Predicting Pennsylvania Population - Megan Hoopes …€¦ · · 2011-07-28Identify and graph the linear parent function. ... How can a graphing calculator be used to graph linear

Predicting Peirce’s Population

Mrs. Megan Hoopes-Myers – EDTECH 542 Page 1


TABLE OF CONTENTS

Begin with the End in Mind

Craft the Driving Questions

Plan the Assessment

Map the Project

Manage the Process

Appendix

NOTE: Information obtained for this Project-Based Learning was adapted and modified from http://www.transformation2013.org/node/17.

http://www.transformation2013.org/node/17



Begin with the End in Mind

Summarize the theme for this project. Why do this project?

Within groups, students will create linear equations, find trend lines, and make predictions based on the student and faculty/staff population of Peirce Middle School in West Chester, Pennsylvania over the last 20-25 years. Each group will be in charge of creating a pamphlet for the School Board President. This pamphlet will

include Peirce’s demographics, population statistics and trends, a linear function logo, and inviting information as to why students should attend Peirce Middle School.

Identify the content standards that students will learn in this project (two to three per subject).

Algebra 1 Pennsylvania State Standards 2.5 Mathematical Problem Solving and Communication

2.5.A1.A Develop a plan to analyze a problem identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solve in grade appropriate

contexts. 2.5.A1.B Use symbols, mathematical terminology, mathematical notation,

mathematical rules, graphing, and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas, and results.

2.6 Statistics and Data Analysis

2.6.A1.E Make predictions based on lines of best fit or draw conclusions on the value of a variable in a population based on the results of a sample.

2.8 Algebra and Functions

2.8.A1.E Use combinations of symbols and numbers to create expressions, equations, and inequalities in two or more variables, systems of equations,

and inequalities, and functional relationships that model problem situations. 2.8.A1.F Interpret the results of solving equations, inequalities, systems of

equations, and systems of inequalities in the context of the situation that motivated the model.

2.11 Concepts of Calculus

2.11.A1.B Describe rates of change a modeled by linear equations. Grade 8 Mathematics Pennsylvania State Standards 2.2 Computation and Estimation

2.2.8.C Use the order of operations to evaluate numerical expressions. 2.4 Mathematical Reasoning and Connections

2.4.8.A Draw inductive and deductive conclusions within mathematical contexts.



2.6 Statistics and Data Analysis 2.6.8.E Determine the effect of extreme values on numerical summaries and

calculate estimates based on survey results or graphs.

2.8 Algebra and Functions

2.8.8.B Evaluate and simplify algebraic expressions and solve and graph linear equations and inequalities.

2.8.8.C Find the missing elements and recognize, describe, and extend patterns to include linear, exponential, and simple quadratic equations.

2.11 Concepts of Calculus

2.11.8.B Describe the concept of unit rate, ratio, and slope in the context of rate of change.

Identify key skills students will learn in this project. List only those skills you plan to assess (two to four per person).

Identify and graph the linear parent function. Describe and predict the effect of changing the slope (“m”) and the y-

intercept (“b”) on the parent graph. Establish how to identify linear functions by making connections between the

various representations.

Define slope and intercepts of linear equations and functions. Calculate slope (rate of change) and intercepts from various representations. Explain how direct variations are related to linear functions.

Identify the habits of mind that students will practice in this project (one to two per project).

Students will recognize connections between mathematics, history, and marketing through the completion of “Predicting Peirce’s Population” project. They will use technology to gather and analyze population growth/decay for Peirce Middle School in West Chester, Pennsylvania over the past 20-25 years. The students will conclude their research and computations with the creation of a flyer providing graphics, research, linear concepts, and a linear function logo for the School Board President to present at the next School Board meeting.

Return to the Table of Contents



Craft the Driving Question

State the essential question or problem statement for the project. The statement should encompass all project content and outcomes, and provide a central focus for student inquiry. Essential Question: How can linear functions help predict population trends?

Sub-Questions: History Related:

1. How many students attended Peirce 25 years ago? 20 years ago? 15 years ago? 10 years ago? 5 years ago? How many students currently attend

Peirce? What population trend do you notice? 2. What are the demographics of Peirce Middle School?

