Algebra, Functions, and Data Analysis
ALGEBRA FUNCTIONS AND DATA ANALYSIS A GUIDE​ (Created 2014)
Amherst County Public Schools
Introduction
The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards
of Learning and amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that
are measured by the Standards of Learning assessments. The Curriculum Framework provides additional guidance to school
divisions and their teachers as they develop an instructional program appropriate for their students. It assists teachers in their lesson
planning by identifying essential understandings, defining essential content knowledge, and describing the intellectual skills students
need to use. This supplemental framework delineates in greater specificity the content that all teachers should teach and all students
should learn.
Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The
format of the Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be
the focus of instruction for each standard. The Curriculum Framework is divided into two columns: Essential Understandings and
Essential Knowledge and Skills. The purpose of each column is explained below.
Essential Understandings and Questions
This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an
understanding of the Standards of Learning.
Essential Knowledge and Skills
Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each
standard is outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be
the key knowledge and skills that define the standard.
The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and
should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to
apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise.
Textbook Overview
Course Text: Algebra, Functions, and Data Analysis: A Virginia Course!
Supplemental Materials: Teacher’s Resource Guide and Printed Test Bank, TestGen Testmaker, www.MathXLforSchool.com website!
Publisher: Pearson Custom Publishing.
Algebra, Functions, and Data Analysis
Suggested Sequence of Instruction and Pacing
First Nine Weeks
SOL
Algebra 1 Review
AFDA 1, 2, 4
AFDA 1, 2, 4
Chapter/Sections/Topic
Review Algebra 1 SOLs for retesters
Chapter 1: Introduction to Problem Solving and Mathematical
Models; Sections 1 - 14
Chapter 2: Linear Function Models and Problem Solving; Sections
1-6
Review and Nine Weeks Benchmark
First Nine Weeks Total
Time Frame (Tentative)
15 days (included in the 24 days for Chapter 1)
24 Days
14 Days
7 Days
45 Days
Second Nine Weeks
SOL
AFDA 1, 3, 4, 8
AFDA 3
AFDA 1, 2, 4
Chapter/Sections/Topic
Chapter 2: Linear Function Models and Problem Solving; Sections
7 – 10
Chapter 3: System of Linear Equations and Inequalities; Sections
1–5
Chapter 4: Problem Solving with Quadratic and Variation Function
Models; Sections 1 – 4
Review and Nine Weeks Benchmark
First Nine Weeks Total
Time Frame (Tentative)
9 Days
16 Days
13 Days
7 Days
45 Days
Algebra, Functions, and Data Analysis
Third Nine Weeks
SOL
AFDA 1, 2, 3
AFDA 7, 8
A9
Chapter/Sections/Topic
Chapter 4: Problem Solving with Quadratic and Variation Function
Models; Sections 5 – 10
Chapter 7: Problem Solving with Graphical and Statistical
Methods; Sections 3, 4, 9, and 10
Mean Absolute Deviation
Review and Nine Weeks Benchmark
First Nine Weeks Total
Time Frame (Tentative)
15 Days
20 Days
3 Days
7 Days
45 Days
Fourth Nine Weeks
SOL
AFDA 1, 2, 4, 6
AFDA 7, 8
Chapter/Sections/Topic
Chapter 6: Probability Models; Sections 1 - 3, and 6
Chapter 7: Problem Solving with Graphical and Statistical
Methods; Sections 1, 2, 7
Chapter 8: Problem Solving with Financial Models; Sections 1 and
2
Review and Nine Weeks Benchmark
First Nine Weeks Total
Time Frame (Tentative)
10 Days
10 Days
10 Days
7 Days
45 Days
Algebra, Functions, and Data Analysis
First Nine Weeks Instruction
SOL/Essential Knowledge and Skills
Textbook/Cha
pter and
Section
1.1: Wild
About Harry
1.2: The
Classroom
Resources
Essential Questions
Student Extra What does the problem-solving
Practice
strategy include?
Workbook: p.
1
What is the four step process for
solving problems?
