©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
Major Concept #1: Linear Function Models
Overarching
Idea
Teacher
Guiding
Questions
Matrix
#
Matrix
Strand
Displaying & Interpreting
Data
Displaying & Interpreting Data
516
12 Days
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving linear equations and inequalities.




How does rate of change relate to the slope of a linear function?
How do you determine when a function has zero slope or undefined slope?
How can you determine the solution to a system of linear equations?
How can you determine the solution set of a linear inequality?
TEKS
Knowledge & Skill
Student Expectation
The student uses graphical
and numerical techniques
to study patterns and
analyze data. (M.2)
TAKS
OBJ
Resource
Interpret information from
various graphs, including
line graphs, bar graphs,
circle graphs, histograms,
and scatter plots to draw
conclusions from data.
(M.2.A)
Use of the graphing calculator is encouraged as an aid in
making connections between numerical, algebraic and
geometric representations of variables and functions. Activities
in the Teacher’s Resource Guide Section 4 can be used with
the whole class to supplement the assigned activities.
Students are encouraged to use the graphing calculator to
verify results after manually sketching the graphs and solving
the problems algebraically.
Group 1:
Activity 3.1
page 239 How Fast Did You
Lose?
Exercises page 244
(M.2.A)
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 1 of 9
Teacher Tools
Principles of Learning Tip: AT and CE
Students will develop both mathematical intuition and algebraic
skills through activities based on real-life situations involving
linear functions.
Accelerated Curriculum for
Mathematics Exit TAKS
(ACM)
Activity 3.2
page 248 The Snowy Tree
Cricket
Exercises page 256
(M.2)
Time/
Pace
Mathematical Models with
Applications:
Chapter 3
Function Models and Problem
Solving
Students will continue to
build on the K-8 and
Algebra I foundations as
they expand their
understanding through
other mathematical
experiences. Students will
use algebraic, graphical,
and geometric reasoning to
recognize patterns and
structure, to model
information, and to solve
problems from various
disciplines. (B.1)
516
Math Models
2 days
Activity 3.1 Vocabulary:
delta notation (), average rate of change, domain, range
Activity 3.1 Objectives
1. Calculate the average rate of change over an
interval.
2. Determine the practical domain and range of a linear
function.
3. Interpret the graphical representation of average
rate of change.
Activity 3.2 Vocabulary:
linear function, graph, slope (positive, negative, zero,
undefined)
Activity 3.2 Objectives
1. Identify linear functions by a constant rate of
change.
2. Develop the concept of slope as rate of change.
3. Determine the slope of a line drawn through two
points.
4. Use slope to identify increasing and decreasing
linear functions.
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
12 Days (cont’d. from previous page)
Major Concept #1: Linear Function Models (Continued)
Overarching
Idea
Teacher
Guiding
Questions
520
519
520
221
Displaying & Interpreting Data
Displaying & Interpreting Data
516
Matrix
Strand
Patterns,
Generalizations,
Displaying &
Relationships,
Interpreting
Proportional
Data
Reasoning &
Making Predictions
Matrix
#
Math Models
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving linear equations and inequalities.




How does rate of change relate to the slope of a linear function?
How do you determine when a function has zero slope or undefined slope?
How can you determine the solution to a system of linear equations?
How can you determine the solution set of a linear inequality?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Activity 3.3 Vocabulary:
Intercepts (vertical, horizontal, x- and y-), equation of
horizontal line, slope-intercept form of the equation of a line (y
= mx + b), parent function
Activity 3.3 Objectives
1. Determine if a real-life situation can be modeled by a
linear function.
2. Determine the practical meaning of x- and yintercepts.
3. Develop the slope-intercept model of an equation of
a line.
4. Use the slope-intercept formula to determine x- and
y- intercepts.
5. Use transformations of the parent function to
investigate, describe, and predict the effects of
changes to m and b on the graph y = mx + b.
Activity 3.3
page 263 Depreciation
Exercises page 269
(M.2)
The student develops and
implements a plan for
collecting and analyzing
data in order to make
decisions. (M.3)
(M.2.A)
Formulate a meaningful
question, determine the
data needed to answer the
question, gather the
appropriate data, analyze
the data, and draw
reasonable conclusions.
(M.3.A)
ACM:
page 47 Solving Real World
Problems
Activity 3.4
page 274 Predicting
Population
Exercises page 277
Determine the
appropriateness of a model
for making predictions from
a given set of data. (M.3.C)
(M.3)
(M.3.A)
The student uses functional
relationships to solve
problems related to
personal income. (M.5)
Use rates, linear functions,
and direct variation to
solve problems involving
personal finance and
budgeting, including
compensations and
deductions. (M.5.A)
Activity 3.5
page 281 Housing Prices
Exercises page 285
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 2 of 9
Teacher Tools
3 days
Activity 3.4 Vocabulary:
relative error
Activity 3.4 Objectives
1. Write an equation for a linear function given its slope
and y-intercept.
2. Write linear functions in slope-intercept form.
3. Use the slope-intercept form of linear equations to
solve problems.
4. Interpret the slope and y-intercept of linear functions
in contextual situations.
5. Determine the relative error in a measurement or
prediction using a linear model.
Activity 3.5 Vocabulary:
slope-intercept form of an equation
Activity 3.5 Objectives
1. Determine the slope and y-intercept of a line
algebraically and graphically.
2. Determine the equation for a linear function that
includes two given points.
3. Interpret the slope and y-intercept of a linear
function in contextual situations.
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
12 Days (cont’d. from previous page)
Major Concept #1: Linear Function Models (Continued)
Overarching
Idea
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving linear equations and inequalities.




