Tyler+Winner's+Lessons

Hey Everyone! This is my first lesson plan for my math Problem Based Lesson.​ The problem I present to them is about the methods people use to predict and measure the spread of disease. How do they do it? I have the students do it themselves. See what you think and leave me a comment if you like! Tyler
 * 

A Standards-Based Approach ** Written by: Tyler Winner This is a equation and modeling lesson for grades 11 or 12.
 * Overview:** In this lesson, students will be presented with the problem of how government agencies us modeling to predict and measure the spread of diseases like the flu. Student will research the internet to find modeling equation and then apply them to a high school population. They will then put there equations on a wiki page along with an evaluation of how well they believe their models fit in real life.
 * Lesson Title:

**Modeling the Spread of the Flu **  || Related Lessons: TBD || · Use recursive functions to model and solve problems; e.g., home mortgages, annuities. · Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences. · Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation.   X Creativity and innovation X Communication and collaboration X Research and information fluency || 
 *  || Unit: **Modeling with Equations** ||
 * ** GOALS ** ||
 * Content Standards:**
 * Standard Taken from Ohio Dept. of Education Math standards (2009)**
 * **<span style="font-family: 'Arial','sans-serif';">ISTE NETS-S **

X Critical thinking, problem-solving, & decision-making X Digital citizenship X Technology operations and concepts || <span style="font-family: 'Arial','sans-serif';">
 * <span style="font-family: 'Arial','sans-serif';">Instructional objective(s): **
 * <span style="font-family: 'Arial','sans-serif';">Students will: **
 * <span style="font-family: 'Arial','sans-serif';">Research and find an equation that models the spread of an illness through a population
 * <span style="font-family: 'Arial','sans-serif';">Apply the information found to model the spread of a flu through the high school
 * <span style="font-family: 'Arial','sans-serif';">Analyze the model they make to determine its accuracy
 * <span style="font-family: 'Arial','sans-serif';">Write up their findings along with graphs on a wiki page

<span style="font-family: 'Arial','sans-serif';"> Get a wiki page set up for every student. Have websites listed that students can search for help. Have graphing software “Geogebra” installed for student use. Get school population data for the students to use. Type up paper with the problem and prompt for students || <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';">
 * ** ACTION<span style="font-family: 'Arial','sans-serif';"> ** ||
 * <span style="font-family: 'Arial','sans-serif';">
 * <span style="font-family: 'Arial','sans-serif';">Before-class preparation: **
 * **<span style="font-family: 'Arial','sans-serif';">During class **
 * <span style="font-family: 'Arial','sans-serif';">Time: 2 day (100 min) || <span style="font-family: 'Arial','sans-serif';">Instructional Activities || <span style="font-family: 'Arial','sans-serif';">Materials & Resources ||
 * <span style="color: #548dd4; font-family: 'Arial','sans-serif';">15 min

30 min

<span style="color: #548dd4; font-family: 'Arial','sans-serif';">5 min <span style="font-family: 'Arial','sans-serif';">30 min

<span style="color: #548dd4; font-family: 'Arial','sans-serif';">20 min <span style="font-family: 'Arial','sans-serif';"> || <span style="color: #548dd4; font-family: 'Arial','sans-serif';">Hand out directions and tell students about the assignment. <span style="font-family: 'Arial','sans-serif';">Let students search the net for useful models <span style="color: #548dd4; font-family: 'Arial','sans-serif';">Q & A with students <span style="font-family: 'Arial','sans-serif';">Students work with models to apply one to the high school scenario <span style="color: #548dd4; font-family: 'Arial','sans-serif';">Post the applied High School model to wiki along with the evaluations of the modeling equations || <span style="color: #548dd4; font-family: 'Arial','sans-serif';">Handout <span style="font-family: 'Arial','sans-serif';">

Internet Access

<span style="color: #548dd4; font-family: 'Arial','sans-serif';"> <span style="font-family: 'Arial','sans-serif';">Geogebra Software

<span style="color: #548dd4; font-family: 'Arial','sans-serif';">Wiki access || <span style="font-family: 'Arial','sans-serif';">Notes: Student groupings, environmental modifications needed, etc.