Vocabulary
Arithmetic Sequence
Geometric Sequence
Fibonacci Sequence
Inductive Reasoning
Deductive Reasoning
1.3: Make Me Student Extra What does the problem-solving
an Offer
Practice
strategy include?
Workbook:
p. 2
What is the four step process for
solving problems?
Formula
1.4:
Proportional
Reasoning
Student Extra What is a ratio?
Practice
Workbook:
What is a proportion?
p. 3
How do you solve for the missing
piece of information in a proportion
Ratio
Cross Multiplication
Proportion
Percent
Equivalent
Proportional Reasoning
1.5: Fuel
Economy
Student Extra What is a rate?
Practice
Workbook:
What are the methods for solving
p. 5
problems with rates?
Rate
Unit Analysis
Direct Method
Proportion Method
Algebra, Functions, and Data Analysis
AFDA.1
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
(f) intervals in which the function is
increasing/decreasing
1.6: Hot in
Texas
Student Extra
Practice
Workbook:
p. 5
What is the relationship between
input and independent variable, and
what is the relationship between
output and dependent variables?
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
AFDA.1
1.7: Fill’er Up
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
(c) domain and range
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
Student Extra What is the domain and range of a
Practice
function?
Workbook:
p. 6
Describe function notation of an
equation.
Variable
Function
Input
Output
Independent
Dependent
Ordered Pairs
Numerically Defined
Function
Rectangular Coordinate
System
Quadrants
Increasing
Decreasing
Constant
Rational Number
Irrational Number
Independent Variable
Dependent Variable
Domain
Practical Domain
Range
Practical Range
Increment
Function Notation
Algebra, Functions, and Data Analysis
AFDA.1
1.8:
The student will investigate and
Mathematical
analyze function (linear, quadratic,
Modeling
exponential, and logarithmic) families
and their characteristics.
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
AFDA.1
1.9:
The student will investigate and
Fund-Raiser
analyze function (linear, quadratic,
Revisisted
exponential, and logarithmic) families
and their characteristics.
(a) continuity
New AFDA.1a – Delete Continuity
AFDA. 4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
What is the process of mathematical
modeling?
Student Extra What does it mean if a graph is said
Practice
to be continuous?
Workbook:
p. 7
Mathematical Model
Mathematical Modeling
Evaluated
Equation
Numerical Method
Graphical Method
Solution
Continuous
Discontinuity
Algebra, Functions, and Data Analysis
AFDA.1
1.10: Leasing
The student will investigate and
a Copier
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
AFDA.1
1.11:
The student will investigate and
Comparing
analyze function (linear, quadratic,
Energy Costs
exponential, and logarithmic) families
and their characteristics.
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
AFDA.4
1.12: Summer
The student will transfer between and Job
analyze multiple representations of
Opportunities
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
What are the steps for solving an
equation algebraically?
Student Extra What are the steps for solving an
Practice
equation algebraically?
Workbook:
p. 8
Inverse Operations
Algebra, Functions, and Data Analysis
AFDA.1
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
(b) local and absolute maxima and
minima ​AFDA.1b – [Moved to
AFDA.1c]
(f) intervals in which the function is
increasing/decreasing
AFDA. 4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
1.13: Graphs
Tell Stories
(focus on
dependent and
independent
variables and
vertical license
test)
Student Extra What is the Vertical Line Test and
Practice
what does it tell us?
Workbook:
p. 9
When looking at the graph of a
function, describe a maximum and
minimum point.
Maximum Point
Local Maximum Value
Minimum Point
Local Minimum Value
Vertical Line Test
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic exponential, and
logarithmic.)
1.14: Heating
Schedule
(focus on
vertical shifts
only and omit
absolute value
functions)
Student Extra What is a translation of a graph?
Practice
Workbook:
p. 10
Vertical Shift
Horizontal Shift
Translation
AFDA.1
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
2.1: How Fast Student Extra Describe the average rate of change.
did You Lose? Practice
Workbook:
p. 11
Scatterplot
Average Rate of Change
Delta Notation
2.2: The
Snowy Tree
Cricket
Linear Function
Slope
Increasing Function
Decreasing Function
Horizontal Line
Student Extra What is a linear function?
