Maths On Track!
When people with diverse skills work together as a team, their collective talents often achieve results beyond what an individual could accomplish. This unit is designed to assist students to use mathematics to better appreciate the value of working in teams. The Essential Question, “What Makes for Success?”, leads on to a specific focus on teamwork through the Unit Questions, “What skills are important?” and “Why are teams important?” The Formula One Grand Prix has been chosen as the context within which to explore these questions.
In this unit, students work in teams to investigate different sets of Content Questions, collaborating and sharing their findings to construct a richer class response to the Unit and Essential Questions. They develop their thinking skills using the Seeing Reason tool and their oral, written and multimedia communications skills using a blog, group discussions and videoed interviews. Team members have the opportunity to demonstrate leadership by taking on different roles and responsibilities. At the conclusion of the unit students apply their findings to the broader perspective of the teams that operate in their lives. They present their final reflections on the Essential Question in a videoed interview that will be published on the class blog. Higher Order Thinking and 21st Century skills are also assessed.
Curriculum Framing Questions
- Essential Question
What makes for success?
- Unit Questions
What skills are important?
Why are teams important?
- Content Questions
(Australian Grand Prix track questions - to be investigated by student teams 1 to 4)
- What is the average speed around the Australian Grand Prix track?
- What are the fastest/slowest parts of the track?
- How do the turns 1 to 16 compare as to speed? (Rate them fastest to slowest and estimate the speed for each corner.)
- What could an Australian Grand Prix circuit speed-time graph look like for a F1* car?
- How would an “acceleration” pattern look like for an F1 car on the Australian Grand Prix circuit?
(F1 team questions - to be investigated by student team 5)
- What maths calculations does the team need to make?
- Who is the most important person in an F1 racing team?
- What does the driver think about during the race?
- What does the driver think about before the race?
- How many people are in a pitstop team? What do they do?
- Who designs the car? What influences their design choices?
- How do these teams rely upon each other?
- (Optional special needs student team 6)
- Questions for teams 1 – 5 to be negotiated and modified to be appropriate to abilities and areas of student interest.
(Acceleration and weight questions - to be investigated by optional gifted student team 7)
- What is acceleration?
- What is “g” force? What are the “g” forces on the driver?
- What is “downforce”?
- What is the “braking zone”?
- How fast are cars coming up behind the cars in the braking zone?
- Is there an ideal height and weight for a driver?
- What does the fuel weigh and how much is needed?
- What is the balance between the amount of fuel needed to complete a race and the need to stop to refuel? (Why not just install a fuel tank large enough to carry sufficient fuel to complete the race and avoid pitstops?)
View how assessment is used in this unit plan. These assessments help students and teachers set understandable goals, monitor student progress, provide feedback, assess thinking, performance and products, and reflect on learning throughout the activities.
Students Prior Knowledge
Some students have knowledge (and interest) in the Grand Prix. These students become a resource for the class.
Teachers Professional Learning
Some research of the Grand Prix is necessary. Ability to administer wikis and blogs would also be useful, although a trusted student could be used to do this.
Teaching and Learning Strategies
In order to emphasise that teams are a powerful and effective way to accomplish more than individuals, the class will work in teams. Each team will be given different sets of content questions to address. Some teams will examine what driving around the track would look like mathematically. They will divide the Australian Grand Prix circuit into sections. Each of these teams will evaluate their section of the Albert Park Circuit and then combine their findings with those of the other teams, thus developing a picture of the speed and acceleration patterns around the entire circuit. Another student team will investigate the roles of the driver, the pit stop team, car designer teams and other F1 teams and consider how these work together to achieve success. Gifted students could work in another team to consider the accelerations and weight forces acting upon the car and the driver. Students with special needs will negotiate their research questions. Collaboration and sharing of findings between teams is required throughout the unit.
At the conclusion of the unit, the student teams will analyse their collective findings and consider their responses to the unit questions. In addressing the essential question, they will discuss the types of “teams” that impact on their lives, considering the “teams” from which they benefit (such as teacher teams, medical teams, friendship “teams” and parent “teams”). They will also evaluate whether these “teams” support or hinder them in terms of achievement of their personal goals.
