timeline: 9 days
Standard:
The student will demonstrate through the mathematical processes an understanding of the real number
system and operations involving exponents and algebraic expressions. EA-2.
.
Essential Vocabulary
Algebraic expression
Commutative property
Associative property
Zero property
Identity
Substitution
Indicator
EA-1.1
Communicate a knowledge of
algebraic relationships by using
mathematical terminology
appropriately.
EA-2.5
Carry out a procedure using the
properties of real numbers
(including commutative, associative,
and distributive) to simplify
expressions.
EA-2.6
Carry out a procedure to evaluate an
expression by substituting a value
for the variable.
Txtbk
Correlations
1.1
1.2
1.5
1.6
Independent variable
Dependent variable
Domain
Resources
Range
Rational Numbers
Irrational Numbers
Radical Sign
Examples of Essential Tasks
Property Memory Game
Irrational Number Video
Vocabulary Matching
Teachers use the vocabulary on a
regular basis and encourage
students to use the proper
vocabulary both in oral and
written math communication.
Rational Expression Video
Students do not have to identify
the property being used. They
will need to identify these
properties on HSAP.
Interactive Algebraic Expressions GIZMO
Simplify 4(2 + x) + (1 – 3x) + 7
Simplify 2Π + 4 Π
xy2 z 3
Evaluate
for x = 5, y =3 and
y
z = -2
EA-3.4
Analyze the graph of a continuous
function to determine the domain
and range of the function.
1.8
Find Domain and Range from Graph
Working Document Summer 2008
ONLY continuous functions
Function, Vertical Line Test, Domain, Range
Determine the domain and range of
this graph.
EA-2.1
Exemplify elements of the real
number system (including integers,
rational numbers, and irrational
numbers).
2.1
2.7
Interactive Number Line
Add, Subtract, Abs Val
Identify -7 as an integer and a
rational number.
Identify
2 as am irrational number.
Numbers (natural, whole, integer, rational,
irat,real)
Classification of Real Numbers
EA-2.2
Apply the laws of exponents and
roots to solve problems
2.7
Square Root Flash Cards
Simplify
81
49
27
3
Literacy Elements
A- Decide if there is an error in this problem. If there is an error
explain how to correct it. If there is not an error explain why it is
correct. Explain your reasoning using mathematical terms.
4 w 4  w 4  3w 2  2 w 2
 ( 4) w4  3  2 w2
 4 w4  1w2
 4 w4  w2
LM- Have students create brochures to share with the class covering
different parts of this unit. Students can lead the review for the test by
presenting their brochures and answering questions. Topics to pick
from could include: distributive property, order of operations,
commutative property, associative property, square roots, real number
system, domain and range of a function and substitution.
NAGR- Have students complete the following sentences at the end of class.
CC- Translate the following two phrases into algebraic terms.
Phrase 1: x times y plus z
Phrase 2: x times the sum of y and z
a. Compare and contrast the two phrases
b. Find values for x, y, and z that make the two phrases equal.
CR- Evaluate and explain what you are doing in each step.
2  7

6
 2 * 3  5 .
 3

E- Explain the difference between the domain and range of a graph.
How do these terms relate to the independent and dependent variable?
J- Describe a use of the commutative property of real numbers.
Teacher Notes:
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Project Interactive
GeoGebra
National Library of Virtual Manipulatives
Connected Mathematics Project
Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
Learn and Use GeoGebra
Working Document Summer 2008
In class today, we…… (describe what was covered) I learned….. (be
specific, include examples as evidence of your understanding.) One or
two questions I still have are….. My plan for getting help with
homework if I need it is…..
V- Depict the terms rational number, irrational number, and integers in
a Venn diagram. Place three examples of each type of number in the
diagram.
Working Document Summer 2008
Concept: Linear Equations and Functions
Timeline: 12 days
Standard:
The student will demonstrate through the mathematical processes an understanding of relationships
and functions. EA-3.