Teacher
Guiding
Questions
221
Matrix
Strand
How does rate of change relate to the slope of a linear function?
How do you determine when a function has zero slope or undefined slope?
How can you determine the solution to a system of linear equations?
How can you determine the solution set of a linear inequality?
TEKS
Knowledge & Skill
Patterns,
Generalizations,
Displaying
Relationships,
&
Communication
Proportional
Interpreting
Reasoning &
Data
Making
Predictions
Matrix
#
Student Expectation
(M.5.A)
TAKS
OBJ
Resource
Time/
Pace
Activity 3.6
page 290 Business Checking
Account
Exercises page 296
609
221
The student uses a variety
of strategies and
approaches to solve both
routine and non-routine
problems. (M.1)
Patterns,
Generalizations,
Displaying
Relationships,
&
Proportional
Interpreting
Reasoning &
Data
Making
Predictions
611
Problem
Solving
(M.5)
514
Analyze data to make
decisions about banking.
(M.5.C)
Use multiple approaches
(algebraic, graphical, and
geometric methods) to
solve problems from a
variety of disciplines.
(M.1.B)
Select a method to solve a
problem, defend the
method, and justify the
reasonableness of the
results. (M.1C)
(M.5.A)
ACM:
page 51 It Costs to Talk
page 52 Yardwork
page 53 Can You Solve It?
page 54 How Much Will It
Cost?
page 56 Heads and Legs
page 57 Football Tickets
3 days
Activity 3.7
page 299 Modeling a
Business
Exercises page 324
(M.5)
514
Math Models
(M.5.C)
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 3 of 9
Teacher Tools
Activity 3.6 Vocabulary:
system of equations, solution
Activity 3.6 Objectives
1. Solve a system of two linear equations numerically.
2. Solve a system of two linear equations graphically.
3. Solve a system of two linear equations using the
substitution method.
4. Identify the connections between the three methods
of solving systems of two linear equations.
5. Interpret the solution to a system of two linear
equations in terms of the problem’s content and
determine reasonableness.
6. Analyze situations and formulate systems of
equations to solve problems.
7. Use the graphing calculator to verify the solution to a
system of two linear equations.
Activity 3.7 Vocabulary:
break-even point, cost function, revenue function, profit
Activity 3.7 Objectives
1. Determine the break-even point of a linear system of
equations algebraically and graphically.
2. Interpret the break-even points in contextual
situations.
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
12 Days (cont’d. from previous page)
Major Concept #1: Linear Function Models (Continued)
Overarching
Idea
Teacher
Guiding
Questions
611
Matrix
Strand
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving linear equations and inequalities.