Math Related:

1. Why is it important to write equations of lines? How does that concept appear in real life?

2. What is the importance of the rate of change? How does rate of change appear in real life?

3. How does the slope and y-intercept help create equations of lines? How do they help graph the equation?

4. How does direct variation relate to linear functions? How does direct variation appear in real life?

5. What inductive and deductive conclusions can be made from linear functions?

What conclusions can be made from their graphs? Technology Related:

1. How can a graphing calculator be used to graph linear functions? 2. How can a graphing calculator help predict trend lines?




Plan the Assessment

Step 1: Define the products for the project. What will you assess?

Early in the Project:

Students will determine the difference between slope-intercept form ( bmxy ) and

two-point form

12

1

12

1

xx

xx

yy

yy. Students will explore graphs and determine the

equation of a line based off of plotting two points. Graphing calculators will be used to

establish the line of best fit for different forms of data.

During the Project:

Students will be engaged in higher order thinking, recording their thoughts in a reflective

journal. Students will create linear equations, find trend lines, and make predictions

resulting in technology incorporation.

End of the Project:

Students will recognize connections between mathematics, history, and marketing.

Students will conclude their research and computations with the creation of a pamphlet

providing graphics, research, linear concepts, and a linear function logo.

Step 2: State the criteria for exemplary performance for each product:

Product: Engage, Explore, & Explain Real World Problems Criteria: (Formative Assessment)

To be completed early in the project. “Engage, Explore, & Explain Real World Problems” worksheet (located below)

Product: Reflecting Journal Entries Criteria: (Formative Assessment)

To be completed during the project. “Reflective Journal Entry Topics” (located below)

Product: Predicting Peirce’s Population Pamphlet Criteria: (Summative Assessment)

To be completed at the end of the project. “Predicting Peirce’s Population Pamphlet” (located below)

“Predicting Peirce’s Population Pamphlet Rubric” (located below)



Predicting Peirce’s Population “Engage, Explore, & Explain Real World Problems”

ENGAGE:

1. Investigate the two-point form formula:

http://www.easycalculation.com/analytical/learn-two-point.php

2. Predict the equation of a line:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=146

a. Plot two points & develop the equation of the line

EXPLORE:

How fast can you run? Sue thought she could run fast enough to try out for

the 2-mile race on the Olympic team. She had been training hard for months

and recently her father hired you to be her personal trainer and keep track

of her progress. You began keeping a journal and table of her progress each

month and, so far, you have the following data recorded:

Month January February March April May June

Time (minutes) 11.0 10.9 10.85 10.7 10.5 10.2

Based on the data that you have collected over the past six months, Sue has

made improvements since you began training her. But she also knows that

the record for the 2-mile race was set by a high school student in 2008 at

9.8 minutes. She doesn’t know if this is good enough for the Olympic team

but this is her goal. Her father as offered you a bonus of $2,000 if she

reaches this goal within the next three months of the training season. So

you decide to develop a trend line representing her progress and see if it is

possible for her to meet this goal.

Use your graphing calculator to answer the following questions.

1. What values did you enter into List 1 (L1)?_____________________

2. What do these values represent?___________________________

3. What values did you enter into List 2 (L2)?____________________

4. What do these value represent?____________________________

5. What helps you determine a good window for viewing the graph in your

calculator?____________________________________________

6. What is the equation for your trend line (round “a” and “b” to the

nearest hundredth)?_____________________________________

http://www.easycalculation.com/analytical/learn-two-point.php

http://illuminations.nctm.org/ActivityDetail.aspx?ID=146



7. Draw a picture of your graph below. Be sure to label the axes

correctly.

8. Based on the data, what will be Sue’s time in July, August, and

September?

____________________________________________________

9. Will you receive your $2,000 bonus? Provide justification for your

response.

____________________________________________________

____________________________________________________

____________________________________________________

EXPLAIN

1. Use the following data, write an equation and then use your calculator

to develop the trend line.

(5, 15), (7, 16), (10, 21), (14, 25), (17, 28)



2. Use the following data, write an equation and then use your graphing

calculator to develop the trend line.

Equation:__________________

3. Fast food is often considered unhealthy because of the amount of fat

(in grams) and calories. The following table represents data that has

been collected from hamburgers. Develop a trend line showing the

association between fat grams and calories in a burger. Label your

axes correctly!

X Y

12 10

15 7

18 4

21 2

23 1



Fat (grams) 19 31 34 35 39 39 43

Calories 410 580 590 570 640 680 660

Equation:__________________



Predicting Peirce’s Population “Reflecting Journal Entries”

Reflecting Journal Entry Topics:

To be answered during the ENGAGE portion. 1. Discuss the difference between slope-intercept and two-point form.

