Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Math Models
Discipline Based Concept
Pacing:
Discipline Based Concept: Data and Statistics
Concept description: Data is the basis of building models to analyze situations
Unit Major Concept #1: Graphs
Unit Overarching
Idea
Unit Pacing:
Unit Vocabulary:
Graphs are a fundamental tool for representing data in a visual format
Unit Teacher
Guiding Questions



How can we use graphed data to make predictions?
When does discrete data begin to take on a continuous function aspect?
What are the major differences between linear and quadratic graphs?
Arc: Analyzing Graphs and Tables
Arc Teacher
Guiding Questions
Mathematical Modeling
Matrix
#




TEKS
Knowledge & Skill
M.2 The student uses
graphical and
numerical techniques
to study patterns and
analyze data.
What is the value of different graph types (bar,line, circle)?
What does a scatterplot tell us about data?
Sometime correlated data sets are not really correlated. How can we tell?
What are clues to tell if a graph is misleading?
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students will represent and interpret relationships
using tables and graphs.
Class syllabus/ 1st day activities
Use the Holt Algebra I “Lesson Tutorial Videos” 10-1 examples 1 (bar
graph 3:28) and example 3 (line graph 1:15) as an introduction to
graphs. Pause as each video plays allowing for students to answer and
further discussion as needed.
http://my.hrw.com/tabnav/controller.jsp?isbn=0030921570
Students will explore the lesson by completing worksheets from Holt’s
Algebra I, 10-1 Texas Practice B and Texas Problem Solving.
Answer questions as needed. Discuss answers at end of class to clear
up any misconceptions.
Perform any first day activities and go over class rules and expectations.
Introduce reading and creating bar, line and circle graphs.
Essential Questions: Name at least three different types of graphs.
Create a graph (bar, line or circle) from a set of data. Compare the
similarities and differences between a bar graph and a circle graph.
Vocabulary: line graph, bar graph, circle graph
M.2A interpret information
from various graphs, including
line graphs, bar graphs, circle
graphs, histograms,
scatterplots, line plots, stemand-leaf plots, and box-andwhisker plots to draw
conclusions from the data
M.2B analyze numerical data
using measures of central
tendency, variability, and
correlation in order to make
inferences
Reading Graphs
(AISD created)
M.3C determine the
appropriateness of a model for
making predictions from a
given set of data
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 1 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students will represent and interpret relationships
using tables and graphs.
Teacher Notes: Choose One:

NF 1-1

Reading Bar Graphs (Pearson Math Modeling with Apps,
Activity 2.2 P 151 #’s 1-3)

Create a bar graph (Pearson Math Modeling with Apps,
Activity 2.2 P 152 # 4)
Use the Holt Algebra I “Lesson Tutorial Videos” 10-1 example 2 (double
bar graph 3:28), example 4 (double line graph 1:15), example 5 (circle
graph) and example 6 (appropriate displays) to introduce various
graphs and how to identify the appropriate graph for a given set of data.
Pause as the video plays allowing for students to answer and further
discussion as needed.
http://my.hrw.com/tabnav/controller.jsp?isbn=0030921570
Students will explore the lesson by completing worksheet “Using Graphs
and Tables” OR Exercises 2.2 P. 157 #’s 1-6, Pearson, Math Modeling
with Applications
Answer questions as needed. Discuss answers at end of class to clear
up any misconceptions.
Present the video clips on various types of graphs and how to choose
the appropriate graph for a set of data. Work on assignment
Essential Questions:

Chose the appropriate type graph for a set of data.

Identify a set of data that would be appropriate when making a
circle graph, line graph or bar graph.
Vocabulary: double line graph, double bar graph, appropriate displays
M.2A
M.2
M.3
M.2B
M.3C
Using Graphs and
Tables
(AISD created)
Math Models
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 2 of 19
5/10/09
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students will use a graphing calculator to create a
scatter plot and determine the line of best fit.
Teacher Notes: NF 1-2
Use the graphing calculator to input a set of data, graph the data,
determine the type of equation, and then calculate the equation.
(attachment with directions and question on school computer)
In groups of 3 or 4, have students input a set of data, sketch the graph,
determine the type of equation, and then calculate the equation. Have
each group member compare their equations, if any are different have
the teams discovery the reason for the discrepancy. Then as a group,
make prediction about the data using the equation. (provide data and
questions on school computer)
Assign worksheet with 3 sets of data and questions.
(worksheet at school)
Using graphing calculators:

input data in lists

graph using stat plot

calculate the equation for the graph
make perditions using equation
Assign a set of data that is not linear, quadratic or exponential.
Essential Questions:

What is a scatter plot?