Practice
Workbook:
What is the slope of a linear function
p. 12
and its formula?
Algebra, Functions, and Data Analysis
(f) intervals in which the function is
increasing/decreasing
Vertical Line
AFDA.1
2.3:
The student will investigate and
Depreciation
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
(d) zeros
(e) intercepts
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
AFDA.1
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
(e) intercepts
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic exponential, and
logarithmic.)
Student Extra What are the x and y intercepts of a
Practice
function?
Workbook:
p. 13
What is the slope-intercept form of
an equation of a line?
What is a positive/negative slope?
2.4: Family of Student Extra What is a vertical/horizontal shift of
Functions
Practice
a graph?
Workbook:
p. 14
What is a reflection of a graph?
Vertical Intercept
Y-Intercept
Slope-Intercept Form
Horizontal Intercept
X-Intercept
Positive Slope
Negative Slope
Vertical Shift
Horizontal Shift
Reflection
Stretch Factor
Vertical Stretch
Vertical Shrink
Transformations
Algebra, Functions, and Data Analysis
AFDA.1
2.5: Predicting
The student will investigate and
Population
analyze function families and their
characteristics.
(d) intercepts
AFDA.3
The student will collect data and
generate an equation for the curve of
best fit to model real-world problems
or applications. Students will use the
best fit equation to interpolate function
values, make decisions, and justify
conclusions with algebraic and/or
graphical models.
AFDA.3 – Delete Generate and use a
best fit logarithmic equation
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
Student Extra What is the relative error and how is
Practice
it calculated?
Workbook:
p. 15
Error
Observed Value
Expected Value
Relative Error
Second Nine Weeks Instruction
SOL/Essential Knowledge and Skills
Textbook/Chapter
and Section
Resources
Essential Questions
Vocabulary
Algebra, Functions, and Data Analysis
AFDA.2
2.7: Body Fat
The student will use knowledge of
Percentage
transformations to write an equation
given the graph of a function (linear,
quadratic exponential, and
logarithmic.)
AFDA.3
The student will collect data and
generate an equation for the curve
(linear, quadratic, exponential, and
logarithmic) of best fit to model realworld problems or applications.
Students will use the best fit equation
to interpolate function values, make
decisions, and justify conclusions with
algebraic and/or graphical models.
AFDA.3 – Delete Describe errors
inherent in extrapolation beyond the
range of the data
AFDA.3 – Delete Estimate the
correlation coefficient when given
data and/or scatterplots
Student Extra
What is a regression line?
Practice
Workbook: p. 17
- 18
AFDA.3
2.8: Plot Before
The student will collect data and
Calculating
generate an equation for the curve
(linear, quadratic, exponential, and
logarithmic) of best fit to model realworld problems or applications.
Students will use the best fit equation
to interpolate function values, make
decisions, and justify conclusions with
algebraic and/or graphical models.
Student Extra
Practice
Workbook: p. 17
- 18
Scatterplot
Outlier
Residuals
Least Squares Regression
Line
Linear Correlation
Coefficient
Lurking Variable
Algebra, Functions, and Data Analysis
AFDA.3
2.9: College
The student will collect data and
Tuition
generate an equation for the curve
(linear, quadratic, exponential, and
logarithmic) of best fit to model realworld problems or applications.
Students will use the best fit equation
to interpolate function values, make
decisions, and justify conclusions with
algebraic and/or graphical models.
Student Extra
What is a linear regression
Practice
equation?
Workbook: p. 17
- 18
AFDA.3
2.10: Body Parts
The student will collect data and
generate an equation for the curve
(linear, quadratic, exponential, and
logarithmic) of best fit to model realworld problems or applications.
Students will use the best fit equation
to interpolate function values, make
decisions, and justify conclusions with
algebraic and/or graphical models.