2. Record notes and data for plotting two points and predicting the

equation of the line.

a. Why is your guess so different from the computer guess?

What can you do to make your guess more accurate?

b. List the “equation of a line” results discussed in your group.

To be answered during the EXPLORE portion. 1. What is the mathematical term for XMIN and XMAX?

2. What is the mathematical term from YMIN and YMAX?

3. What help you determine how to set your window for good viewing?

4. What is the difference in a “trend line” and a linear equation?

5. Is it possible to continue decreasing Sue’s speed at this same rate?

Why or why not? What other factors could affect her speed?

To be answered during the EXPLAIN portion. 1. Write the graphing calculator steps required to calculate a line of

best fit.

2. List the pros and cons of a trend line.

3. Why is your equation found by hand different from other groups?

To be answered during the PAMPHLET portion. 1. What similarities and differences did you notice from other group’s

pamphlets?

2. Discuss other ways of finding populations and other information that

would be useful to have on the pamphlet if students were interested

in attending Peirce Middle School.

3. Discuss the usefulness of linear functions in real life and describe

other areas where linear functions are seen in the real world.



Predicting Peirce’s Population Pamphlet

You and your group need to create a pamphlet that includes Peirce’s

demographics, population statistics and trends, a linear function logo, and

inviting information as to why students should attend Peirce Middle School.

You will use technology to gather and analyze population growth/decay over

the past 20-25 years. The School Board President will present your

pamphlet at the next School Board meeting.

Part 1:

1. Research the data representing the population growth/decay of

Peirce Middle School from 1986-1990 at the following site:

http://documents.wcasd.k12.pa.us/dsweb/Get/Document-

1682/DAE459.pdf

[Note: this site will not give you all of the information that you need.

You will need to perform additional research]

Make a table showing the population from 1986-1990.

2. Use the data in the above table to calculate the equation for the

trend line and graph that data below (label your axes correctly).

Equation: _________________________

http://documents.wcasd.k12.pa.us/dsweb/Get/Document-1682/DAE459.pdf

http://documents.wcasd.k12.pa.us/dsweb/Get/Document-1682/DAE459.pdf



3. Use your line to predict the population for the years 1996 and 2000.

1996:____________________ 2000:____________________

4. In 2008, the population of Peirce was estimated to be 907 students

and 70 teachers. Does your trend line indicate a higher or lower

population and by how

much?_______________________________________________

____________________________________________________

____________________________________________________

____________________________________________________

____________________________________________________

5. List a minimum of three additional ways we can apply linear functions

in real-life.____________________________________________

____________________________________________________

____________________________________________________

____________________________________________________

____________________________________________________

Part 2:

Part two of your project is to develop your logo using only linear functions.

Use the bottom of this page to brainstorm your design. Please note that the

logo cannot take up more than two inches at the top of your pamphlet, but it

can be scaled to fit in the appropriate area of the page. After

brainstorming designs, draw a 20 x 20 grid on graph paper to chart your

final design. Upon completion of your drawing, calculate the equations for

each of your lines and document them neatly on your graph.



Part 3:

Complete the pamphlet. Your pamphlet must include your population analysis

(table, graph, predictions, and justifications), your logo, Peirce’s

demographics, and inviting information as to why students should attend

Peirce Middle School.



Predicting Peirce’s Population Pamphlet Rubric

Category 4 3 2 1 Mathematical

Concepts

Explanation shows

complete

understanding of

the mathematical

concepts used to

solve the

problem(s).

Explanation shows

substantial

understanding of

the mathematical

concepts used to

solve the

problem(s).

Explanation shows

some understanding

of the mathematical

concepts needed to

solve the

problem(s).

Explanation shows

very limited

understanding of

the underlying

concepts needed to

solve the problem(s)

OR is not written.

Mathematical

Reasoning

Uses complex and

refined

mathematical

reasoning.

Uses effective

mathematical

reasoning

Some evidence of

mathematical

reasoning.

Little evidence of

mathematical

reasoning.

Mathematical

Terminology and

Notation

Correct

terminology and

notation are always

used, making it easy

to understand what

was done.

Correct

terminology and

notation are usually

used, making it

fairly easy to

understand what

was done.

Correct terminology

and notation are

used, but it is

sometimes not easy

to understand what

was done.