Determine the type of graph, linear, quadratic, or exponential.

Explain how to use a graphing calculator to calculate the
equation of a graph.
Vocabulary: scatter plot, linear, quadratic, exponential, list,
M.2D use regression
M.2
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
Scatter Plots
(AISD created)
Math Models
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 3 of 19
5/10/09
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
A.7 Linear functions.
The student Formulates
equations and
inequalities based on
linear functions, uses a
variety of methods to
solve them, and analyzes
the solutions in terms of
the situation.
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
Student Expectation
A7.B investigate methods for
solving linear equations and
inequalities using concrete
models, graphs, and the
properties of equality, select a
method, and solve the
equations and inequalities;
TAKS
OBJ
Resource
Misleading
Graphs
(AISD created)
Math Models
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students gain an understanding of the misuse of
graphs and data. Misleading scale views, data bias, etc.
Teacher Notes: NF 1-3
Vocabulary Flash card activity
Use the Holt Algebra I “Lesson Tutorial Videos” 10-4 example 1
(misleading bar graph), example 2 (misleading line graph), and
example 3 (misleading circle graph) to introduce misleading graphs and
how to identify the strategy for making the graph misleading. Pause as
the video plays allowing for students to answer and further discussion as
needed. http://my.hrw.com/tabnav/controller.jsp?isbn=0030921570
Use the Holt Algebra I “Interactivities” 10-4 Misleading Graphs &
Statistics to LEARN, EXPLORE, and PRACTICE.
http://my.hrw.com/tabnav/controller.jsp?isbn=0030921570
Assign WS 10-4 Texas Practice B and Texas Problem Solving (Algebra
I) for further analyzes.
Introduce various types of misleading graphs using the videos
developed by Holt Algebra I, and then practice determining how graphs
are misleading and who would benefit from the bias.
Essential Questions:

List three different ways graphs can be misleading.

Evaluate the differences between one set of data displayed in a
non bias graph and in a misleading graph.

Construct a misleading graph from data to show an indicated
bias.
Vocabulary: misleading graph, bias,
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 4 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Mathematical Modeling
M.2A
M.2
M.3
M.2C analyze graphs from
journals, newspapers, and
other sources to determine
the
validity of stated
arguments;
M.2D
M.3A formulate a
meaningful question,
determine the data needed
to answer the question,
gather the appropriate
data, analyze the data, and
draw reasonable
conclusions;
M.3B communicate
methods used, analyses
conducted, and
conclusions drawn for a
data analysis
project by written report,
visual display, oral report,
or multi-media
presentation
Graphing Activity
(Computer Lab AISD created)
45 min
Math Models
Teacher Tools
Intended Learnings: Students will use excel to create a bar, line and
circle graph and a misleading graph. (Assessment)
Review computer lab expectations.
Using a projector show two examples of how to input data into excel and
how to use the graphing tools in excel to create specific graphs.
In the computer lab, have students work in groups of two, to input data
into excel and create bar, line and circle graphs. Then have the students
create a misleading graph for their assigned topic. Worksheet: Graphing
Activity (worksheet is at school, will get Monday)
Share misleading graphs in a gallery walk and have students compare
the graphs determining how each graph is misleading. (All students
have the same data, but there are two different perspectives for the
graphs.)
Using excel, students will create four different graphs, bar, line, circle,
and misleading. Then students will be challenged to determine how
each misleading graph is misleading.
The four graphs created by the students, showing appropriate
information (title, scale, type graph, etc.)
(rubric at school will add Monday)
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 5 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
M.2B
TAKS
OBJ
Resource
Measures of
Central Tendency:
Dog Lab
(AISD created)
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Use the graphing calculator to calculate the
mean, median and range, and understand the relationship between the
mean, median, mode and range when one data point is added, deleted,
or changed.
Teacher Notes: NF 1-4
Use a graphing calculator to enter a list of data and calculate the mean
(average), median (middle), mode (most) and range of the data. Explain
what symbols go with what vocabulary word. (activity with notes at
school, will get Monday)
Whole class discussion, Gone to the Dogs. Calculate the statistical data
using the graphing calculator, then complete the front of the worksheet
as a whole class discovering what happens as the data changes, what
new data points need to be so the statistical analysis points do not
change. (worksheets at school, will get Monday)
Class completes worksheet individually or in small groups.
Show how to use a graphing calculator to find mean, median and range,
then using whole class discussion discover how the statistics are
affected by various changes.
Essential Questions:
What keys on a graphing calculator are used to calculate the mean of a
set of data? When is the median a value in a set of data? How does an
outlier affect the mean, median, mode or range?
Compare and Contrast what happens to the median and mean when the
mean is added to the data set.
Vocabulary: mean, median, mode, range, outlier
Mathematical Modeling
M.2
Student Expectation
Math Models
Continue Dog Lab activity. Students display and discuss created posters.
Review for Test 1.1
M.3A
M.3
M.3B
Graph
Presentation/
Review for Test
1.1
45 min
Test 1.1
AISD Created Test
45 min
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 6 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Math Models
Discipline Based Concept
Pacing:
Discipline Based Concept: Direct and Inverse Variation
Concept description: Use math models to describe sets of data and the relationships between two of more variables
Unit Overarching
Idea
Unit Major Concept # 2: Directly Proportional Relationships
Directly proportional relationships are linear, have a constant of proportionality, and can be described by
a direct variation function.
Unit Teacher
Guiding Questions