How does rate of change relate to the slope of a linear function?
How do you determine when a function has zero slope or undefined slope?
How can you determine the solution to a system of linear equations?
How can you determine the solution set of a linear inequality?
TEKS
Knowledge & Skill
Communication
Matrix
#
Student Expectation
(M.1.B)
Problem Solving
(M.1)
609
Math Models
(M.1C)
TAKS
OBJ
Resource
Time/
Pace
Activity 3.8
page 306 How Long Can You
Live?
Exercises page 314
ACM:
page 63 Solving Inequalities
page 66 Real World Inequality 2 days
Problems
page 67 Inequality
Concentration Problems
page 73 Graphing the
Solution Set
page 76 Can You Shade It?
page 77 Word Problems with
Inequalities
Group 1:
review skills
page 319 What Have I
Learned?
page 321 How Can I
Practice?
assess mastery
2 days
Teacher Tools
Activity 3.8 Vocabulary:
linear Inequality, compound inequality, solution set
Activity 3.8 Objectives
1. Translate given situation statements into an
algebraic inequality or compound inequality.
2. Solve linear inequalities numerically, algebraically,
and graphically.
3. Use the properties of inequalities to solve linear
inequalities algebraically.
4. Solve compound inequalities algebraically and
graphically.
5. Interpret the solution set of an inequality in
contextual situations and determine reasonableness.
6. Analyze situations and formulate an inequality or
compound inequality to solve problems.
Teachers can use the Section 6 Skills Checks worksheets in
the Pearson Teacher’s Resource Guide to assess the
student’s understanding of the concepts/skills covered in
Chapter 3 Group 1 activities as an in-class quiz or as an athome assignment. The Section 7 Assessment of the Teacher’s
Resource Guide includes samples of quizzes, tests, and
exams that can be used as is or modified as needed. Teachers
are encouraged to include TAKS formatted problems from the
numerical fluency focus objectives on all formal assessments.
Students should be reminded that they have access to tutorials
and extra practice problems using the MathXL CD in addition
to the Interact Math and MyMathLab websites/software.
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 4 of 9
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
Major Concept #2: Quadratic Function Models
Overarching
Idea
Teacher
Guiding
Questions
611
519
237
516
Displaying & Interpreting
Data
Equations,
Displaying &
Functions &
Interpreting Communication
Function
Data
Models
519
Matrix
Strand
Displaying & Interpreting Data
Matrix
#
Math Models
10 Days
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving quadratic functions.


How can you determine if the graph of a function is quadratic?
How can you find the solution(s) of a quadratic equation?
TEKS
Knowledge & Skill
Student Expectation
The student develops and
implements a plan for
collecting and analyzing
data in order to make
decisions. (M.3)
Determine the
appropriateness of a model
for making predictions from
a given set of data. (M.3.C)
The student uses a variety
of strategies and
approaches to solve both
routine and non-routine
problems. (M.1)
Use multiple approaches
(algebraic, graphical, and
geometric methods) to
solve problems from a
variety of disciplines.
(M.1.B)
(M.3)
(M.3.C)
The student uses algebraic
and geometric models to
describe situations and
solve problems. (M.8)
Use direct and inverse
variation to describe
physical laws such as
Hook’s, Newton’s and
Boyle’s laws. (M.8.C)
TAKS
OBJ
Resource
Time/
Pace
Group 2:
Activity 3.9
page 334 College Tuition
Exercises page 337
Activity 3.10
page 340 The Amazing
Property of Gravity
Exercises page 346
Activity 3.9 Vocabulary:
linear regression equation, line of best fit, regression line,
method of least squares, interpolation, extrapolation
Activity 3.9 Objectives
1. Determine a line of best fit using a straightedge.
2. Determine the equation of a regression line using a
graphing calculator.
3. Use the regression equation to interpolate and
extrapolate y-values for the x-values of given data,
1 day
ACM:
page 85 Ball Toss
page 87 Exploring Parabolas
Activity 3.11
page 349 Baseball and the
Sears Tower
Exercises page 355
The student uses graphical
and numerical techniques
to study patterns and
analyze data. (M.2)
Interpret information from
various graphs, including
line graphs, bar graphs,
circle graphs, histograms,
and scatter plots to draw
conclusions from data.
(M.2.A)
ACM:
page 90 Matching Quadratics
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 5 of 9
Teacher Tools
2 days
Activity 3.10 Vocabulary:
quadratic function, parabola, square root, solution
Activity 3.10 Objectives
1. Evaluate functions of the form y = ax2.
2. Graph functions of the form y = ax2.
3. Interpret the coordinates of points on the graph of y
= ax2 in context.
4. Solve an equation of the form ax2 = c graphically.
5. Solve an equation of the form ax2 = c algebraically
by taking square roots.
Activity 3.11 Vocabulary:
standard form, quadratic term, linear term, constant term,
coefficient, parent function, magnitude, absolute value, vertex
(turning point), minimum value, maximum value
Activity 3.11 Objectives
1. Identify functions of the form y = ax2 + bx +c.
2. Determine if a quadratic function is in standard form.
3. Use transformations of the parent function to
investigate, describe, and predict the effects of
changes to a, b, and c on the graph of y = ax2 + bx
+c.
4. Determine the practical domain and range of a
quadratic function.
5. Use the graphing calculator to verify the graphs of
quadratic functions
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
10 Days (cont’d. from previous page)
Major Concept #2: Quadratic Function Models (Continued)
Overarching
Idea
Teacher
Guiding
Questions
611