Student Extra
Practice
Workbook: p. 17
- 18
AFDA.5
3.1: Business
The student will determine optimal
Checking Account
values in problem situations by
identifying constraints and using linear
programming techniques.
Student Extra
Practice
Workbook: p. 21
- 22
AFDA.5
3.2: Modeling a
The student will determine optimal
Business
values in problem situations by
identifying constraints and using linear
programming techniques.
Student Extra
Practice
Workbook: p. 21
- 22
What are the ways to find the
solution to a System of
equations?
What does the solution to a
system of equations represent?
What is a consistent and
inconsistent system of
equations?
Regression Line
Line of Best Fit
System of Linear Equations
Numerical Method
Graphical Method
Substitution Method
Consistent
Inconsistent
Algebra, Functions, and Data Analysis
AFDA.5
3.3: Healthy
The student will determine optimal
Lifestyles
values in problem situations by
identifying constraints and using linear
programming techniques.
Students Extra
Practice
Workbook: p. 23
- 24
Addition Method
AFDA.5
3.4: How Long
The student will determine optimal
Can You Live
values in problem situations by
identifying constraints and using linear
programming techniques.
Student Extra
Practice
Workbook: p. 25
- 26
What des to solution set to an
inequality represent?
Inequality
Compound Inequality
Closed Interval
Open Interval
AFDA.5
3.5: Will Trees
The student will determine optimal
Grow
values in problem situations by
identifying constraints and using linear
programming techniques.
Student Extra
Practice
Workbook: p. 25
- 26
What is a system of Linear
Inequalities?
Half - Plane
System of Linear
Inequalities
Corner Points
AFDA.1
4.1: The Amazing
The student will investigate and
Property of Gravity
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic, exponential, and
logarithmic).
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
Student Extra
Describe a parabola.
Practice
Workbook: p. 29
- 30
Parabola
Quadratic Equation
Algebra, Functions, and Data Analysis
AFDA.1
4.2: Baseball and
The student will investigate and
Sears Tower
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics. Key concepts
include:
(c) domain and range
(e) intercepts
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic, exponential, and
logarithmic).
Students Extra
Practice
Workbook: p. 29
- 30
What is the general form of a
quadratic function?
What are the quadratic, linear
and constant terms of a
quadratic function?
What is the shape of the graph
of a quadratic function?
AFDA.1
4.3: The Shot Put
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics. Key concepts
include: (b) local and absolute maxima
and minima
(c) domain and range
(e) intercepts
(f) intervals in which the function is
increasing/decreasing
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic, exponential, and
logarithmic).
Students Extra
Practice
Workbook: p. 31
- 32
What is axis of symmetry of a
parabola?
What is the vertex of a
parabola?
What are x-intercepts and
y-intercepts?
In general what is the domain
of a quadratic function?
What is the range of a quadratic
function?
Quadratic Term
Linear Term
Constant Term
Coefficients
Turning Point
Algebra, Functions, and Data Analysis
AFDA.1
4.4: Per Capita
The student will investigate and
Personal Income
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics. Key concepts
include:
(c) zeros
(d) intercepts
Students Extra
What is the standard form of a
Practice
quadratic equation?
Workbook: p. 31
- 32
Third Nine Weeks Instruction
Quadratic Equation
Zero of the Function
Algebra, Functions, and Data Analysis
SOL/Essential Knowledge and Skills
Textbook/Chapter
and Section
Resources
Essential Questions
Vocabulary
What is the common factor of a
group of terms?
What is the Zero Product
Principle?
Zero Product Principle
Factoring
Common Factor
Greatest Common Factor
AFDA.1
4.5: Sir Isaac
The student will investigate and
Newton
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics.
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
Student Extra
Practice
Workbook: p. 33
- 34
AFDA.1
4.6: Ups and
The student will investigate and
Downs
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics. Key concepts
include: (b) local and absolute maxima
and minima
(d) zeros
(e) intercepts
AFDA.4
The student will transfer between and
analyze multiple representations of
functions including algebraic
formulae, graphs, tables, and words.