Unit Pacing:
Unit Vocabulary:
How do we determine which variable is independent?
How do we determine which variable is dependent?
How do we determine the domain of a situation?
How do we determine the range of a situation?
How do we determine if a relationship is proportional?
Arc: Proportional Relationships
Arc Teacher
Guiding Questions



Tables and graphs both model data. Which is a better predictor of future events?
Based on modeling, when are variable positively related?
How can we determine if data in a table has a positive relationship?
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 7 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
M.1 The student uses
a variety of strategies
and approaches to
solve both routine and
nonroutine problems.
M.3
M.8 The student uses
algebraic and
geometric models to
describe situations and
solve problems
Student Expectation
M.1B use multiple
approaches (algebraic,
graphical, and geometric
methods) to solve
problems from a variety of
disciplines
M.3A
M.8C use direct and
inverse variation to
describe physical laws
such as Hook's, Newton's,
and Boyle's laws.
TAKS
OBJ
Resource
Time/
Pace
Modeling with
Mathematics: 1.1
Archimedes and
the Crown,
1.2 Displacement
Investigation
45 min
Math Models
Teacher Tools
Intended Learnings: Students begin to work through the modeling
process using volume and displacement using direct variation to
describe physical laws.
Teacher Notes: NF 1-5
Class syllabus/ 1st day activities
Have students do a Think-Pair-Share to read and answer questions 1-6.
Begin the teacher-led demonstration on displacement. It is suggested
that you have a transparency or other projection method available to
display the scenario and questions for students to see, as many
students may not bring the textbook to class on the first day.
End the lesson with a whole group discussion of questions 7-11.
Students identify volume as the cause of displacement.
1.1 Archimedes and the Crown P 6, #’s 1-11
Start a word wall from the vocabulary list.
Complete 1.1 P 6, 1-11 if needed.
Solving Proportions (Pearson, Math Models w/ Apps., Exercises 1.4,
page26 #’s 3, 5-7.
Students work in pairs to answer questions 1-6, page 6, Region 4
Modeling w/ Mathematics. Debrief by having each group share their
answers. Begin the teacher-led demonstration on displacement. Student
pairs are to answer remaining questions 7-14. It is suggested that you
have a transparency or other projection method available to display the
scenario and questions for students to see, as many students may not
bring the textbook to class on the first day.
In this displacement activity students will conduct a similar experiment.
Students will record their data in the table given as they collect it and
answer some follow- up questions and create a scatter plot. The scatter
plot should be drawn on large paper and posted around the room
displaying the data “Total Volume Displaced vs. Number of Canisters”.
Groups present their display to the class comparing similarities and
differences. Complete questions on Section 1.2, page 8, #’s 1- 7, Region
4 Modeling w/ Mathematics.
Students identify volume as the cause of displacement, and conduct
their own displacement investigation, record data, make a scatter plot,
and answer questions pertaining to their data.
Start a word wall from the vocabulary list.
Complete 1.2 P 8, 1-7, Region 4 Modeling w/ Mathematics, if needed.
Essential Questions:
What is math modeling? What is volume? How do you calculate the
volume of a cylinder? What is displacement? Give an example where
displacement relates to volume. Explain how displacement identifies
volume. Describe what rate of change means in this problem situation.
Vocabulary: displacement, rate of change, scatter plot, volume
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 8 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
M.1
M.3A
M.3
M.1B
M.8
M.8C
TAKS
OBJ
Resource
Modeling with
Mathematics: 1.3A
A Question of
Variation
Time/
Pace
45 min
Math Models
Teacher Tools
Intended Learnings: Students will collect and analyze data to draw
conclusions while formalizing the concepts of proportional relationships
and direct variation.
Teacher Notes: NF 1-6
Solving Proportions (Pearson, Math Models w/ Apps., Exercises 1.4,
page26 #’s 8-11