There is little use,

or a lot of

inappropriate use,

of terminology and

notation.

Graphs Graphs are clear

and greatly add to

the reader's

understanding of

the procedure(s).

Graphs are clear

and easy to

understand.

Graphs are

somewhat difficult

to understand.

Graphs are difficult

to understand or

are not used.

Attractiveness

& Organization

The brochure has

exceptionally

attractive

formatting and

well-organized

information.

The brochure has

attractive

formatting and well-

organized

information.

The brochure has

well-organized

information.

The brochure's

formatting and

organization of

material are

confusing to the

reader.

Content –

Accuracy

All facts in the

brochure are

accurate.

99-90% of the

facts in the

brochure are

accurate.

89-80% of the

facts in the

brochure are

accurate.

Fewer than 80% of

the facts in the

brochure are

accurate.

Collaboration Student was an

engaged partner,

listening to

suggestions of

others and working

cooperatively

throughout lesson.

Student was an

engaged partner but

had trouble listening

to others and/or

working

cooperatively.

Student cooperated

with others, but

needed prompting to

stay on-task.

Student did not

work effectively

with others.




Map the Project

What do students need to know and be able to do to complete the tasks successfully? How and when will they learn the necessary knowledge and skills? Look at one major product for the project and analyze the tasks necessary to produce a high-quality product.

Product: Predicting Peirce’s Population

KNOWLEDGE AND SKILLS NEEDED ALREADY HAVE LEARNED

TAUGHT BEFORE THE PROJECT

TAUGHT DURING THE PROJECT

1. Problem solving skills

X X X

2. The use of symbols and mathematical notation

X

3. Evaluate and simplify algebraic expressions

X X

4. Creating, writing, and evaluating equations of lines

X X

5. Describe the concept of slope and y-intercept

X X

6. Graphing Lines

X

7. Using a calculator to develop trend lines

X X

8. Making predictions based upon trend lines, understanding correlation

X X

9. Draw inductive and deductive conclusions

X X X

10. Applying skills to develop a logo

X X

11. Develop key vocabulary (slope, y-intercept, slope formula, slope-intercept formula, point-slope formula, two-point form formula, scatterplot, trend lines, correlation)

X X X



What project tools will you use?

□ Know/need to know lists

□ Daily goal sheet

□ Task lists

□ Reflection journals

□ Graphing calculators

□ Computers with Internet access

□ Problem-solving worksheets

□ Pamphlet guidelines

□ Graph paper

□ Writing utensil

□ Art supplies

List the key dates and important milestones for this project.

Day 1 Introduction to Predicting Peirce’s Population Entry Scenario

Days 2-3 Internet-Based Activity Engaging portion of the “Enga e, Explore, & Explain Real

World Problems” worksheet

Days 4-5 Exploring portion of the “Engage, Explore, & Explain Real World Problems” worksheet

Day 6 Explaining portion of the “Engage, Explore, & Explain Real World Problems” worksheet

Day 7 “Predicting Peirce’s Population Pamphlet” part 1

Day 8 “Predicting Peirce’s Population Pamphlet” part 2

Days 9-10 “Predicting Peirce’s Population Pamphlet” part 3

Day 11 Display and present pamphlets

Each day equals a 45 minute class period.

Use the Tuning Protocol with other teachers or a group of students to refine the project design or guide you further in your planning. What other thoughts do you now have on the project? Thoughts from fellow classmates to better prepare the project design:

Do you know that access to historical demographic and population information is available?

It appears to me that you have a lot of standards to reach during this project, which may make it a lot of work to assess all of them.

What about collaborating with a social studies teacher/class to determine WHY the changes that have happened over the last 20 years happened?

Possible sub-questions are "What are the parameters of your equation?" and "Is your equation always appropriate to describe your data?"

Don't cut the students off at linear functions. I realize that is the goal and the standard that is behind the question, but if the students are realizing that the data follows a curve, encourage them to try to explain that phenomenon and relate that to how well the linear model fits it.



Timeline



Entry Scenario You and your group need to create a pamphlet that includes Peirce’s demographics,

population statistics and trends, a linear function logo, and inviting information as to why students should attend Peirce Middle School. You will use technology to gather and analyze population growth/decay over the past 20-25 years. The School Board President will present your pamphlet at the next School Board meeting. But before the construction of a pamphlet takes place, you and your group will travel

on a linear functions journey. On this journey you will reinforce your skills at writing equations of lines and use those skills to find trend lines so you can make predictions.