Students will select and use
appropriate representations for
analysis, interpretation, and prediction.
Student Extra
What is the quadratic formula
Practice
and what is it used for?
Workbook: p. 35
Quadratic Formula
Algebra, Functions, and Data Analysis
AFDA.2
4.7: Air Quality in
The student will use knowledge of
Atlanta
transformations to write an equation
given the graph of a function.
AFDA.3
The student will collect data and
generate an equation for the curve
(linear, quadratic, exponential, and
logarithmic) of best fit to model realworld problems or applications.
Students will use the best fit equation
to interpolate function values, make
decisions, and justify conclusions with
algebraic and/or graphical models.
AFDA.3 – Delete Describe errors
inherent in extrapolation beyond the
range of the data
AFDA.3 – Delete Estimate the
correlation coefficient when given
data and/or scatterplots
Student Extra
What is the shape of the graph
Practice
of a quadratic regression
Workbook: p. 36 equation?
Quadratic Regression
Equation
AFDA.1
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics. Key concepts
include: (b) local and absolute maxima
and minima
(f) intervals in which the function is
increasing / decreasing
(g) end behaviors
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic, exponential, and
Student Extra
Practice
Workbook: p. 37
- 38
Vary Directly
Proportionality Constant
Direct Variation
Constant of Variation
Power Functions
4.8: A
Thunderstorm
4.9: The Power of
Power Function
Describe the graph of direct
variation.
What is the equation for direct
variation?
What is the constant of
proportionality?
What is the general for of a
power equation?
Algebra, Functions, and Data Analysis
logarithmic).
AFDA.1
4.10: Speed Limits
The student will investigate and
analyze function (linear, quadratic,
exponential, and logarithmic) families
and their characteristics. Key concepts
include: (b) local and absolute maxima
and minima
(f) intervals in which the function is
increasing / decreasing
(g) end behaviors
AFDA.2
The student will use knowledge of
transformations to write an equation
given the graph of a function (linear,
quadratic, exponential, and
logarithmic).
Student Extra
Practice
Workbook: p. 37
- 38
What is a horizontal and vertical
asymptote?
What is the general form of a
inverse variation function?
What is the general shape of the
graph of inverse variation?
Horizontal Asymptote
Vertical Asymptote
Inverse Variation Function
Constant of Variation
AFDA.8
The student will design and conduct
an experiment/survey. Key concepts
include: (d) data collection
(e) data analysis and reporting
Students Extra
Practice
Workbook: p. 55
- 56
What is a frequency
distribution?
Frequency
Dot Plot
Frequency Distribution
Classes
Class Width
Stem
Leaf
Student Extra
Practice
Workbook: p. 57
- 58
What are the measures of central Central Tendency
tendency and what information Mean
does each provide?
Median
Midrange
Mode
Resistant Measure
7.3: The Class
Survey
AFDA.8
7.4: Class Surveys
The student will design and conduct
Continued
an experiment/survey. Key concepts
include: (e) data analysis and reporting
Algebra, Functions, and Data Analysis
AFDA.7
The student will analyze the normal
distribution. Key concepts include:
a) characteristics of normally
distributed data
7.9: A Switch
Decision
Students Extra
Practice
Workbook: p. 61
- 62
AFDA.7
The student will analyze the normal
distribution. Key concepts include:
a) characteristics of normally
distributed data
c) normalizing data using z-scores
7.10: What is
Normal
Students Extra
What is the formula for
Practice
calculating a z-score?
Workbook: p. 63
- 64
A.9
The student, given a set of data, will
interpret variation in real world
context and calculate and interpret
mean absolute deviation, standard
deviation and z-scores
What is the standard deviation
Standard Deviation
of a group of data?
Boxplot
What is the variability of a
Five-number Summary
frequency distribution?
What is the range of a frequency
distribution?
What is a box and whisker plot
and its five number summary?
How do you calculate the mean
absolute deviation?