Pair/Share Vocabulary Matching – There are a lot of
vocabulary words in this section, most of which are review. This
activity will narrow down which words need more attention.
(MM 1st 1-3 Launch Vocab)

Debrief students on section 1-2 by having them share displays.
As they share fill in any missing concepts, process, or skill.
In the displacement activity students will use the data collected from the
activity in Section 1.2 and create a new scatter plot this time displaying
Total Volume vs. Number of Canisters. Break students into the same
groups as the previous day. Suggested rolls for students in groups:

1 recorder

1 presenter

1 material collector

1 time keeper

1 artist
Review the scatter plot feature of the graphing calculator. Using whole
class discussion answer questions in section 1.3, page 10-13, #’s 1- 13,
Region 4 Modeling w/ Mathematics.
Students review vocabulary of section and then use collected data to
answer questions and analyze the data to draw conclusions.
Essential Questions:

Describe the difference between the independent and
dependant variables.

Identify the domain and range in a problem situation.

Express how the constant of proportionality and rate of change
related.

Explain the properties of a direct variation.
Vocabulary: axes, Boyle’s Law, constant of proportionality, continuous
graph, coordinate plane, coordinates, dependent variable, direct
variation function, discrete graph, domain, function, independent
variable, mass, negative relationship, positive relationship, proportional
relationships, proportions, range, units, variable
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 9 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
M.1
M.3A
M.3
M.1B
M.8
M.8C
TAKS
OBJ
Resource
Modeling With
Mathematics: 1.3B
Variation
Continuation
Math Models
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students will collect and analyze data to draw
conclusions while formalizing the concepts of proportional relationships
and direct variation.
Teacher Notes: NF 1-7
Direct Variation (Pearson, Math Models w/ Apps., Exercises 5.15,
page621 #’s 3-6
Complete Assignment 1.3, page 14-15, #’s 1- 15, Region 4 Modeling w/
Mathematics. Create a graphic display including answers from questions
8-15.
Students review direct variation and complete assignment 1.3.
Assess student knowledge as they work to complete the assignment.
Complete Section 1.3, page 14-15, #’s 1- 15, Region 4 Modeling w/
Mathematics.
Essential Questions:
Describe the difference between the independent and dependant
variables. Identify the domain and range in a problem situation.
Express how the constant of proportionality and rate of change related.
Explain the properties of a direct variation.
Vocabulary: axes, Boyle’s Law, constant of proportionality, continuous
graph, coordinate plane, coordinates, dependent variable, direct
variation function, discrete graph, domain, function, independent
variable, mass, negative relationship, positive relationship, proportional
relationships, proportions, range, units, variable
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 10 of 19
5/10/09
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
M.1
M.3
M.8
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students will make a table and scatter plot for a
relationship that is not proportional.
Teacher Notes: NF 1-8
Solve basic algebraic equations (Pearson, Math Models w/ Apps.,
Exercises 1.10, page93 # 10a, c, e, g, i)
Discuss the similarities of the graphic displays created in sections 1.2
and 1.3.
As a pair/share use the data from section 1-2 to make predictions by
answering questions in section 1.4, page 16-17, #’s 1- 12, Region 4
Modeling w/ Mathematics. 15 minutes to complete. As students are
working ask questions within each group to determine the level of
mastery.
Individually have students complete Assignment 1.4, page 18-19, #’s 116, Region 4 Modeling w/ Mathematics. Turn in assignment at end of
class.
Students will use graphs or tables to problem solve, they will be able to
create a scatter plot and make predictions based on their model. They
should also be able to decide if a relationship is proportional.