Vocabulary
Addition Property of Equality
Multiplication property of Equality
Equivalent Equations
Division property of Equality
Subtraction Property of Equality Consecutive Integers
Indicator
EA-4.7
Carry out procedures to solve linear
equations for one variable
algebraically.
Txtbk
Correlations
3.2
3.3
3.4
3.5
Identity
Relation
Inverse
Function Notation
Resources
x-intercept
y-intercept
Function
Vertical line test
Examples of Essential Tasks
Interactive Translating Equations into English Sentences
GIZMO
Solve
-2 (x – 5) = 3x + 4
Balancing One-Variable Equations (Choose Solving
Equations)
In which step did the first error
occur?
3(2 x  1)  6
Modeling One-Step Equations - Activity Gizmo
Interactive Solving 2-Step Equations GIZMO
Solving One Step Equations – Video – Math Dude
Motivation of Lesson
Equation Balance
EA-3.8
Ratio/Proportions Video
Step 1 : 6 x  3  6
Step 2 :
6x  3
Step 3 :
x
1
2
Apply proportional reasoning to
solve problems
3.6
3.7
Interactive Ratios
Percent of Change GIZMO
EA-3.7
Carry out a procedure to solve literal
equations for a specified variable.
3.8
EA- 3.1
Classify a relation as being either a
function or not a function when
given data as a table, set of ordered
pairs, or graph.
4.3
4.4
Working Document Summer 2008
A statue is to be constructed using a
10:1 (height of statue: height of
person) scale. If the person to be
depicted is 76 inches tall, how tall
should the statue be built?
Solve I = PRT for T
Solve ax = b + cd for c
Introductions to Functions GIZMO
Classify as a function or not
Functions, Vertical Line Test, domain range
X
1
2
2
3
4
Y
6
8
10
12
16
Classify the relationship
shown on the mapping
below as a function or
not a function.
Answer: not a Function
-3
5
6
2
-4
7
8
Working Document Summer 2008
EA – 5.5
Carry out a procedure to determine
the x-intercept and y-intercept of
lines from data given numerically in
a table, graphically, symbolically,
and verbally.
4.5
A cell phone provider charges a flat
rate of $15 plus $.10 per minute
each month. What is the y-intercept
of this function? What is
represented by the y-intercept?
What is the y-intercept and the xintercept of the graph of
4y – 2x = 6
The table of values below represents
the points on a line. What is the yintercept? What is the x- intercept?
EA- 3.2
Use function notation to represent
functional relationships.
EA- 3.3
Carry out a procedure to evaluate
a function for a given element in the
domain.
4.6
Functions, Vertical Line Test, domain range
x
-1
0
1
2
y
6
3
0
-3
Express the relation q is a function
of r and 2 times r equals q in
function notation.
Answer: q(r) = 2r
Given g(t) = 2t -6, evaluate g(2)
Literacy Elements
A- During sections 3.6 and 3.7, have students analyze their errors when
working a word problem. The students could write an explanation of
why the error occurred and an explanation of how they will avoid the
error in the future. It is also helpful to have students analyze each
others work and write responses.
CC- Compare and contrast these two sets of points:
Set A: {(-3, 6), (2, 5), (3, 1), (2, 4)}
Set B: {(-3, 6), (2, 1), (3, 6), (1, 4)}
LM- The class creates a newspaper about this unit. Allow pairs of
students to pick topics from the unit. The articles must contain at least
one graphic. Have two students be editors and but the paper together.
Use copies of the paper for student review sheets. ONLINE
TEMPLATES
NAGR- The most difficult problem in this unit for me is…You must use
Be sure to include the terms domain, range, function, and relation in
your comparison.
y 5
CR- In the proportion  , what happens to the value of y as x
5 x
increases?
E- Entry Slip- List these terms on the board: Function, Domain, Range,
x-intercept, y-intercept, and Vertical Line test. Have students copy the
terms and indicate their knowledge of the term. Have the students use
the categories A lot, some, and not much to signal their knowledge.
Use this as a starting point to introduce functions. There is a printed
version of this activity in Algebra Out Loud page 9.
J- Write a letter to a friend explaining how to solve a two step equation.