How can you determine if the graph of a function is quadratic?
How can you find the solution(s) of a quadratic equation?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
ACM:
page 93 Quadratic Functions
(M.2)
(M.2.A)
(M.1.B)
(M.1)
518
Displaying &
Interpreting Data
(M.2)
519
(M.3)
Select a method to solve a
problem, defend the method,
and justify the
reasonableness of the
results. (M.1C)
Use regression methods
available through technology
to describe various models
for data such as linear,
quadratic, exponential, etc.,
select the most appropriate
model, and use the model to
interpret information. (M.2.D)
Activity 3.13
page 371 Per Capita
Personal Income
Exercises page 374
ACM:
page 106 Solving Quadratic
Equations by Factoring
page 107 Magic Box
Quadratic Equations
page 108 Quadratic
Equations for the Graphing
Calculator
page 117 Nonlinear
Functions (problems 1-8)
Teacher Tools
Activity 3.12 Vocabulary:
vertex (turning point), minimum value, maximum value, axis of
symmetry, x-intercepts
Activity 3.12 Objectives
1. Determine the vertex (turning point) of a parabola.
2. Determine if the vertex is a maximum value or a
minimum value.
3. Determine the axis of symmetry of a parabola.
4. Identify the practical domain and range of a
parabola.
5. Determine the y-intercept of a parabola.
6. Determine the x-intercept(s) of a parabola
graphically.
6. Interpret the practical meaning of the vertex and
intercepts in a given real-life situation.
Activity 3.12
page 359 The Shot Put
Exercises page 366
Displaying
&
Interpreting
Data
609
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving quadratic functions.
Problem
Solving
516
Displaying & Interpreting Data
Matrix
Strand
Communication
Matrix
#
Math Models
3 days
Activity 3.13 Vocabulary:
zero feature (graphing calculator)
Activity 3.13 Objectives
1. Solve quadratic equations numerically.
2. Solve quadratic equations graphically.
(M.3.C)
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 6 of 9
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
10 Days (cont’d. from previous page)
Major Concept #2: Quadratic Function Models (Continued)
Overarching
Idea
Teacher
Guiding
Questions
Matrix
#
Matrix
Strand
Students use mathematical intuition and algebraic skills to model and solve real-life situations involving quadratic functions.


How can you determine if the graph of a function is quadratic?
How can you find the solution(s) of a quadratic equation?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
519
Displaying & Displaying &
Interpreting Interpreting
Data
Data
518
Communication
Activity 3.14
page 376 Ups and Downs
Exercises page 378
611
Math Models
(M.1)
(M.2)
(M.1.B)
(M (M.2.D)
1 day
Activity 3.15
page 383 Air Quality in
Atlanta
Exercises page 386
1 day
(M.3)
(M.3.C)
Group 2:
review skills
page 389 What Have I
Learned?
page 392 How Can I
Practice?
page 407 Gateway Review
assess mastery
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 7 of 9
Teacher Tools
Activity 3.14 Vocabulary:
quadratic formula
Activity 3.14 Objectives
1. Solve quadratic equations using the quadratic
formula.
2. Identify the solutions of a quadratic equation with
points on the corresponding graphs.
3. Interpret the practical meaning of the vertex and
intercepts in a given real-life situation.
4. Analyze graphs of quadratic equations and draw
conclusions.
Activity 3.15 Vocabulary:
quadratic regression model
Activity 3.15 Objectives
1. Determine quadratic regression models using the
graphing calculator.
2. Solve problems using quadratic regression
models
Teachers should assess the student’s ability to use the
concepts/skills covered in the Chapter 3 Group 2 activities.
The Gateway sections of the text can be used as the review
for a chapter test.
2 days
Students should be reminded that they have access to
online tutorials and extra practice problems using the
MathXL CD in addition to the Interact Math and
MyMathLab websites/software.
7/1/2016
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
Major Concept #3: Probability
Overarching
Idea
Teacher
Guiding
Questions
504
504
Displaying & Interpreting
Data
Proportional Reasoning in
Probability
504
Proportional
Reasoning in
Probability
512
Matrix
Strand
Probability & Statistics
Matrix
#
Math Models
6 Days
Students use mathematical intuition and algebraic skills to model and solve everyday problems involving chance.