 * ** MONITOR ** ||

<span style="font-family: 'Arial','sans-serif';">**Ongoing assessment(s):** Q & A with student during work and internet search Teacher will also have students show what they have found after the search so as to ensure they have a viable model

<span style="font-family: 'Arial','sans-serif';">URLs will be provided for any students with poor internet searching skills Enrichment activity for advanced students will be to write how the different variables affect how the equation works
 * <span style="font-family: 'Arial','sans-serif';">Accommodations and extensions: **

<span style="font-family: 'Arial','sans-serif';">Lesson reflections and notes:
 * <span style="font-family: 'Arial','sans-serif';">Backup plan: **<span style="font-family: 'Arial','sans-serif';"> If Internet/computers are not available, graphing calculators and TI-Connect software can be used in place of Geogebra and Wikis. Also, the modeling functions can be found in texts in the classroom
 * <span style="font-family: 'Arial','sans-serif';">Evaluation: **<span style="font-family: 'Arial','sans-serif';"> Students will be evaluated for content by the wiki page. A rubric will be used that takes into account: effort, mathematical reasoning, Communication, and their own evaluations of their models.
 * ** EVALUATE AND EXTEND ** ||

Lesson template taken from the Student Companion Site for the text: <span style="font-family: 'Times New Roman','serif';">Cennamo, K., Ross, J. & Ertmer, P. (2009). //Technology integration for meaningful// //<span style="font-family: 'Times New Roman','serif';">classroom use: A standards-based approach //<span style="font-family: 'Times New Roman','serif';"> (Laureate Education custom edition). Belmont, CA: Wadsworth, Cengage Learning.

I think I could adapt a variation of this activity to fit into my advanced biology class. Nice activity. Any critique that I could offer would be in the realm specificity. I had to read this several times to figure out exactly how you would execute this lesson. Other than that nice work. Norm

Tyler,

I think this is a great lesson and will work well. If I were to give any suggestions, I would ask a few questions. Do you plan on creating each wiki that was described in the pre-lesson objectives? Do you plan on installing that program "geogebra" on each computer that will be used? How much time have you allocated towards prepping for such a lesson? I have done a similar lesson with similar preparations were needed. I spend an absorbent amount of time setting everything up and the lesson only seemed to last about half as long as expected. Just keep in mind how time consuming some things are. Maybe you have an alternate solution to such a problem and if so, please share because I seem to spend more time on research and development. Also, when you mentioned having students "search the net for useful models"; are you going to allow the simple "google it" approach? I have wondered what others did when they wanted their students to conduct basic research. Thanks. Kevin <span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">

Hey Everyone, here is lesson number two! I tried to be more specific this time. I agree Norm, my last lesson was a little vague. This lesson has to do with using Sine curves to graph temperature data. I really like the idea of this one. See what you think! Tyler

** A Standards-Based Approach ** Written by: Tyler Winner This is an equation and modeling lesson for grades 11 or 12.
 * Overview:** For this lesson, students will be corresponding with other students from around the country for the majority of the school year. Once a week, the students will correspond and get the high and low temperature data from other places in the country and other places in the world. Once a sufficient amount of data has been collected, the students will use sinusoidal regression software to write an equation that represents the data that they have been collecting throughout the year. They will then graph the data and compare and contrast all of the class’s graphs and see how temperature works with climate and how the parts of the sin graph (period, amplitude, phase) all work together. The written assignment will be on a wiki page.