Although you may include an example at the end, your explanation
should be in complete sentences. I will follow your steps to see if they
really tell how to solve a two step equation.
Teacher Notes:
Check your Navigation series of books
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Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
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Learn and Use GeoGebra
Working Document Summer 2008
complete sentences and explanations.
V- Vocabulary note cards- List the term on one side – write a definition
in your own words and create an illustration that helps you know what
the term really means.
Working Document Summer 2008
Concept: Lines
Timeline: 11 days
Standard:
. The student will demonstrate through the mathematical processes an understanding of the procedures
for writing and solving linear equations and inequalities. EA-4
The student will demonstrate through the mathematical processes an understanding of the graphs and
characteristics of linear equations and inequalities. EA-5
Vocabulary
Slope
Direct variation
Family of graphs
Slope-intercept form
Point-slope form
Perpendicular lines
Positive correlation
Negative correlation
Trend line
Working Document Summer 2008
Indicator
EA-5.6
Carry out a procedure to determine
the slope of a line from data given
tabularly, graphically, symbolically,
and verbally.
EA-5.7
Analyze the concept of slope as a
rate of change to solve problems
Txtbk
Correlations
5-1
Resources
Interactive slope activity
Slope Cartoon
Slope Matching Game
Working Document Summer 2008
What is the slope of the line with
the equation 3x + 2y = 7
If a roof rises 9 feet for every 15
feet of run, what is the slope of the
roof?
Linear Function Explorer
Linear Equations, Mdpt, Dist
.
EA-3.5
Carry out a procedure to graph
parent functions (including y = x)
EA- 3.6
Classify a variation as either direct
or inverse.
EA- 3.8
Apply proportional reasoning to
solve problems.
Examples of Essential Tasks
5-2
Given
x
-2
-1
y
-8
-5
Find the slope of the line.
0
-2
Investigating slope and Linear Equations
In the equation y=4x, if the value of
x is increased by 2, what is the
effect on the value of y?
Graph of Linear Equations
John has a lemonade stand. His
profit is modeled by y = .75x - 9.85
Where y is the profit and x is the
number of cups of lemonade sold.
If he sells five more cups of
lemonade today than he sold
yesterday, how much more money
does he make today?
Classify each of the following as
direct or inverse variation.
xy = 20
hands on activity - direct variation
d = 20t
Graph Classic Functions
Students must be able to identify
variation equation from graphs also.
The distance traveled by a car
moving at a constant speed varies
directly with the length of time it
travels. If the car travels 172 miles
in 4 hours, how many miles will it
travel in 9 hours?
EA-4.1
5-3
How does changing the c in
Working Document Summer 2008
Teacher Notes: EA-5.9 Analyze given information to write a linear function that models a given problem situation should be covered
throughout this unit.
Literacy Elements
A-After giving a quiz on sections 5.1 – 5.3 have students correct
their mistakes and write a paragraph for each incorrect problem. The
paragraph should contain an explanation of the errors with correct
mathematical terminology.
CC- Compare and contrast the graphs of y = 4x + 3 and y = -4x + 3
CR- A friend wants to purchase a cell phone plan. There are three
different plans available.
Plan 1 charges $.59 per minute.
Plan 2 charges a monthly fee of $10, plus $.39 per minute.
Plan 3 charges a monthly fee of $59.95.
a. Write an equation that represents the monthly cost for each plan.
b. Graph each equation.
c. Your friend expects to use 100 minutes each month. In complete
sentences explain which plan she should pick and why.
E- Exit slip – explain slope and how slope and rate of change are
related
J- Given two points on a line, explain how you would write the
equation of the line and graph the line. Be sure to use complete
sentences and correct mathematical terminology.
Check your Navigation series of books
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GeoGebra
National Library of Virtual Manipulatives
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Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
L- Have students create a children’s book that explains graphing lines.
The book should be illustrated and written on an elementary level. You
may choose the book students use as a model or allow them to pick.
M-Create a brochure that explains scatter plots and trend lines. Use
brochure templates to download a template for students to complete.