How do you determine the sample space for an experiment in probability?
What is the difference between theoretical and experimental probability?
TEKS
Knowledge & Skill
The student uses graphical
and numerical techniques
to study patterns and
analyze data. (M.2)
Student Expectation
Analyze numerical data
using measures of central
tendency, variability, and
correlation in order to
make inferences. (M.2.B)
TAKS
OBJ
Resource
Chapter 2
Problem Solving with
Graphical and Statistical
Models
Group 2:
Activity 2.6
page 187 A Switch Decision
Exercises page 192
Activity 2.7
page195 Chances Are!
Exercises page 200
The student uses
probability models to
describe everyday
situations involving chance.
(M.4)
Compare theoretical and
empirical probability.
(M.4.A)
Time/
Pace
Activity 2.6 Vocabulary:
frequency distribution, variability, range, deviation, standard
deviation, boxplot, quartile, sigma (, )
Activity 2.6 Objectives
1. Determine the range for a set of data.
2. Measure the variability of a frequency distribution.
3. Calculate the standard deviation of a distribution
using the standard deviation formula.
2 days
ACM:
page 222 Marbles
page 225 Tossing Coins
page 233 Probability and
Statistics (problems 1-5)
Activity 2.8
page 203 Choices
Exercises page 206
(M.4)
(M.4.A)
1 day
Activity 2.9
page 208 Selecting and
Rearranging Things
Exercises page 213
(M.4)
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
1 day
Page 8 of 9
Teacher Tools
Activity 2.7 Vocabulary:
relative frequency, event, experimental probability, theoretical
probability, sample space, probability properties, law of large
numbers, simulation
Activity 2.7 Objectives
1. Determine the relative frequencies for a collection of
data.
2. Determine theoretical and experimental probabilities.
3. Determine the sample space for an experiment.
4. Apply the properties of probabilities.
5. Simulate an experiment and observe the law of large
numbers.
Activity 2.8 Vocabulary:
multiplication principle of counting, tree diagram, sample space
Activity 2.8 Objectives
1. Apply the multiplication principle of counting.
2. Determine the sample space for a probability
distribution.
3. Use a tree diagram to display a sample space.
Activity 2.9 Vocabulary:
permutations, factorial notation, combinations, independent
events
Activity 2.9 Objectives
1. Simplify factorial expressions.
2. Compute the number of permutations.
3. Compute the number of permutations of n objects
taken r at a time.
4. Compute the number of combinations.
5. Compute the number of combinations of n objects
taken r at a time.
7/1/2016
Austin ISD Instructional Planning Guide – Mathematics
4 h Six Weeks IPG - January 8th – February 22nd (32 days; 2 days for 6 weeks review/test, 2 days for MoY)
©2007 Austin Independent School District
6 Days (cont’d. from previous page)
Major Concept #3: Probability (Continued)
Overarching
Idea
Teacher
Guiding
Questions
Matrix
#
Matrix
Strand
Math Models
Students use mathematical intuition and algebraic skills to model and solve everyday problems involving chance.


How do you determine the sample space for an experiment in probability?
What is the difference between theoretical and experimental probability?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
T
i
m
e
/
Teacher Tools
P
a
c
e
Group 2:
review skills
page 223 What Have I Learned?
(problems 1-10)
page 225 How Can I Practice?
(problems 1-13)
page 235 Gateway Review
assess mastery
DRAFT
Math Models
ACM: Accelerated Curriculum for Mathematics Exit Level TAKS, Student Edition, by Region IV
Page 9 of 9
Teachers should assess the student’s ability to use the
concepts/skills covered in the Chapter 2 Group 2 activities.
2
The Gateway sections of the text can be used as the review
for a chapter test.
d
a
Students should be reminded that they have access to online
y
tutorials and extra practice problems using the MathXL CD in
s
addition to the Interact Math and MyMathLab
websites/software.
7/1/2016