Informally assess students during the engage activity, section
1.4, page 16-17, #’s 1- 12, Region 4 Modeling w/ Mathematics.
Grade individual papers from the Assignment 1.4, page 18-19, #’s 1- 16,
Region 4 Modeling w/ Mathematics.
Essential Questions:

What are the domain and range for this situation?

Describe the relationship displayed in your scatter plot.

Do you think there is a proportional relationship between the
data? Why or Why not.

Make a linear graph, and write the equation for the graph. What
could you change in the equation to make it a proportional
relationship?
Vocabulary: linear relationship
M.3A formulate a meaningful
question, determine the data
needed to answer the
question, gather the
appropriate data, analyze the
data, and draw reasonable
conclusions
M.1B use multiple
approaches (algebraic,
graphical, and geometric
methods) to solve problems
from a variety of disciplines
Modeling with
Mathematics: 1.4
Displacement
Round 2
M.8C use direct and inverse
variation to describe physical
laws such as Hook's,
Newton's, and Boyle's laws
Math Models
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 11 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Mathematical Modeling
Matrix
#
TEKS
Knowledge & Skill
M.1
M.3
M.8
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Students will use multiple approaches to solve
problems by collecting and analyzing date to identify a mystery metal.
Teacher Notes: NF 1-9
Working in pairs, have students complete Section 1.5 Mystery Metals,
page 20, #’s 1- 2, Region 4 Modeling w/ Mathematics. Allow
approximately 15-20 minutes to complete. Students will need this time to
use all three methods (table, graph, and equation) to examine this
problem. They will see this question again on a test.
Assign two pairs to share with each other making a list of similarities and
differences. Then at the end of class make a final class list of all
similarities and differences.
Students will review what they have learned and apply it in the Mystery
Metals activity, then assess their knowledge with a brief quiz.
Assignment 1.5
Quiz: Sections 1.11.5
Essential Questions:

Describe the difference and similarities between a direct
variation and a linear relationship.

What mathematical tools can you use to help you solve
problems?

Describe the independent and dependent variables in the
demonstration?

Identify the relationship between the independent and
dependent variables.

Develop an experiment that would further explore the
relationship between the stretch and weight.
Vocabulary: direct variation function
M.1A compare and
analyze various methods
for solving a real-life
problem
M.1B
Modeling with
Mathematics: 1.5
M.3A
M.3C
M.8C
Math Models
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 12 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Math Models
Discipline Based Concept
Pacing:
Discipline Based Concept: Direct and Inverse Variation
Concept description: Use math models to describe sets of data and the relationships between two of more variables
Unit Overarching
Idea
Unit Major Concept # 2: Directly Proportional Relationships
Directly proportional relationships are linear, have a constant of proportionality, and can be described by
a direct variation function.
Unit Teacher
Guiding Questions

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
Unit Pacing:
Unit Vocabulary:
How do we determine which variable is independent?
How do we determine which variable is dependent?
How do we determine the domain of a situation?
How do we determine the range of a situation?
How do we determine if a relationship is proportional?
Arc: Non-proportional Relationships
Arc Teacher
Guiding Questions
Mathematical Modeling
Matrix
#




TEKS
Knowledge & Skill
Can all non-proportional relationships be modeled with linear functions?
How can do we determine the independent variable in a non-proportional relationship?
How can do we determine the dependent variable in a non-proportional relationship?
Using the independent and dependent variables, how can we find the constant of proportionality?
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Describe a non-proportional relationship modeled with
linear function modeling.
Teacher Notes: NF 1-10
Begin the demonstration as described in the text, students will answer a few
questions about what they see.
After completing the demonstration, students will break into groups to explore and
analyze Hooke’s law. This activity should be set up prior to students entering
class and will take approximately 40 minutes. Suggested rolls for group members:

1 recorder

2 measurers (accuracy is key)

1 time keeper/task manager

1 marble dropper
The reinforcement activity for this evening is Section 1.7
Essential Questions: Is the relation between the independent and dependent
proportional? Does increasing pennies create a positive relationship between
weight and stretch? What can we say about the stretch for every 5 pennies
added?
Materials Needed (for each group)
Film canisters with 2 holes to affix a paper clip or string handle
Film canisters with 3 holes to affix paper clips for hangers
2 jumbo paper clips
15 pennies
Metal Slinky for each group
About 10 marbles
Bent paper clips for pointers
Meter sticks
Graphing calculator
M.3A
M.3
M.3C
M.8
M.8C
Modeling with
Mathematics: 1.6
This is really a
stretch
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 13 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
M.3A
M.3C
M.8
M.8C
Mathematical Modeling
M.3
Modeling with
Mathematics: 1.7
Hooke’s Law,
Quiz
M.1B
M.1
M.2
M.2A
M.2B
M.3
M.3C
M.8
Modeling with
Mathematics: 1.8
Variation on a
Theme
M.8C
Time/
Pace
Math Models
Teacher Tools
Intended Learnings: To use function rules to describe linear functions.
Teacher Notes: NF 1-11
Briefly discuss the demonstration from the day before (1.6)
Arrange students in groups of 3 to 4. Students will make a spring with a
basket then add marbles to the basket. Measure the stretch of the Slinky
each time one marble is added and record the data in a table. Identify
the independent and dependent variables, and domain and range. Make
a scatter plot of the stretch of the slinky versus the number of marbles
added and describe the graph. Use the table and a graph to identify a
proportional relationship. 1.7 Hook’s Law, page 24, #’s 1- 20, Region 4
45 min
Modeling w/ Mathematics.
Quiz over units 1.1-.16
Essential Questions:

How do you determine what the independent and dependent
variable is in a situation?

Describe the difference between a proportional relationship and
a linear relationship.

Develop an experiment that would further explore the
relationship between the stretch and weight.
Vocabulary: , Hook’s Law, versus
Intedned Learnings: Students will examine negative correlation and no
correlation and formalize the terminology and characteristics of direct
variation.
Teacher Notes: NF 1-12
Begin Section 1.8 by breaking students into small groups to answer one
of questions 1-8. Allow students 3 to 5 minutes to formulate answers and
then have a representative from each group share answers for the rest of
the class. This should take another 10 minutes, approximately.
Give students about 5 minutes to answer questions 9-12 independently,
then they can share answers with a partner for another 5 minutes.
Questions 13-16 lend themselves to a teacher-led class discussion, which
45 min
could take about 15 minutes. Allow students to work with partners to
answer questions 17-21 and then come back together for a class
discussion on question 22.
Essential Questions:

Explain the difference between a direct variation and a linear
function.

Give an example of when you would use the point-slope
formula.

What are some other names for slope?

Formulate a set of data that is positive (or negative).
Vocabulary: point-slope formula, slope, slope-intercept form, y-intercept
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 14 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
M.1B
M.1
M.2A
Modeling with
Mathematics: 1.9
M.2B
This Floors Me
M.2
45 min
M.3
Mathematical Modeling
M.3C
Math Models
Teacher Tools
Intended Learnings: Students demonstrate an understanding of developing a
function to model a relationship
Teacher Notes: NF 1-13
Discuss Section 1.8 Assignment #1-18
Test: Chapter 1 Part I
Section 1.9 Assignment #1-17
Distribute the test and allow approximately 40 minutes for students to answer all
the questions.
The reinforcement activity for this evening is Section 1.9 Assignment #1-17.
Essential Questions: What is the dependent variable? How can you say this
is(or isn’t) a dependent relationship? This appears to be a negative correlation.
How could the data be reinterpreted to be a positive correlation?
Materials Needed:
Answers for Section 1.8 Assignment #1-18
Test: Chapter 1 Part I
Graphing calculator
Vocabulary: Correlation, no correlation, constant ratio
M.1A
M.1
M.1B
Modeling with
Mathematics: 1.10
Distance vs. Ramp
Height
45 min
Intended Learnings: Students demonstrate an understanding of developing a
function to model a relationship
Teacher Notes: NF 1-14
Allow about 25 minutes to review the test from the previous class. (You may
choose to use a test reflection.)
Complete Section 1.10 Distance vs. Ramp Height. This is a brief activity that asks
students to determine whether or not a real-life data set is proportional or not.
This may prompt a valuable discussion about proportional vs. non-proportional.
Ask students to take a side and defend it. If other activities run long, this can be
assigned as homework.
Essential Questions: Between the table, graph, and function, which best
predicts a ball’s travel distance based on future books stacked? How is rate of
change related to constant of proportionality?
Materials: Worksheet to review slope and various ways of finding slope with and
without a graphing calculator., Test reflection, Section 1.10 Distance vs. Ramp
Height, Graphing calculator, Graph paper
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 15 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Math Models
Discipline Based Concept: Direct and Inverse Variation
Discipline Based Concept
Pacing:
Concept description: Use math models to describe sets of data and the relationships between two of more variables
Unit Major Concept #2: Directly Proportional Relationships
Unit Overarching
Directly proportional relationships are linear, have a constant of proportionality, and can be described by
Idea
a direct variation function.
Unit Pacing:
Unit Vocabulary:
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