Normal Distribution
Normal Curve
Z-scores
Mean Absolute Deviation
Algebra, Functions, and Data Analysis
Fourth Nine Weeks Instruction
SOL/Essential Knowledge and Skills
Textbook/Chapter
and Section
Resources
Essential Questions
Vocabulary
AFDA.6
The student will calculate
probabilities. Key concepts include:
(e) Law of Large Numbers
6.1: Chances Are
Students Extra
Practice
Workbook: p. 49
- 50
How do you calculate the
probability of an event
happening and what does it
mean?
What are the properties of
Probabilities?
Relative Frequency
Event
Probability of an Event
Random
Sample Space
Probability Distribution
Theoretical Probability
Experimental Probability
Simulation
AFDA.6
The student will calculate
probabilities. Key concepts include:
(d) counting techniques
6.2: Choices
Students Extra
Practice
Workbook: p. 49
- 50
What can a Tree Diagram tell
us?
What is a sample space?
What is the complement of an
event?
Tree Diagram
Complement of an Event
Venn Diagram
Algebra, Functions, and Data Analysis
AFDA.6
The student will calculate
probabilities. Key concepts include:
(b) dependent and independent events
(c) addition and multiplication rules
6.3: Experimenting Student Extra
with Probabilities
Practice
Workbook: p. 51
- 52
AFDA.6
The student will calculate
probabilities. Key concepts include:
(d) counting techniques
6.6: Colorful
Probabilities
What is the Multiplication
Independent
Principle of Probability?
Dependent
What does it mean if two events Mutually Exclusive
are mutually exclusive?
What are dependent and
independent events?
Algebra, Functions, and Data Analysis
AFDA.8
The student will design and conduct
an experiment/survey. Key concepts
include:
b) sampling technique
c) controlling sources of bias and
experimental error
d) data collection
e) data analysis and reporting
What is statistics?
7.1: Visualizing
Trends
Student Extra
Practice
Workbook: p. 55 56
7.2: Bald Eagle
Population
Student Extra
Practice
Workbook: p. 55 56
7.7: Statistical
Survey
7.8: What’s the
Cause?
Students Extra
Summarize what a good
Practice
experimental design is.
Workbook: p. 59
- 60
8.1: Income and
Expense
Workbook: p. 65
– 66
Scale Factor
Experimental Unit
Control Group
Treatment
Statistically Significant
Double-blind
Design of Experiments
Placebo
Placebo-Effect
Replication
Algebra, Functions, and Data Analysis
8.2: Time is
Money Revisited
Workbook: p. 65
- 66
Simple Interest
Compound Interest
Future Value
Effective Annual Yield
Annual Percentage Yield
Present Value
Instructional Example Questions
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
a) continuity;
The distance between two cities on a map is directly proportional to the actual distance between the two cities.
Algebra, Functions, and Data Analysis
a) On a map, the distance between Richmond and Roanoke is 3 inches. In actuality, there are 180 mile between Richmond and Roanoke.
Determine the constant of proportionality.
b) On the same map, Richmond and Alexandria are 1.5 inches apart. What is the actual distance between Richmond and Alexandria?
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
b) local and absolute maxima and minima;
Consider the equation. Determine whether the function has maximum or
minimum value. State the maximum or minimum value. Graph the function.
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
c) domain and range;
Algebra, Functions, and Data Analysis
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
d) zeros;
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
Algebra, Functions, and Data Analysis
e) intercepts;
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
f) intervals in which the function is increasing/decreasing;
Algebra, Functions, and Data Analysis
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
g) end behaviors; and
AFDA.1 The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include
h) asymptotes.
AFDA.2 The student will use knowledge of transformations to write an equation, given the graph of a function (linear, quadratic, exponential, and logarithmic).
Perform a sequence of transformations to obtain the graph of the following
function. Do this step by step and explain each step along the way.
y = (x + 4)2 − 7
Algebra, Functions, and Data Analysis
AFDA.3 The student will collect data and generate an equation for the curve (linear, quadratic, exponential, and logarithmic) of best fit to model real-world
problems or applications. Students will use the best fit equation to interpolate function values, make decisions, and justify conclusions with algebraic
and/or graphical models.
