The document describes a 7th grade math capstone project where students will work in groups to plan a 3-day bike tour. They will create graphs of time and distance for each tour day, write an equation to determine potential profit, and develop a marketing component. The teacher will provide mini-lessons on creating graphs and equations. Students will research bike tours, plan costs and routes, and present their project to the class. The goal is for students to apply math skills to an authentic project and take the lead in their own learning.
2. Purpose My project will address the need for students to lead their learning and find information on their own with only guidance from the teacher. The project will address this need because students will work in small groups to design a three-day bike tour. The students will create graphs showing time and distance for each day, write an equation used to determine potential profit for the company, and create a marketing component describing the bike tour. All of the information will be displayed in tables, graphs, and equations, which will meet the content standards. Throughout the project I will help students organize their information and teach them how to create a graph and equation from their data.
3. Program Objectives Student-centered: The students will complete the project and will have the ability to make several decisions about the data included within their project, how to gather the information, and how to share the information. The project also provides students with a real-world example of gathering, analyzing, and comparing data using tables, graphs, and equations. The only teacher led instruction will be mini-lessons on creating tables, graphs, and equations. Learning and doing: The students are learning the content through the completion of the project instead of completing practice problems during class. Using information: The students are using the information they gather to create tables, graphs, and equations and plan their bike tour instead of just memorizing how to make a graph or how to write an equation. Facilitator: The teacher will facilitate each group throughout the project and the students will guide their learning by collecting the data, creating the displays, and sharing their information.
4. Program Objectives Continued Higher order thinking: The students will apply the ideas of creating tables, graphs, and equations to a real-world situation and plan a bike tour that could actually be used. Collaboration: The students will work together in order to complete the project. Performance-based assessment: The students will be graded based upon their project outcomes – materials, costs, and profit of their individual groups bike tour, not by a unit test. Multiple sources of information: The students will use a textbook as a reference for completing the mathematical components but will gather the majority of their information from outside sources such as the Internet or local businesses. Teachers addressing the learning styles of all learners: The students will be able to choose how they gather information and use various ways to present the information in order to best fit their learning styles.
5. Program Objectives Continued Learning how to learn: Instead of the teacher feeding the students knowledge through lecture and practice problems, the students will learn how to learn the information through collaboration, inquiry, and technology. Using a variety of types of information to complete authentic projects: The students will have to combine all of the information they find to create their final product. This information includes pricing, costs, graphs, and equations. Students acting as a professional: The students will be acting as the tour operators, not seventh grade math students, making decisions and creating their bike tour.
6. Timeline Day 1: Present students with their task, discuss the overall project, and assign groups. Allow students time to research three-day bike tours on the Internet in order to get an understanding of what they are, average cots, and how far people can ride each day. Day 2: Using their research from Day 1, the students will start to plan their bike tour. Students will generate a list of items to be included in their tour for customers and how much each item costs. The students will calculate the total start-up cost per customer on their bike tour. Day 3-4: The students will complete a jumping jack experiment in order to get a first hand idea of the energy exerted on a bike tour which will help them in planning their bike tour and in deciding how many miles to ride each day. The students will also learn how to create coordinate graphs from a table and discuss analyzing information presented in tables and graphs.
7. Day 5 - 8: The students will plan their bike tour. The following must be completed during these three days: Make a time/distance graph for each day of the bike tour showing how far they will ride, how long they will ride each day, and when they will stop to take breaks. Using their start-up costs as a guide, determine costs to the company and the customers. Write an equation to determine the potential profit for different numbers of customers on their tour. Create a marketing component to advertise their bike tour. This must include costs to customers, description of bike tour (destinations), items included with the tour, and dates of the tour. This must also include a selling point such as health benefits, scenery, weekend getaway, etc. A mini-lesson on writing equations will be presented on Day 6.
8. Days 9-10: The students will combine all of their information to share with the class. The students can decide how they would like to share the information (display, presentation, paper, etc.) The students will create this presentation and prepare to share it with the class. Days 11-12: Each group will present their project to the class. The students will demonstrate mastery of the content by submitting the following with their project: a graph of each day of the bike tour relating time and distance, an equation relating the cost and number of customers to determine potential profit for the company, a marketing aspect for their company (brochure, advertisement, etc), and the presentation of their bike tour to the class (each days travel, items included, costs, potential profits).
9. Project Components Inquiry: Inquiry is included because the students will generate questions they need to answer in order to complete the project. The students will guide their learning and use the teacher as an aid if necessary. The project is very open-ended and the students can end up with several different bike tours. Projects: The students will complete the project of actually planning a bike tour. The students will create the graphs, equations, marketing aspect, and presentation. Technology: Technology will be used to collect information, record information, and possibly share information. The students will be required to use technology at the beginning of the project and from then on they will have the option of how they would like to record and share their information. Dynamic Flexible Grouping: The grouping will be flexible in that each group can decide who will complete what task and how, but the main groups will remain the same throughout the project. The students will be grouped based on results from their learning style inventories. I will mix the different learning styles in order to allow each student to shine in their own way. Authentic Teaching and Learning Experiences: The project is authentic because the students will see a real-world example of how to use tables, graphs, and equations to create a bike tour and manage the costs and customers. The students will have many choices throughout the project. They will decide how far the tour will cover each day, what items are to be included in their bike tour, how they want to market their bike tour, how much they are going to charge customers, and how they want to present their bike tour to the class.