NAG-Have students compare the linear equations of y = 5x and
y = -5x + 2 by using a chart and a graph. Students should write a
paragraph explaining what the equations reveal about the similarities and
differences of the two lines and how they are related.
R- The reason it is important to rewrite a word problem in my own words
is ….
V- Math Story activity: (Algebra Out Loud page 109).
Use the following terms to create a short story: graph, line, slope, xintercept, y-intercept, parallel, perpendicular, vertical line test. You must
use all of the listed terms. Each term must be correctly used. You may be
creative, but in at least one place, use the term in a manner that clearly
demonstrates what it means. Your story may be fiction or nonfiction.
Your story should contain an introduction and a conclusion. Be creative
and choose a theme that has relevance to you.
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Working Document Summer 2008
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
Concept: Inequalities and Systems of Equations
Timeline: 10 days
The student will demonstrate through the mathematical processes an understanding of the procedures
for writing and solving linear equations and inequalities. EA-4
The student will demonstrate through the mathematical processes an understanding of the graphs and
characteristics of linear equations and inequalities. EA-5
Standard:
Vocabulary
Set builder notation
Addition Property of
inequalities
Subtraction Property of
inequalities
Multiplication property of
inequality
Division property of inequality
System of Equations
Indicator
EA-4.8
Carry out procedures to solve linear
inequalities for one variable
algebraically and then to graph the
solution.
EA-5.12
Analyze given information to write a
linear inequality in one variable that
models a given problem situation.
Txtbk
Correlations
6.1
6.2
6.3
Resources
Interactive Number Line
Interactive Solving (and Graphing) Linear Inequalities
using Add/Sub Gizmo
Interactive Solving (and graphing) Linear Inequalities
using Add/Sub Gizmo
linear inequalities
Examples of Essential Tasks
Solve and graph
-3b + 15 < 2b
7 – 2(x – 3) ≥ 25
Todd wants to make at least $250
this week. Todd makes $6.00 per
hour and will earn a $25 bonus this
week. Write a linear inequality in
Working Document Summer 2008
one variable that models the
problem.
EA-4.9
Carry out a procedure to solve
systems of two linear equations
graphically.
EA-4.10
Carry out a procedure to solve
systems of two linear equations
algebraically.
EA-5.11
Analyze given information to write
a system of linear equations that
models a given problem situation.
7.1
7.2
7.3
7.4
Systems Overview
Graphing Instructions
Graphing Practice
Substitution Instructions
Elimination Instructions
Systems Practice
Does this system have one solution,
infinitely many solutions or no
solution?
 a  2b  5
2a  4b  10
Perpendicular Lines
2.5
2
1.5
Parallel Lines
1
0.5
-3
-2
0
-1 -0.5 0
1
2
3
4
-1
-1.5
Which system of
linear equations is
graphed above?
a.  4 x  3 y  2
 2x  y  1
b.  x  2 y  2
 3x  4 y  2
c. 2 x  y  1
4x  3y  2
5
Working Document Summer 2008
d. x  2 y  2
x  2y  0
Literacy Elements
A-Tell what mistakes (if any) the student made at each step in the
problem, and explain what the student should do instead. Remember to
4 x  6  28
use complete sentences
x6  7
x  13
CC- Compare and contrast the strategies for solving systems of
equations.
CR- Students complete wacky water world activity (student
worksheet). This introduces the student to real life uses of systems of
equations and provides detailed instructions on using the graphing
calculator. The answer sheet is also available. answer key
E- Exit Slip - The muddiest point covered in class today was…… The
clearest point covered in class today was…….
J- When I solve inequalities, the hardest part for me is …
because…Two things I can do to improve my understanding of solving
inequalities is ..
Teacher Notes:
Check your Navigation series of books
 Project Interactive
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


GeoGebra
National Library of Virtual Manipulatives
Connected Mathematics Project
Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
LM- Students create original word problems that can be solved using a
system of equations. The problems should contain artwork and
solutions. Have a group of students check the problems for accuracy
and compile the problems into a book.
