make that prediction

Transformation 2013 Design Challenge Planning Form

Guide

Design Challenge Title: Make That Prediction Teacher: Bonnie McClung School: Transformation 2013 T-STEM Center Subject: Algebra I Abstract: In this design challenge, students will reinforce their skills at writing equations of lines and use those skills to find trend lines so they can make predictions. This challenge also reinforces scatterplots and correlation.

MEETING THE NEEDS OF STEM EDUCATION

THROUGH DESIGN CHALLENGES

© 2008 Transformation 2013 1 last update 10.8.2008

Begin with the End in Mind

The theme or “big ideas” for this design challenge:

Students will write equations of lines, find trend lines, and make predictions.

TEKS/SEs that students will learn in the design challenge:

(A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

The student is expected to:

(A) describe independent and dependent quantities in functional relationships;

(B) gather and record data and use data sets to determine functional relationships between quantities;

(C) describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and

(E) interpret and make decisions, predictions, and critical judgments from functional relationships.

(A.2) Foundations for functions. The student uses the properties and attributes of functions.


(C) interpret situations in terms of given graphs or creates situations that fit given graphs; and

(D) collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.


(A.3) Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.


(A) use symbols to represent unknowns and variables; and

(B) look for patterns and represent generalizations algebraically.

(A.5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.


(A) determine whether or not given situations can be represented by linear functions

(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.


(B) interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

(D) graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

(F) interpret and predict the effects of changing slope and y-intercept in applied situations.

Key performance indicators students will develop in this design challenge:

Identify and sketch the linear parent function; describe and predict the effect of changing “m” and “b” on the parent function; determine how to identify linear functions by making connections between the various representations; define slope and intercepts of linear functions; determine slope (rate of change) and intercepts from various representations; describe how direct variations are related to linear functions

21st century skills that students will practice in this design challenge: www.21stcenturyskills.org

Demonstrating creativity using applied concept, contributing and collaborating with a


http://www.21stcenturyskills.org/

group, assuming shared responsibility

STEM career connections and real world applications of content learned in this design challenge:

Students will see the connection between math and marketing through the completion of this design challenge. They will use technology to gather and analyze population growth for the State of Texas over the past 15-20 years and create a flyer with graphics, research, and a logo.



The Design Challenge You and your team have been hired as consultants to the Texas Governor’s Office of Information to make flyers advancing the State of Texas as a great place to live and relocate companies. One of the things that makes moving to a state attractive is an increase in population over the years. This generally means other benefits are attractive as well. Your team is charged with developing a trend line showing the growing/declining population in Texas over the past 15-20 years. Your team will design a flyer illustrating the results of your investigation and encouraging others to join the trend and move to Texas. Your flyer must have a logo designed using only linear functions and it must also include some Texas history, symbols and emblems that represent the State of Texas , and enticing information supporting why people should move to Texas. The Governor wants to reference your research and the flyer in his upcoming speech, so your team must work quickly!

Map the Design Challenge Performance Indicators

Already Learned

Taught

before the project

Taught

during the project

1. Writing equations of lines x x

2. Using a calculator to develop trend lines x x

3. Making predictions based upon trend lines, understanding correlation

x x

4. Applying skills to designing a logo x x

5. Graphing lines x

6. Develop key vocabulary (slope, y-intercept, slope formula, slope-intercept formula, point-slope formula, two-point form formula, scatterplot, trend line, correlation, association)

x x x


5E Lesson Plan Engage Activity

TEKS/TAKS objectives: A.1A,B,C,D,E; A.2C,D; A.3A,B; A.5A; A.6B,D,F

Design Challenge Title: Make That Prediction

**Students should have experienced writing equations of lines and interpreting slope and y-intercept prior to this PBL. The purpose is to reinforce the writing of equations and to understand the importance of the concept as it relates to real-life experiences** Identify the concepts to be explored with leading questions such as: “Why is it important to write equations of lines?” “How does that concept appear in real life?” Have students work five warm-up problems as a refresher of the concepts. These problems can be in the form of a handout or have students complete the practice found at http://regentsprep.org/Regents/math/glines/PracLine.htm. Also, have the students investigate the two-point form formula using the following link: http://www.easycalculation.com/analytical/learn-two-point.php. Discuss the solutions and have students contribute information such as the difference

between slope-intercept (y = mx +b) and two-point form . Tell the students there are many reasons for studying equations of lines and one of those is to enable us to make predictions based upon our equation. Explain to them that they will be participating in an activity in which they will make guesses about the equation of a line and the computer will also make a guess http://illuminations.nctm.org/ActivityDetail.aspx?ID=146. Students will be plotting two points of their choice and developing the equation of the line (they should use their math journal to keep notes and records of problems). They will record their observations in their math journal and you should debrief them with questions such as “Why is your guess so different than the computer guess?” “What can you do to make your guess more accurate?” (Plot more points) When students return from the lab, have them draw from a basket in which you have squares, triangles, circles and quadrilaterals. (You may use any objects you wish to establish groups—this reinforces classification.) They will match their shapes/objects to establish their groups. Have students assemble into their groups and provide time for them to discuss the results of their lab experience and their thoughts/questions. Debrief and begin a vocabulary word wall for them to refer to and keep in their math journal.