AFDA.4 The student will transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and
words. Students will select and use appropriate representations for analysis, interpretation, and prediction
Algebra, Functions, and Data Analysis
AFDA.5 The student will determine optimal values in problem situations by identifying constraints and using linear programming techniques.
AFDA.6 The student will calculate probabilities. Key concepts include
a) conditional probability;
AFDA.6 The student will calculate probabilities. Key concepts include
b) dependent and independent events;
Find the probability that you will roll a six and then a five when you roll a die
twice.
A bag contains 3 red marbles, 2 green marbles, and 4 blue marble. Two marble
are drawn randomly from the bag and not replaced. Find the probability that
both marbles are blue.
Algebra, Functions, and Data Analysis
AFDA.6 The student will calculate probabilities. Key concepts include
c) addition and multiplication rules;
AFDA.6 The student will calculate probabilities. Key concepts include
d) counting techniques (permutations and combinations); and
AFDA.6 The student will calculate probabilities. Key concepts include
e) Law of Large Numbers
A local sub restaurant offers 3 types of bread, 4 types of meat, and 3 types of cheese.
a) If a sub has to have exactly one type of bread, one type of meat, and one type of cheese, how many subs can be made?
b) H0w many subs can be made if you do not have to have cheese?
AFDA.7 The student will analyze the normal distribution. Key concepts include
a) characteristics of normally distributed data;
Algebra, Functions, and Data Analysis
Determine the z-score for the given value in a normal curve with mean 60 and standard deviation 5.
a) 63
b) 57
AFDA.7 The student will analyze the normal distribution. Key concepts include
b) percentiles;
Your teacher reported that the class average on the last test was 80 with a standard deviation of 10. Students’ grades followed a normal curve. Your teacher had
the whole class retake the test. On the second test, score were approximately normal, but the mean increased to 95 with a standard deviation of 5. You
got a 93 on the first test and a 98 on the second test. Relative to the rest of the class, on which test did you perform better?
AFDA.7 The student will analyze the normal distribution. Key concepts include
c) normalizing data, using z-scores; and
AFDA.7 The student will analyze the normal distribution. Key concepts include
d) area under the standard normal curve and probability.
Using the z-tables or a graphing calculator to find the probability of the given x-value in a normal curve with mean 150 and standard deviation 25.
a) x less than 140
Algebra, Functions, and Data Analysis
b) x between 135 and 160
AFDA.8 The student will design and conduct an experiment/survey. Key concepts include
a) sample size;
There are 1700 students at your school. You would like to know how many enjoy the food in school. Would it be reasonable to conduct a census to obtain this
information. Explain.
AFDA.8 The student will design and conduct an experiment/survey. Key concepts include
b) sampling technique;
There are 1700 students at your school. You would like to know how many enjoy the food in school. What are the ways to select a random sample?
AFDA.8 The student will design and conduct an experiment/survey. Key concepts include
c) controlling sources of bias and experimental error;
A research doctor has developed a new medication to relieve the joint swelling of arthritis. Twenty patients have volunteered to take part in an experiment to
determine if the new medication is more effective than their old medication. How can the control group and placebo effect be managed so patients still
receive some medication?
AFDA.8 The student will design and conduct an experiment/survey. Key concepts include
d) data collection; and
A research doctor has developed a new medication to relieve the joint swelling of arthritis. Twenty patients have volunteered to take part in an experiment to
determine if the new medication is more effective than their old medication. Describe how this experiment should be conducted and the data collected?
AFDA.8 The student will design and conduct an experiment/survey. Key concepts include
e) data analysis and reporting.
(Integrated throughout the course)
Algebra, Functions, and Data Analysis
Additional Instructional Resources
http://www.corealgebra1.com/
http://www.glencoe.com/sites/virginia/teacher/mathematics/index.html
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/solreview.htm
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/modules.html