 * <span style="font-family: 'Arial','sans-serif';">Lesson Title:

**<span style="font-family: 'Arial','sans-serif';">Modeling Temperatures Around the World **<span style="font-family: 'Arial','sans-serif';"> <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';">Related Lessons: <span style="display: block; font-family: 'Arial','sans-serif'; text-align: center;"> **<span style="font-family: 'Arial','sans-serif';">Modeling the Spread of the Flu ** <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';"> ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: 'Palatino-Roman','serif'; font-size: 12.5pt;">Use recursive functions to model and solve problems; e.g., home mortgages, annuities. ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: 'Palatino-Roman','serif'; font-size: 12.5pt;">Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences. ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: 'Palatino-Roman','serif'; font-size: 12.5pt;">Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation. <span style="font-family: 'Arial','sans-serif';"> <span style="font-family: 'Arial','sans-serif';"> o <span style="font-family: 'Arial','sans-serif';"> Creativity and innovation X Communication and collaboration X Research and information fluency || <span style="font-family: 'Arial','sans-serif';">
 * <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';">Unit: **Modeling with Equations** ||
 * ** GOALS ** ||
 * <span style="font-family: 'Arial','sans-serif';">Content Standards: **
 * Standard Taken from Ohio Dept. of Education Math standards (2009)**
 * **<span style="font-family: 'Arial','sans-serif';">ISTE NETS-S **

X Critical thinking, problem-solving, & decision-making X Digital citizenship X Technology operations and concepts || <span style="font-family: 'Arial','sans-serif';"> <span style="font-family: 'Arial','sans-serif';"> ||
 * <span style="font-family: 'Arial','sans-serif';">Instructional objective(s): **
 * <span style="font-family: 'Arial','sans-serif';">Students will collaborate with students from around the United States and other places around the world to collect temperature data and model them with trigonometric functions. **
 * <span style="font-family: 'Arial','sans-serif';">The will write up their findings on a blog. **
 * ** ACTION<span style="font-family: 'Arial','sans-serif';"> ** ||
 * <span style="font-family: 'Arial','sans-serif';">
 * <span style="font-family: 'Arial','sans-serif';">Before-class preparation: **
 * <span style="font-family: 'Arial','sans-serif';">The teacher must get the class ePals from around the country. This can be done on the ePals site or other online collaboration site.
 * <span style="font-family: 'Arial','sans-serif';">The teacher must have sinusoidal regression software for the students to use.
 * <span style="font-family: 'Arial','sans-serif';">The teacher must also have Geogebra Software to display the student findings.
 * <span style="font-family: 'Arial','sans-serif';">Data collection for this project must be done over a long period of time. This is going to almost be a yearlong project. So this prep work must be done before the year starts. The teacher will also collect the data from the local weather for a base graph ||
 * <span style="display: block; font-family: 'Arial','sans-serif'; text-align: center;">During class


 * <span style="font-family: 'Arial','sans-serif';">Time || <span style="font-family: 'Arial','sans-serif';">Instructional Activities || <span style="font-family: 'Arial','sans-serif';">Materials & Resources ||
 * <span style="font-family: 'Arial','sans-serif';">First 8 months of school

First day of lesson:

10 min

15 min

15 min

10 min || <span style="font-family: 'Arial','sans-serif';">Students will communicate with their ePals to get the temperature data from other parts of the world

Explain the sin regression software. Show how to enter the data and interpret the results. Use the local temperatures to make the base graph

Give students time to create equations. Teacher should circulate to help students

Have students all come up an help them graph their equation onto the class Geogebra graph. Label the graphs with their geographic region and do so in different colors. The teacher needs to graph the base graph of the local data

Have group discussion about the collection of graphs. Have the students start writing a three paragraph response in the wiki. The first paragraph is about the similarities between their graph from their particular geographic region and the base equation. The second paragraph is contrast, and the third equation is about the surprising things they notice in the graph


 * Email the Geogebra graph to the students at home so they can finish the wiki posting for homework.** || <span style="font-family: 'Arial','sans-serif';">Internet access, ePal account, Excel software

Sin regression software.

Sin regression software.

Geogebra Software.