Internet-Based Activity The Internet will be a required resource during the engaging portion of the “Engage, Explore, & Explain Real World Problems” worksheet and during part 1 and part 3 of the “Predicting Peirce’s Population Pamphlet”. The following introduction activity will take place during Day 1 of the project. This website will give the students a brief overview of what to expect during the project.

Slope-Intercept Form http://www.mathwarehouse.com/algebra/linear_equation/slope-intercept-form.php

Video tutorial on Slope Intercept Form Slope intercept equation of vertical and horizontal lines overview Interactive slope intercept form Interactive slope-intercept form of graphed lines Interactive slope-intercept form for lines (given the slope & y-intercept)

All notes, answers, and observations will be recorded in the student’s reflection journal.

http://www.mathwarehouse.com/algebra/linear_equation/slope-intercept-form.php



Introductory Letter

Dear Students and Parents/Guardians: Over the next three weeks my students will be collaborating to create a “Predicting Peirce’s Population Pamphlet” for the School Board’s President. Through this journey the following standards-based topics will be covered:

Identify and graph the linear parent function.

Describe and predict the effect of changing the slope (“m”) and the y-intercept (“b”) on the parent graph.

Establish how to identify linear functions by making connections between the various representations.

Define slope and intercepts of linear equations and functions. Calculate slope (rate of change) and intercepts from various representations. Explain how direct variations are related to linear functions.

The students will be responsible for writing daily journal entries, calculating multiple real-world problems presented through multimedia resources and worksheets, mastering graphing calculator techniques, and recognizing relationships between mathematics, history, and marketing. While on this journey, the students will be answering the essential question, “How can linear functions help predict population

trends?” This is an engaging project-based learning activity, which requires critical thinking, problem solving, collaboration, and various forms of communication. By completing this activity, students will gain a deeper understanding of linear functions and build lifelong habits of learning!

I have read and understand the three-week long activity entitled, “Predicting Peirce’s Population.” I realize it is my responsibility to communicate with my group if I plan to miss class due to enrichment, band lessons, or field trips. It is my responsibility

to make-up all missed work. _________________________________ _________________________________ Printed Student Name Student Signature

I have read and understand the three-week long activity entitled, “Predicting Peirce’s Population.” _________________________________ _________________________________

Printed Parent/Guardian Name Parent/Guaridan Signature




Manage the Process

List preparations necessary to address needs for differentiated instruction for ELL students, special-needs students, or students with diverse learning styles.

English Language Learners (ELL): may complete the project using an English

electronic translator. ELL students may complete a modified version of the project, based on his/her transition step, which will be created by the individual’s ELL teacher.

Special-Needs Students: may complete a modified version of the project that will be created by the individual’s case worker. An adjusted schedule and “chunking” will be provided based off of each student’s individualized education plan (IEP). The

resource room will be provided to those in need.

At-Risk Students: will be creatively placed in groups with motivating and encouraging students. Gifted Students: An adjusted schedule and enrichment will be provided based off

of each student’s gifted individualized education plan (GIEP).

How will you and your students reflect on and evaluate the project?

□ Class Discussions: held throughout the project (led by students and/or teacher)

□ Student Learning Log*: used to prompt writings in Reflective Journal

□ Group-Member Observation Checklist*: to be completed throughout the project

□ The Fishbowl Method*: used to display and present pamphlets

□ Oral Presentation Checklist**: used to prepare pamphlet presentation

□ End-of-Project Self-Assessment*: to be completed at the conclusion of the project

*Modifications made from Project Management Tools

**Modifications made from Project Based Learning Checklists

http://pbl-online.org/ManagetheProject/ProjectPlanningTools/PlanningTools.htm

http://pblchecklist.4teachers.org/testing.php?idunique=3&max=6&checklist=1



Student Learning Log

Predicting Peirce’s Population Student: Date:

I had the following goals:

I accomplished the following:

My next steps are:

My most important concerns/problems/questions are:

I learned:



Group-Member Observation Checklist

Predicting Peirce’s Population Group Members: Date:

Write each group

member’s name under the correct column

that best describes his/her participation.