10. Resources The resources essential to the project are websites, math textbook, mini-lessons, maps, and professionals within the community. The students will access the websites to gather information about bike tours and costs of items using the Internet. The students will have the math textbooks, Connected Mathematics: Variables and Patterns Introducing Algebra,available in the classroom for use on creating tables, creating graphs, and writing equations. The students can visit or contact professionals within the community in order to gather information about bike tours as well. All resources that the students need to create the project (paper, computers, presentation boards, etc.) will be in the classroom.
11. Desired Outcomes With this project I hope the students master the content objectives and begin to learn how to guide their own learning. The students should be able to collect and display data in tables and graphs, show relationships between data in graphs and equations, and solve problems using a variety of strategies. The students should also gain an understanding of how to attack a problem using inquiry and by guiding their own learning. The students will work together on this project to aid in their problem solving skills as well. I will evaluate the success of the projects implementation in many ways. I will check the mathematical component by making sure all parts of their tables, graphs, and equations are correct and the students demonstrate understanding of how each is used. I will evaluate the success of the students learning to guide their own learning based on how they attack the problem, how they work together throughout the project, what questions they have throughout the project, and how they present their information. Rubrics will be used to evaluate the students.
12. Lessons, Activities, & Rubrics The next few slides explain the activities and mini-lessons presented during the project in detail. Day 1 – Task Introduction Day 2 – Jumping Jack Experiment Day 4 – Creating Coordinate Graphs Lesson Day 6 – Writing Equations Lesson The rubrics used to grade the students final projects follow the lesson plans. Mathematics Components Rubric Marketing Component, Presentation, & Collaboration Rubric
13. Day 1 Project Task: Design a three-day bike tour that you and your friends could operate for the summer. The bike tour must go from Atlantic City, New Jersey to Norfolk, Virginia. You will need to submit a graph of the bike tour for each day showing time and distance, an equation used to determine potential profit for the company, and a marketing component describing the bike tour – costs, items included, destinations. At the completion of the project all groups will present their bike tour to the class.
14. Day 2 Activity: Jumping Jack Experiment While planning your bike tour you will need to determine how far the group can ride each day. Think about the following questions: How far do you think you could ride in a day? How do you think the speed of your ride would change during the day? What conditions would affect the speed and distance you could ride? To help you answer these questions you are going to perform a jumping jack experiment that should give you an idea of the patterns commonly seen in tests of endurance. Each member of your group will need to be one of the following: A jumper (to do jumping jacks) A timer (to keep track of the time) A counter (to count jumping jacks) A recorder (to write down the number of jumping jacks) As a group, decide who will do each task. When the timer says “go” the jumper begins doing jumping jacks. The jumper continues jumping for 2 minutes. The counter counts the jumping jacks out loud. Every 10 seconds, the timer says “time” and the recorder records the total number of jumping jacks the jumper has done. Complete the jumping jack experiment for each person in your group, rotating jobs each time. Record the time in seconds and total number of jumping jacks in a table. After you have completed the experiment, answer the following questions: How did the jumping jack rates in your group change as time passed? How is this shown in your table? What might this pattern suggest about how bike-riding speed would change over a day’s time on the bike tour? Jumping Jack Experiment taken from: Lappan, G., Fey, J.T., Fitzgerald, W.M., Friel, S.N., & Phillips, E.D. (2006). Connected mathematics: variables and patterns introducing algebra. Upper Saddle River, NJ: Pearson Prentice Hall.
15. Day 4 Lesson: Creating Graphs Objectives: Using data collected in a table, the students will be able to create a coordinate graph to display the data. The students will be able to analyze information presented in a graph. Anticipatory Set: 1. Discuss the results of the Jumping Jack Experiment. Review answers to the questions from the experiment (How did the jumping jack rates in your group change as time passed? How is this shown in your table? What might this pattern suggest about how bike-riding speed would change over a day’s time on the bike tour?) Guided Instruction: 1. Teach the students the five steps to creating a coordinate graph: Identify the variables Select an axis to represent each variable Select a scale for each axis. Plot the points. Give the graph a title. 2. Use a set of jumping jack experiment data to complete the steps as a class and explain what each step means. 3.Discuss what the graph shows about the jumping jack rate as time passes.
16. Creating Graphs Continued Independent Practice: 1. Have the students complete their own graph of one set of jumping jack data following all five steps and discuss the results as a group. (To be collected) Closure: 1. Discuss the positives and negatives of using a table and a graph to display information. 2. Analyze the information shown and discuss what this data explains about bike-riding speeds throughout the day. Grading Checklist for Graph: 9 points total Axes Labeled – 1 pt, Appropriate Scale – 1 pt, Points Plotted Correctly – 6 pts, Title on Graph – 1 pt
17. Day 6 Lesson: Writing Equations Objectives: The students will learn how to write equations to represent real-world problems. Anticipatory Set: Discuss what students already know about equations, their purpose, and the benefits of using equations. Guided Instruction: Explain the ISAW steps used to write an equation. I – identify the variables S – state the relationship in words A – assign a letter to each variable W – write the equation Complete a few examples of writing equation for a real-world problem using these steps as a class. Answer any questions and review steps. Independent Practice: Have students work on using these steps to write an equation for potential profits for their bike tour. Closure: Discuss the benefits of using equations to analyze information as compared to tables and graphs.