NAG- A system of linear equations can have three different types of
solutions. Explain how you can know how many solutions there are by
using a graph of the system and solving the system
R- When I start solving a system of equations I begin by…. because….
V- Students create mini posters depicting one of the vocabulary terms.
Display the artwork and have students present their work. The posters
should contain pictures and definitions in the students own words.
Working Document Summer 2008
Concept: Polynomials
Timeline: 11 days
Standard:
The student will demonstrate through the mathematical processes an understanding of the real number
system and operations involving exponents and algebraic expressions. EA-2.
.
Essential Vocabulary
Monomials
Constants
Polynomials
Indicator
EA-2.7
Carry out a procedure
(including addition,
subtraction, multiplication, and
division by a monomial) to
simplify polynomial
expressions.
EA-2.2
Apply the laws of exponents
and roots to solve problems
Binomial
Trinomial
Degree of a monomial
Textbook
Correlations
8.1
8.2
Degree of a polynomial
Resources
Multiply Polynomials
Examples of Essential Tasks
Simplify (- 5 rm)2 (
1 3 4 2
rm) .
2
Evaluate (4-1)-2
Polynomial Video
Matching Polynomial Terms
Multiplying Monomials PowerPoint
Multiplying Monomials GIZMO
Multiplying Powers with the Same Base Video
Power to a Power Video
Evaluate 90.
Simplify
 2 x 1
.
8 x 2 y 3
3
 zy 3 
 .
Simplify 
2 3 
  5z y 
Working Document Summer 2008
Power of a Product Video
Cryptic Cubes- Multiplying Monomials Game
Dividing Monomials Video
Dividing Monomials GIZMO
Zero and Negative Exponents Video
Quotient of Powers Video
EA-2.3
Carry out a procedure to
perform operations (including
multiplication and division)
with numbers written in
scientific notation.
8.3
Exponents and Power Rules GIZMO
Scientific Notation PowerPoint
Multiplying Numbers in Scientific Notation Video
Simplify
Dividing Numbers in Scientific Notation
Scientific Cards Line-Up Game
Scientific Cards Match Up Game
Scientific Notation Practice
EA-2.7
Carry out a procedure
(including addition,
subtraction, multiplication, and
division by a monomial) to
simplify polynomial
expressions.
The numbers will be given in
scientific notation.
8.4
8.5
8.6
8.7
8.8
(6.3 x 10 7 )
(2.1 x 10 4 )
(5.0 x 103) (2.0 x 106)
(8.0 x 10 4 )
(2.0 x 10 -2 )
Simplify
Multiply Polynomials
6 x 4  9 x 3  3x 2
3x 2
Foil Instruction Video
(x – 1) (-4x2 + x + 12)
Adding And Subtracting Polynomials PowerPoint
(3x4 – 8x3 + 2x2 – 3) – (6x3 –
2x2 + 5)
Adding Polynomials Video
Working Document Summer 2008
Subtracting Polynomials Video
(2x3 + 5x2 – 3) + (-4x3
+ 9x – 1)
2
Cryptic Cubes: Dividing Polynomials by Monomials
Multiplying a Monomial and a Polynomial
PowerPoint
Multiplying Polynomials PowerPoint
Application of Multiplying Polynomials Video
Multiplying a Binomial and a Trinomial Video
Simplifying Polynomials
Algebra Tiles – Visualize multiplying and factoring
algebraic expressions
Literacy Elements
A- Judy thinks the degree of the polynomial -4x2y2 + 3x2 + 5 is 6. What
mistake has she made? What is the degree of the polynomial?
CC- Compare and contrast the pattern for finding the square of a sum
and the square of a difference.
CR- a. Simplify Error! Objects cannot be created from editing field
codes.by using the Quotient of Powers property first, and then use the
Power of a Power property.
b. Simplify Error! Objects cannot be created from editing field
codes.by using the Power of a Quotient property first, and then use the
Quotient of Powers property.
c. Write a statement that generalizes the results of part a and part b.