DID DID NOT Not

Applicable

When starting a new task, group members:

Agree on an agenda or plan Begin work promptly Get out project materials Figure things out without teacher assistance

Share responsibilities When conducting research, group members:

Consult primary sources Take notes

Have relevant

conversations Evaluate the significance of new information

Stay on task

When discussing project work, group members:

Ask clarifying questions Give each other a chance to speak Make decisions efficiently Record decisions and plans Share essential information Stay on task



The Fishbowl Method

The Fishbowl Method will be used on Day 11 (display and present projects)

1. Arrange students in a large circle. 2. Place a smaller circle of five to seven chairs in the center of the larger circle. 3. Have one group sit in the inside circle. Keep one chair vacant. 4. Students in the inner circle discuss the outcomes of their project. The

audience in the outer circle listens. 5. The vacant chair is for any member of the audience who wants to join the

discussion to add a comment or ask a question. Once the comment has been made or the question asked, the participant returns to the audience so that another member of the audience may join the inner circle.

6. Repeat steps 3-5 until all groups have presented their project.

Note: Only one day is allotted for project presentations. Divide the time for presentations by the number of groups in the class.

Oral Presentation Checklists

Predicting Peirce’s Population Student Name: Date:

Content I used facts and logical appeals where appropriate.

I was well-informed on my topic.

I presented information that others didn't know.

I was able to answer questions from the audience. Delivery My body language was alert and relaxed.

My voice varied in pitch. It was not monotone.

I used notes sparingly. I did not read from them unless

presenting a quote.

I spoke to the entire audience, not just one or two people.

My volume was neither too loud nor too soft. Organization I included necessary background information.

The body or the presentation contained support for the

main points.

The audience could distinguish the introduction, body

and conclusion. Presentation Aids Presentation aids were used during the speech.

Presentation aids were relevant to the topic.

Visual aids were easy to read or see.



End-of-Project Self-Assessment

Predicting Peirce’s Population Student: Date:

I completed the following tasks during the project:

As a result, I learned the following:

About the subject matter

About working in a group About creating a pamphlet

About presenting to an audience

I learned that my strengths are:

I learned I need to work on:

I would make the following changes if I were to do the project again:




Appendix

GROUPING STRATEGIES

Students will be placed into groups after the Engaging portion of the “Engage, Explore, & Explain Real World Problems” worksheet. The following links are to assist the teacher in creatively organizing the students into groups. Creative Ways to Organize Students for Small Group Activities Fun Ways to Group Students

Fun Ways to Split into Groups

GRAPHING CALCULATOR GUIDELINES

These directions are to assist the teacher. The teacher should act as a facilitator in this process that should be demonstrated prior to the Exploring portion of the

“Engage, Explore, & Explain Real World Problems” worksheet. Demonstrate this warm-up problem on an overhead calculator or on the TI-SmartView software. Encourage the students to copy this information into their Reflective Journal for future reference.

“BEST FIT LINE FOR DATA” WARM-UP PROBLEM

The given data describes the correlation between the cost of a concert ticket and the seating row for the venue.

Seating Row 2 4 8 15 22 30 38

Cost of Ticket $70.00 $68.50 $55.00 $42.00 $30.00 $20.00 $12.00

Based on the given data, develop a trend line representing the negative correlation and use the equation for that line to determine the price of a ticket for the 45th row. Graphing Calculator Directions:

1. Make sure your Y= functions are cleared and STAT PLOTS is turned on. 2. Press STAT and select 1: Edit by pressing ENTER. 3. The data you can put in L1 is the seating row (2, 4, 8, 15, 22, 30, 38) 4. The data you will put in L2 is the information from the table representing the

cost of the ticket without the dollar sign ($70.00, $68.50, $55.00, $42.00, $30.00, $20.00, $12.00)

5. Press WINDOW to set up the proper window for your data XMIN 1 XMAX 40 XScale 5 YMIN 0

http://www.projectalert.com/assets/0/318/Creative-Ways.pdf

http://insights-into-tefl.blogspot.com/2007/03/fun-ways-to-groups-students.html

http://www.girlscoutsnorcal.org/documents/LE-Fun_Splitters.pdf



YMAX 75 YScale 5

6. Press STAT again and select CALC: 4. This will generate the equation for your

trend line (also known as a linear regression). 7. Round off the “a” and “b” to the nearest hundredth and enter your equation in

Y1. 8. Graph your line on graph paper. Be sure to label your axes correctly.


Documents

Predicting Pennsylvania Population - Megan Hoopes …€¦ · · 2011-07-28Identify and graph the linear parent function. ... How can a graphing calculator be used to graph linear