Wiki access || <span style="font-family: 'Arial','sans-serif';">Notes: Student groupings will be individual. Some students may have very similar data if their geographic regions are close to each other. These students may work together with permission


 * MONITOR ||

<span style="font-family: 'Arial','sans-serif';">Ongoing assessment(s): <span style="font-family: 'Arial','sans-serif';">Accommodations and extensions: <span style="font-family: 'Arial','sans-serif';"> Backup plan: **<span style="font-family: 'Arial','sans-serif';"> Have data ready to use (printed) in case the collaboration does not go according to plan. Also, TI graphing calculators may be used to do the sinusoidal regressions if no easier software can be found. **
 * <span style="font-family: 'Arial','sans-serif';">The teacher must check to make sure that data is being collected on a weekly basis.
 * <span style="font-family: 'Arial','sans-serif';">If students are not experienced with the software, the teacher must circulate and assess how well the students are handling the work
 * <span style="font-family: 'Arial','sans-serif';">The final assessment will be based on if the student gets the sinusoidal regression plotted and on the three paragraph writing assignment. There will be rubric used to grade the writing assignment
 * <span style="font-family: 'Arial','sans-serif';">Students who move into class at a later date or who have problems collaborating may use data collected by some other internet source.
 * <span style="font-family: 'Arial','sans-serif';">Students who may not have the writing skills needed may do a podcast or oral interview about their graphs.

<span style="font-family: 'Arial','sans-serif';">Lesson reflections and notes:
 * EVALUATE AND EXTEND ||

Tyler, on the first day, you stated that you will "explain" the software. What exactly will that entail? I am not being rude or picky, but was curious to know if you intended on utilizing a "grabber" to introduce the lesson or if you simply just stood and spoke with certain introductions? I am always fascinated with how other teachers approach the introductions to their lessons. Very good follow up lesson to the previous and seems to be a successful one when implemented. Kevin

Wow I have had one heck of a time posting comments to this page. I don't know what the issue is. I like this lesson a lot. It reminds me of something that I do in one of my classes. However, instead of collecting data for such a long time from such a wide array of locations we collect data for a more specified region. In addition we only collect data from early winter to late spring. This typically yields enough data for my purposes. Have you considered working with the Earth science class as a thematic unit? You could turn your data and graphs over to them when you have finished your work and they can analyze it and eplain the trends within. Or perhaps make them partners in data collection. I dont know it is just an idea. Your project is very good as it is. Norm

A Standards-Based Approach This is an equation and modeling lesson for grades 11 or 12. **Overview: **For this lesson, students will go out and find a curve in the real world. They will use what they know about curve modeling and find an equation that represents the curve. The students will then take a still life picture and overlay that with the graph that they picked to see how well the curves fit. The students will document this process with either still life pictures or video.**
 * Written by: Tyler Winner
 * <span style="font-family: 'Arial','sans-serif';">Lesson Title:

Modeling a Real World Curve <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';">Related Lessons: <span style="font-family: 'Arial','sans-serif';">Modeling the Spread of the Flu <span style="display: block; font-family: 'Arial','sans-serif'; text-align: center;"> <span style="font-family: 'Arial','sans-serif';">Modeling Temperatures Around the World <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';">Content Standards: ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: 'Palatino-Roman','serif'; font-size: 12.5pt;">Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences. ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: 'Palatino-Roman','serif'; font-size: 12.5pt;">Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation. ** Standard Taken from Ohio Dept. of Education Math standards (2009) X Creativity and innovation o <span style="font-family: 'Arial','sans-serif';"> Communication and collaboration o <span style="font-family: 'Arial','sans-serif';"> Research and information fluency ** || <span style="font-family: 'Arial','sans-serif';">
 * <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';">Unit: Modeling with Equations
 * GOALS ||
 * ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="font-family: 'Palatino-Roman','serif'; font-size: 12.5pt;">Use recursive functions to model and solve problems; e.g., home mortgages, annuities.
 * <span style="font-family: 'Arial','sans-serif';">ISTE NETS-S
 * <span style="font-family: 'Arial','sans-serif';">