http://regentsprep.org/Regents/math/glines/PracLine.htm

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

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

Introduce the students to the design challenge: You and your team have been hired as consultants to the Texas Governor’s Office of Information to make flyers advancing the State of Texas as a great place to live and relocate companies. One of the things that makes moving to a state attractive is an increase in population over the years. This generally means other benefits are attractive as well. Your team is charged with developing a trend line showing the growing/declining population in Texas over the past 15-20 years. Your team will design a flyer illustrating the results of your investigation and encouraging others to join the trend and move to Texas. Your flyer must have a logo designed using only linear functions and it must also include some Texas history, symbols and emblems that represent the State of Texas , and enticing information supporting why people should move to Texas. The Governor wants to reference your research and the flyer in his upcoming speech, so your team must work quickly! Before we begin the design challenge, let’s work a practice problem to sharpen our skills using the graphing calculator and interpreting data.

Engage Activity Products and Artifacts

Completed warm-up problems, journal entry

Engage Activity Materials/Equipment

Computer with internet access, journal, pencil, graph paper

Engage Activity Resources

http://regentsprep.org/Regents/math/glines/PracLine.htm http://illuminations.nctm.org/ActivityDetail.aspx?ID=146 http://www.easycalculation.com/analytical/learn-two-point.php

Explore Activity

Provide the students with the following “warm-up” problem and guide them through the calculator steps required to determine the line of best fit for the data. 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 $68.50 $55 $42 $30 $20 $12


http://regentsprep.org/Regents/math/glines/PracLine.htm

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

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


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. Let’s begin by using your graphing calculators: 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 ($70, $68.50, $55, $42, $30, $20, $12)…no dollar signs are necessary for entry into your table! 5. Press WINDOW to set up the proper window for your data XMIN 1 XMAX 40 XScale 5 YMIN 0 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 provided. Be sure and label your axes correctly. 9. Reflect in your math journal regarding the following:

What is the mathematical term for XMIN and XMAX (domain)? What is the mathematical term for YMIN and YMAX (range)? What helps you determine how to set your window for good viewing? (the x and y

values from the table) What is the difference in a “trend line” and a linear equation (Answers may differ

but students should realize that a trend line is used for prediction only to a certain extent whereas an equation represents some exact information)

Teacher should act as facilitator in this process, perhaps demonstrating on an overhead calculator as students progress, stopping to answer questions and providing help as needed with the calculators. Tell students to copy this information in their journals for future reference and discuss how the window may change with other information. Once you are certain that the students have a firm grasp of the calculator steps required to calculate a line of best fit, provide them with the “How Fast Can You Run?” problem below and explain that they will be using the same process from the warm-up problem to determine the line of best fit (trend line) for this problem.

Explore Activity Products and Artifacts

Equations representing the student’s trend line, graph of the problem, clearly labeled axes with correct numbering, journal entries

Explore Activity Materials/Equipment

Graphing calculators, graph paper, pencils, rulers

Explore Activity Resources

None

Explain Activity

Have the students graph the data from the Explore Activity on large chart paper and discuss the trend line they found. In your debriefing, bring the focus back to the concept being studied (using equations of lines to make predictions). Ask for questions and check that the students entered the calculator directions into their journals. Clear up any misunderstandings and provide assistance to groups needing help with the calculator. Discuss the pros and cons of this trend line. Is it possible to continue decreasing her speed at this same rate? Why or why not? What other factors could affect her speed? Have students get into their groups and give them a handout with four problems containing data. Data should be in the form of ordered pairs and tables. Instruct them to find the trend line for each of the problems by hand and using their calculators and explain the meaning of the slope and y-intercept in each of the problems. (See example problems below.)

Explain Activity Products and Artifacts

Presentation of explore problem, completed data example problems

Explain Activity Materials/Equipment

Large chart paper, markers, rulers, graphing calculators, Explain handout

Explain Activity Resources

None

Elaborate Activity

Provide a debriefing for the equations found in the previous activity. Have students


explain why their equations found by hand differ from other groups (It depends upon which two points were used to write the equations). Present students with design challenge and provide each group with a copy of the problem (see document below). Provide each team several sheets of graph paper in case of mistakes. Have students research the data representing the population growth in the State of Texas from 1990-1994 at the following site: http://www.learner.org/interactives/dailymath/population.html They will use this information to discover a trend line for population growth in Texas. You will need to serve as a facilitator, helping some students with conversions (ie. 17,045,000 to 17.045 million), some with setting their calculator window to display the correct domain and range, others with questions regarding the design challenge, etc.