Unit Teacher
Guiding Questions
How do we determine which variable is independent?
How do we determine which variable is dependent?
How do we determine the domain of a situation?
How do we determine the range of a situation?
How do we determine if a relationship is proportional?
Arc: Inverse Variation Relationships
Arc Teacher
Guiding Questions
Mathematical Modeling
Matrix
#

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How is an inverse relationship different from a strictly linear representation?
How is a proportional relationship similar/different from an inverse variation?
How is a direct variation relationship similar/different from inverse variation?
TEKS
Knowledge & Skill
M.1
M.2
Student Expectation
Resource
Time/
Pace
2A.4C The student is
expected to describe and
analyze the relationship
between a function and its
inverse
M.1B
Modeling with
Mathematics:
M.2A
1.11 Apparent
Size, 1.12 The
Farther You Go
M.3
M.3A
M.8
TAKS
OBJ
M.3C
M.8C
45
mins
Teacher Tools
Intended Learnings: Students begin to work through the modeling
process using volume and displacement using direct variation to
describe physical laws. Students develop an inverse variation function
from gathered data
Teacher Notes: 1-15
Have students do a Think-Pair-Share to read and answer questions 1-6.
Begin the teacher-led demonstration on displacement. It is suggested
that you have a transparency or other projection method available to
display the scenario and questions for students to see, as many
students may not bring the textbook to class on the first day.
End the lesson with a whole group discussion of questions 7-11.
Students identify volume as the cause of displacement.
1.1 Archimedes and the Crown P 6, #’s 1-11
1.2 Start a word wall from the vocabulary list.
Complete Section 1.12 The Farther You Go. Students can either collect
their own data, or use the data provided to continue to examine inverse
functions. This activity will most likely carry over to the next class day.
The reinforcement activity for this evening is Section 1.12 Assignment
#1-6.
Essential Questions
When can we say variables are positively related? When can we say
variables have a negative relationship? Is it important to know which
variable we are controlling? Which column usually lists the independent
data in a two column table? Which column usually lists the dependent
data? Which function produces a more accurate prediction, linear or an
inverse variation? How many points are necessary to prove a relation is
an inverse variation?
Vocabulary: volume, displacement
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 16 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Math Models
Teacher Tools
Intended Learnings: Students formalize the concept of an inverse
variation relationship. Specifically, develop the general form of the
inverse variation equation, y  k .
Mathematical Modeling
x
M.1
M.1B
M.2
M.2A
M.3
M.3C
M.8
M.8C
Modeling with
Mathematics: 1.13
One Goes Up, one
Goes Down
45 min
Teacher Notes: NF 1-17
Be sure to discuss #6 with the class because they will need that
information to complete the Section 1.13 activity.
Remind students what the activity was about before letting them get
back into groups to finish. Allow approximately 20 minutes to complete.
As groups complete the Section 1.12 The Farther You Go activity,
distribute Section 1.13 One Goes Up, One Goes Down. This is a followup activity for Section 1.12.
The reinforcement activity for this evening is Section 1.13 Assignment
#1-10. Students should have enough time to begin, and possibly finish,
at least #1-4 in class.
Essential Questions: What are differences between a graphed inverse
variation and a graphed direct variation? What are some inverse
variation relationships in our everyday environment? In Boyle’s
volume/pressure experiments, which is the dependent variable? Which
is the independent variable?
Materials:
Worksheets or transparency for One Goes Up
Graphing calculator
Vocabulary: Inverse Variation, Indirect Variation, Inversely Proportional
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 17 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Mathematical Modeling