E- Exit slip – The two concepts I need the most help on in this chapter
are…………….
J- Write a paragraph explaining how to simplify polynomial
expressions. Be sure to include the characteristics of a simplified
polynomial expression and use correct terminology.
LM- Students can produce a joke book about polynomials. Each student
writes a joke or riddle that contains facts from this unit. Encourage the
students to be creative but require the finished product to demonstrate
mathematical knowledge.
NAGR- Three things I really understand about polynomials are… Two
things I am a little confused about are… One thing I really do not
understand at all is…
V- Students create a visual representation that depicts the relationship
of the key vocabulary in this chapter. the students can create a map,
Venn diagram, or any original means to show how the terms are related.
Working Document Summer 2008
Teacher Notes:
Check your Navigation series of books
 Project Interactive
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
GeoGebra
National Library of Virtual Manipulatives
Connected Mathematics Project
Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
Concept: Factoring
Timeline: 12 days
Standard:
The student will demonstrate through the mathematical processes an understanding of the real number
system and operations involving exponents and algebraic expressions. EA-2.
.
Essential Vocabulary
Factoring
Zero product property
Indicator
Prime Polynomial
Difference of squares
Txtbk
Corre-
Resources
Examples of Essential Tasks
Working Document Summer 2008
EA-2.8
Carry out a procedure to factor
binomials,
trinomials,
and
polynomials by using various
techniques (including the greatest
common factor, the difference
between two squares, and quadratic
trinomials).
lations
9.2
9.3
9.4
9.5
Algebra Tiles – Visualize multiplying and factoring
algebraic expressions
Students do not have to factor by
grouping.
Factoring Speical Products GIZMO
Factor
x2+2x+5
Multiply Polynomials
2x2y+4xy-30y
-3x2-3
X2-25
3x2y-21xy+3xy2
Literacy Elements
A- This factoring problem is done incorrectly. Factor it correctly (if
factoring is possible), and then explain what the student may have been
thinking when they made the mistake.
x2  5x  6
x  2x  3
x2  5x  6  0
CC- Compare and contrast
and
5 x  6  4
CR- Have students complete a method of operation activity for
factoring. Part 1: Write out in words the steps for factoring the
difference of two squares ( x 2  b 2 ). Part 2: Write out the steps for
factoring a perfect square trinomial ( x 2  4 x  4 ). Part 3: Complete this
statement “One thing I discovered about factoring in general is …”
This activity can be found in reproducible form in Algebra Out Loud
Page 99.
LM- Create a class power point about mistakes students make when
factoring. To begin this assignment have students write a paragraph
about what they believe is the most common mistake when learning to
factor. Use this assignment to group students for the assignment. The
completed assignment would be a great way to review factoring before
the EOC.
NAGR- Write a paragraph explaining the Zero Property product. Be sure to
include when it can be used to solve a problem and how to use it.
V- Have students work in groups to create a rap or jingle that explains
factoring. Encourage students to be creative. Have groups perform
their creation. Make copies of the work for all students to use when
studying.
Working Document Summer 2008
E- Explain the greatest common factor, how to factor it out of a
problem, and why it is an important first step in factoring.
J- Compare the process of factoring with the process of simplifying
polynomial equations. Consider the factors (x – 2) and (x + 3) to guide
your writing.
Teacher Notes:
Check your Navigation series of books
 Project Interactive









GeoGebra
National Library of Virtual Manipulatives
Connected Mathematics Project
Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
Working Document Summer 2008
Concept: Quadratics
Timeline: 8 days
Standard:
The student will demonstrate through the mathematical processes an understanding of quadratic
relationships and functions. EA-6
Essential Vocabulary
Quadratic
Parabola
Maximum
Minimum
Indicator

EA-6.1
Analyze the effects of changing the
leading coefficient a on the graph of
y  ax 2 .
EA-6.2
Analyze the effects of changing the
constant c on the graph of
y  x2  c.
EA-6.5
Carry out a graphic procedure to
approximate the solutions of
quadratic equations.