Elaborate Activity Products and Artifacts

Research, logo design, logo equations, completed design challenge guide

Elaborate Activity Materials/Equipment

Computer, Internet access, graph paper, pencils, design challenge guides, calculators

Elaborate Activity Resources

http://www.learner.org/interactives/dailymath/population.html http://www.enchantedlearning.com/usa/states/texas/

Evaluate Activity

Have students make a copy of their flyer and create a poster outlining their work. Their posters should include a view of both the front and back of their flyers, justifications supporting the population analysis (table, graph, predictions, etc.), and the original graph of the logo. Have the students participate in a gallery walk with a docent and complete a rubric for each product (reassign groups so that there is one “expert” per poster). Refer to the following website for a more detailed description of the activity: http://highschool.concord.k12.in.us/ateachsite/processing/gallerywalk.pdf Upon completion of the gallery walk, debrief the activity with them. What were some of the similarities? Differences? Etc.


http://www.learner.org/interactives/dailymath/population.html


http://www.enchantedlearning.com/usa/states/texas/

http://highschool.concord.k12.in.us/ateachsite/processing/gallerywalk.pdf

Discuss other ways of finding populations and other information that would be useful to have on the flyer if people are to be attracted to Texas. Have students discuss the usefulness of linear functions in real life and describe other areas where linear functions are seen in the real world.

Evaluate Activity Products and Artifacts

Gallery walk, rubrics from gallery walk, discussions

Evaluate Activity Materials/Equipment

Posters displaying finished products

Evaluate Activity Resources




How Fast Can You Run?

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 improvement 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 calculator and the terms from the word bank below to answer the following questions. All terms from the word bank will be used, and some terms may be used more than once.

1. What values did you enter into List 1 (L1)? _________________________________ 2. What do these values represent? __________________________________________ 3. What values die you enter into List 2 (L2)? _________________________________ 4. What do these values 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)?

_____________________________________ 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 times in July, August, and September? _______________________________________________________________________ 9. Will you receive your $2000 bonus? Provide justification for your response. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Explain Sample Problems

1. Using 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. Using the following data, write an equation and then use your calculator to develop the trend line.

Equation: ____________

X Y 12 10 15 7 18 4 21 2 23 1


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 (don’t forget to label your axes correctly).

Fat (grams) 19 31 34 35 39 39 43 Calories 410 580 590 570 640 680 660

Equation: ______________


Design Challenge Guide

You and your team have been hired as consultants to the Texas Governor’s Office of Information to make flyers advancing the State of Texas as a great place to live and relocate companies. One of the things that makes moving to a state attractive is an increase in population over the years. This generally means other benefits are attractive as well. Your team is charged with developing a trend line showing the growing/declining population in Texas over the past 15-20 years. Your team will design a flyer illustrating the results of your investigation and encouraging others to join the trend and move to Texas. Your flyer must have a logo designed using only linear functions and it must also include some Texas history, symbols and emblems that represent the State of Texas , and enticing information supporting why people should move to Texas. The Governor wants to reference your research and the flyer in his upcoming speech, so your team must work quickly! Part 1: 1. Research the data representing the population growth in the State of Texas from 1990-1994 at the following site: http://www.learner.org/interactives/dailymath/population.html. Make a table showing the population from 1990-1994. 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: ______________________________

3. Use your line to predict the population for the years 2000 and 2004. 2000: ____________________ 2004: _______________________



4. In 2006, the population of Texas was estimated to be 23.508 million people. Does your trend line indicate a higher of 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 design challenge 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 flyer, 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…these equations play a huge role in the computer designer’s work. She must have them to use during programming to finalize the logo.


Part 3: Complete the flyer. Your flyer must include your population analysis (table, graph, predictions, and justification), your logo, some Texas history, symbols and emblems that represent the State of Texas , and enticing information supporting why people should move to Texas.


Plan the Assessment Engage Artifact(s)/Product(s): Completed warm-up problems, journal entry

Explore Artifact(s)/Product(s): Equations representing the student’s trend line, graph of the problem, clearly labeled axes with correct numbering, journal entries

Explain Artifact(s)/Product(s): Presentation of explore problem, completed data example problems

Elaborate Artifact(s)/Product(s): Research, logo design, logo equations, completed design challenge guide

Evaluate Artifact(s)/Product(s): Gallery walk, rubrics from gallery walk, discussions


Rubrics

Rubric Points + Worksheet Points + Creativity + Teamwork + Self Reflection = Final Grade



Story Board Day 1 Day 2 Day 3 Day 4 Day 5

Week 1 Activities

Engage (45 minutes)

Explore (45 minutes)

Explain (45 minutes)

Elaborate (45 minutes)



Evaluate (90 minutes)

make that prediction

Documents

linear situations

graphs of linear functions

parameters of linear

zeros of linear functions

situations d

problem situations

attributes of functions

mathematical situations