Teacher Tools
M.1C
Modeling with
Mathematics:
M.2A
1.14 Boyle’s
Law, 1.15 Using
Inverse Variation
45 min
AISD Generated
AISD Generated
Test
45 min
Intended Learnings: Apply inverse variation to Boyle’s Law by modeling data of
a gas’ volume and its pressure. Students solve a problem using skills and
concepts of inverse variation.
Teacher Notes: NF 1-18
The quiz should take about 15 minutes.
Distribute the Section 1.14 Boyle’s Law Worksheet. This is a guide for students to
use as the class discusses the PowerPoint for the section. Students will need
calculators to enter data. To save time, you may want to enter the data on the
calculators for the students; however, if students are still struggling to remember
how to enter data, this is a good opportunity to address questions from students
and guide them through the process of entering data.
The reinforcement activity for this evening is Section 1.14 Assignment #1-2.
Section 1.15 Using Inverse Variation. This should take approximately 10 minutes
for students to complete and about 5 minutes to discuss.
Allow about 10 minutes to answer student questions on homework and another
10 minutes to discuss the quiz from last class before beginning the quiz.
The quiz should take about 15 minutes.
Essential Questions: Graphed direct variation functions all pass through which
point? If we graph another inverse variation, what commonalities will it have with
Boyle’s Law? How can your graphing calculator lists help you to set up a
solution? How can you test your driveway findings before pouring actual
cement? Do you have enough information to create a budget for constructing the
longest 12 foot driveway as described in the problem?
Materials:
PowerPoint Boyle’s law
Quiz 4: Sections 1.11-1.13
Graphing calculators
Boyle’s law worksheet
Review: Test
45 min
Test :1.3
Modeling with
Mathematics
Project: Scope it
Out
90 min
Intended Learnings: Students will gather their own data to investigate the size
of a telescopes viewing circle and two other variables.
Teacher Notes: MF 1-19
Discuss with students the need for accurate data collection. The data collected
and calculations will contribute to a successful class presentation. Discuss
grading through use of a class-constructed rubric.
Emphasize the need to keep the distance from the meter stick constant and
examine the relationship between viewing circle diameter and telescope length.
Also, keep telescope length constant and examine the relationship between
viewing circle diameter and distance from the meter stick.
The report should contain a written component as well as visual representation of
the project.
Essential Questions: What relationship does the data graph? Linear? Direct?
Inverse?
Vocabulary:
Review
45 min
Review: Six Weeks Test
Test
45 min
Test: Six Weeks Test
M.1A
Mathematical Modeling
Math Models
M.1B
M.1
M.2
M.3
M.2B
M.8
M.3C
M.8C
M.1
M.1C
M.8
M.8C
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 18 of 19
5/10/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Dates (29 of days; 2 days for 6 weeks review/test, 2 days for BoY)
©2009 Austin ISD
Matrix
#
TEKS
Knowledge & Skill
M.1
Student Expectation
M.1C
TAKS
OBJ
Resource
Modeling with
Mathematics
Project
Presentations
Math Models
Time/
Pace
Teacher Tools
45 min
Intended Learnings: Using their own and others’ data, student understand the
different methods used to arrive at a conclusion based on roughly the same data.
Teacher Notes: Decide a presentation order of the different groups. Review
respectful peer evaluating and inquiry. Limit presentation time to how many
groups can feasibly present within the 35-40 minutes of class time.
Essential Questions: How does your data compare to the findings of other
students? Do variables appear constant throughout the different groups? What
are the criteria for well represented data? A well presented project?
Adopted Text: Mathematical Models with Applications (Pearson) Supplemented Text (2009 to bridge to Algebra II): Modeling with Mathematics: A Bridge to Algebra II (Region IV ESC)
Math Models with Applications
Page 19 of 19
5/10/09