EA-3.5
Carry out a procedure to graph
parent functions (including y = x2)
Txtbk
Correlations
10.1
Roots
Zeros
Resources
Compare Parent Graph to Transformations
Solutions
Leading coefficient
Domain
Examples of Essential Tasks
How do the graphs of y  ax 2
and y  ax 2 differ?
Graph Transformation Practice
How do the graphs of y  3x 2
Graph Transformation Discovery
and y  3x 2 differ?
Algebra Tools
How do the graphs of y  x 2
Quadratic Function Explorer
and y 
1 2
x differ?
2
What does decreasing the
constant c by 2 units in an
equation of the form
y  x 2  c do to its graph?
Estimate the solutions to the
graph below.
Working Document Summer 2008
Estimate the solutions to
0  16t 2  10t  1
graphically.
Graph y = x2
And know it is a parent
function.
EA-6.3
Analyze the graph of a quadratic
function to determine its equation.
EA-6.4
Carry out a procedure to solve
quadratic equations by factoring.
EA-6.6
Analyze given information to
determine the domain of a quadratic
function in a problem situation.
10.2
Family of Graphs
Matching graphs to factored forms
of equations by recognizing roots.
Algebra Tools
The area of a rectangle with a
perimeter of 500 cm is
modeled by the function
A  l 2  500l where l is the
length of the rectangle. What
is the reasonable domain for
this problem?
A steel wrecking ball is
dropped from the roof of a 64
foot tall building. The ball’s
height is modeled by
h  16t 2  64 where t is time
and h is height. Find the
domain of the function in this
context.
Working Document Summer 2008
A fish jumps out of the water.
His path is given by
h  2d 2  2d as shown in the
graph
What is the domain of the
function h  2d 2  2d in this
context?
Literacy Elements
A- David says the quadratic y x 4 has one solution. He says the
2
solution is 4. Is David correct? What is the correct solution? How will
you prove this to David? Where do you think David made his mistake?
 2x2  4  0
CC- Compare and contrast the quadratics and
.
2x2  4  0
Be sure to include write complete sentences and use correct
terminology.
CR- Write a word problem involving two real numbers that could be
solved with the equation x (9 – X) = 14. Explain how to solve the
problem by graphing and algebraically. Solve the problem.
E- Entry Slip – List the homework problem you thought was the
hardest. What did you do to try and solve the problem? Were you
successful?
L- Depict the nursery rhyme Jack and Jill with a parabola. Be sure to
label the x and y axis properly. What are a reasonable range and
domain for your graph?
M- Create a handout or foldable for fellow students that explains
quadratics and how their graphs are changed when a and c change. Be
creative.
NAG- Describe how to find the roots of x 2  2 x  8 by factoring,
graphing, and using a table. Using your description find the roots all
three ways.
R- A quadratic model (equation) is a good model for describing …
V- Write a math concepts paragraph about Parabolas. The paragraph
must contain at least ten mathematical terms, two or three sentences that
describe the features and characteristics of a parabola, complete
sentences, an introduction, and a conclusion. A template for this
activity: Algebra Out Loud Page 126
Working Document Summer 2008
J- Explain in detail how to use a graphing calculator to find the roots of
a quadratic equation. Be sure to use correct terminology and assume
the person you are talking to has never used a graphing calculator.
Also, include what to do if the answer is not an integer.
Teacher Notes:
Check your Navigation series of books
 Project Interactive









GeoGebra
National Library of Virtual Manipulatives
Connected Mathematics Project
Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer
Working Document Summer 2008
Concept: Other Topics – Matrices, Radicals, Parent Functions
Timeline: 6 days
Standard:
The student will demonstrate through the mathematical processes an understanding of the real number
system and operations involving exponents and algebraic expressions. EA-2.
.
Vocabulary
Radical Expression
Radicand
Indicator
EA-2.2
Apply the laws of
exponents and roots to solve
problems.