X Critical thinking, problem-solving, & decision-making o <span style="font-family: 'Arial','sans-serif';"> Digital citizenship X Technology operations and concepts || <span style="font-family: 'Arial','sans-serif';">Instructional objective(s): <span style="font-family: 'Arial','sans-serif';">Students will curve fit an equation to a real world curve (skate park, sculpture, etc.) <span style="font-family: 'Arial','sans-serif';">Students will evaluate how well the curve is modeled by the equation. <span style="font-family: 'Arial','sans-serif';">Students will become fluent with digital storytelling applications. Before-class preparation: <span style="font-family: 'Arial','sans-serif';"> <span style="font-family: 'Arial','sans-serif';"> || <span style="font-family: 'Arial','sans-serif';"> ||
 * ACTION<span style="font-family: 'Arial','sans-serif';">  ||
 * <span style="font-family: 'Arial','sans-serif';">
 * <span style="font-family: 'Arial','sans-serif';">Teacher must get digital cameras
 * <span style="font-family: 'Arial','sans-serif';">Teacher must get access to digital storytelling software or Voice thread software
 * <span style="font-family: 'Arial','sans-serif';">Teacher must get an example set up. A bowling pin works well as a workable example
 * <span style="display: block; font-family: 'Arial','sans-serif'; text-align: center;">During class
 * <span style="font-family: 'Arial','sans-serif';">Time || <span style="font-family: 'Arial','sans-serif';">Instructional Activities || <span style="font-family: 'Arial','sans-serif';">Materials & Resources ||
 * <span style="font-family: 'Arial','sans-serif';">15 min

45 min

1-2 days || <span style="font-family: 'Arial','sans-serif';">Teacher explains the project. Gives an example of curve fitting on a bowling pin.

Student groups leave to go find curves and start measurements and documentation

Students get to come back and work in groups curve fitting with Geogebra and other graphing software.

Then, after the curves are fit, students will work to produce a digital story explaining and documenting the curve fitting process. The students will use VoiceThread or another software program. || <span style="font-family: 'Arial','sans-serif';">Sample curve and Software Demonstration

Tape measures, cameras

Curve fitting software Digital Storytelling software || <span style="font-family: 'Arial','sans-serif';"> Notes: Students will be in groups of about 4 or 5. The teacher may have to bring in curves or identify curves around the school that are easily fit. Some students who are new to the building may not know where to find a decent object to curve-fit.
 * MONITOR ||

Ongoing assessment(s**): Teacher should circulate around the groups while they are curve-fitting to make suggestion and help students. <span style="font-family: 'Arial','sans-serif';">The final Digital Story will be assessed with a rubric (see attached). ** <span style="font-family: 'Arial','sans-serif';">Accommodations and extensions **<span style="font-family: 'Arial','sans-serif';">: If some students have issues working with groups, that should be considered before the groups are assigned. Any other issues with technology or math should be worked out within the groups. Have the students help each other with the accommodations. Backup plan: Scale pictures of curves may be used if not enough real world examples are available. ** <span style="font-family: 'Arial','sans-serif';">Lesson reflections and notes: <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;"> <span style="display: block; font-family: 'Arial','sans-serif'; text-align: center;">Digital Story Rubric <span style="display: block; font-family: 'Arial','sans-serif'; text-align: right;">Name:_ __<span style="font-family: 'Arial','sans-serif';"> Is the purpose of the story clear? /5
 * EVALUATE AND EXTEND ||

Does the story show all of the aspects of the curve? /5

Does the equation generally fit the curve? /5

Are all group members represented in the story? /5

Is the story put together well and in a logical manner? /5

Does the group give a good evaluation of their curve? /5

Total /30 <span style="font-family: 'Arial','sans-serif';"> <span style="font-family: 'Arial','sans-serif';">Comments: **<span style="font-family: 'Arial','sans-serif';">

____

I like your idea about "curve fitting using a bowling pin." I am already intrigued and I am fairly certain that a teenage student would be dually enthused. I also think that your rubric at the end of your lesson will be very beneficial in this lesson. I like to think that rubrics are important, and they are. However, I seem to be guilty of forgetting to incorporate them more than I should. I like the lesson and am interested in hearing more about how it turned out afterwards. Kevin.