Inverse variation
Dimensional analysis
Txtbk
Correlations
11.1
Matrix
Scalar Multiplication
Resources
Laws of Exponents
Exponent Practice
Examples of Essential Tasks
Simplify

3

2
2 3
90
2 8
EA-3.5
Carry out a procedure to graph
parent functions (Including y 
x)
11.3
follow
up
Compare Parent Graph to Transformations
Working Document Summer 2008
Graph y  x .
Graph Transformation Practice
Graph Transformation Discovery
EA-3.6
Classify a variation as either direct
or inverse.
12.1
Direct Variation GIZMO
Students must be able to identify
problems as direct or inverse
variation.
EA- 3.8
Apply proportional reasoning to
solve problems.
EA-2.4
Use dimensional analysis to convert
units of measure within a system.
12.3
Proportions in similar triangles
Students must be able to recall the
conversions contained in the
support document conversions.
(page 13)
Students do not have to convert
between systems.
A bedroom has 11,664 square
inches of floor space. How many
square feet of floor space does the
bedroom have?
A car is traveling at 70 miles per
hour on an interstate highway. a.
How many feet per second is the
car traveling? b. If a football field
is 300 feet long, how many football
field lengths does the car travel in
one second?
Working Document Summer 2008
 2  1  1
 8 7    5

 
 2  13 1
 0 17   6

 
 1 20  5
 3 11  5
4  6 0 10 
 8 2 1 
EA-2.9
13.2
Carry out a procedure to perform
operations with matrices (including
addition, subtraction, and scalar
multiplication).
EA-2.10
Represent applied problems by using
matrices.
1
3
 4
 1
0 
The following is sales data from a
department store sales person who
works part time.
Sales Data:
Monday: 10 shirts, 8 pants, 10
shorts, 2 hats
Tuesday: 9 shirts, 13 pants, 7
shorts, 0 hats
Wednesday: 15 shirts, 14 pants, 6
shorts, 7 hats
Represent the sales data using a
matrix.
EA-3.5
Carry out a procedure to graph parent
functions including
y  x, y  x 2 , y  x , y  x , and
y
1
x
Compare Parent Graph to Transformations
Graph Transformation Practice
Graph Transformation Discovery
Some of these parent functions
are not covered in the book. Be
sure to cover how these graphs
look.
Working Document Summer 2008
Literacy Elements
A- Silent Conversation – Pick 4 difficult dimensional analysis
problems. Divide students into groups of four. Each student in the
group has a different problem. Students are given one minute to start
working on the problem. After a minute they pass papers to the right.
Students are to review their peers work and continue if they agree or
indicate any errors they find, correct them, and continue. This
continues until all four students have worked on all four problems. If a
problem is completed and a student agrees with the work, encourage
them to come up with a different method for solving the problem. Have
the group review all of the work and come to agreement on the correct
answers. This is a great way to review dimensional analysis. Students
work extra hard if prizes are awarded to the group with the most correct
answers and/or for most ways to solve a problem.
CC- Compare and contrast direct variation and inverse variation. Give
one algebraic, graphically, and word problem example of each.
CR- Explain in words how you would simplify 50  100  4 2 .
Then simplify the expression.
E- Entry Slip- Write everything you know about direct variation and
inverse variation.
J- Write a paragraph explaining what a matrix is and how it is useful in
the real world.
Teacher Notes:
Check your Navigation series of books
 Project Interactive


GeoGebra
National Library of Virtual Manipulatives
LM- Have students find an example of a matrix in the newspaper and
write a paragraph explaining the matrix.
NAG- Represent each of the parent functions in a graph and a table.
Write one algebraic equation that belongs to each family of equations.
Write at least one complete sentence describing each of the parent
functions.
R- The most confusing idea with parent functions is … The easiest
parent function for me to remember is …because… The hardest parent
function for me to understand is …because…
V- Create an editorial cartoon that defines and illustrates one of the
vocabulary words from this unit.

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Working Document Summer 2008
Connected Mathematics Project
Select Math
MathBits
Math / Scientific Calculator
NCTM Illuminations
Graphical Linear Function Explorer
Graphical Quadratic Function Explorer