During, and at the conclusion of the unit, students will present their reflections on the Curriculum Framing Questions:
i. through individual contributions to a blog
ii. through their completion of a teacher specified problems solving task that will test their mathematical skills and thinking
iii. through the production of a causal map using the Intel online Seeing Reason Tool to demonstrate their understanding of the relationship between working in a team and successful endeavour
iv. through a videoed personal interview in which they individually present their reflections on the essential question.
Teaching and Learning Activities
Setting the Scene/Introductory Activity
Teacher reviews Unit Implementation Plan (doc) when deciding when and how to implement unit.
Teacher outlines the unit. Gives information on Grand Prix by viewing web based Formula 1 information including the official Australian Grand Prix Website*. Map of track is examined and discussed as a class. Using an interactive whiteboard (IWB) with the map of the track displayed group tries to imagine what driving the circuit might look like. As a gauging needs activity teacher poses the UQs: What skills are important? Why are teams important? Students consider these as a group using a KWHL on an IWB. A poster of ALL CFQs is displayed in the classroom.
1. Whole class: Students complete a KWHL. Discussion as a class to help determine what needs to be researched. (Teacher uses this activity to gauge student needs and adjust learning activities as appropriate.)
2. Whole class: Students are introduced to the blog* that will be used throughout the unit and explains how to post if necessary. The information contained on the blog is explained. Students are directed to download the Team Organisation and Roles (doc) (student support document) from the blog. The purpose of this document is discussed with the class.
3. Student Teams 1 to 4: Working in teams of 3 or 4, students will address the Content Questions on the Australian Grand Prix circuit. These teams will collaborate with each other, divide a map of the Australian Grand Prix circuit into several sections and use race statistics (track length, fastest lap time and other measurements) to estimate speeds over their section of the track. They compare their estimates with other teams and make adjustments until all teams have produced times for their sections that total the fastest lap time (ie that harmonise with actual race times). They seek feedback from an available racing expert/enthusiast on their estimates.
4. Student Team 5: This team investigates the roles of individuals and the many teams that collaborate together in the Formula One. They investigate Content Questions on the F1 teams and use the findings of the other student teams to inform them on the specifics of the overall team goal.
5. Student Team 6 (Optional group for students with special needs only): Collaborating with teams 1 to 5, this team will investigate a negotiated set of Content Questionsappropriate to their abilities.
6. Student Team 7 (Optional group for gifted students only): Collaborating with teams 1 to 4, this team will investigate the Content Questions on Acceleration and Weight.
7. All students: Complete a Problem Solving Analysis Task (doc) in which they use the mathematical skills they have developed through direct instruction from the teacher and text exercises from the Rates of Change area of study. The task is evaluated using a rubric provided at the same time students are given their task booklets. The purpose of this task is for students to use mathematics to see the race circuit through the eyes of the driver and the teams that provide support. They will quantify the speeds and acceleration/braking rates that the driver must achieve in order to be competitive. They analyse the circuit layout and the demands this places upon car and driver. This provides a context for the mathematics students are learning. It also helps them to see the race in terms of demands upon the driver and the supporting team, thus providing valuable insights into the Unit Questions What skills are important? and Why are teams important? They will later use this information in responding to these questions within other tasks.
8. All teams: During the unit all teams will use the Seeing Reason Tool, to produce a series of causal maps (minimum of 5 edits) as they learn. View the Causal Map (doc) document, which provides details of the Seeing Reason Tool project outline plus a student sample map and examples of relationships and factors. Use of this tool helps them visualize how the work of race teams impacts upon success. The causal maps are created to reflect the interactions and interdependency between the various Formula One teams (eg pit stop, design, marketing, race officials, and so on) and upon car and driver performance. Peer feedback is required throughout as part of their assessment. A final map is assessed at the end of the unit by a peer and by an adult of the student’s choice (parent or another teacher) using a scoring guide. This activity will prepare student to answer the unit question Why are teams important? in the next activity.
9. All teams and individual students: During the unit all teams, and individual students, will post to the class blog* to share findings, resources or ask questions. The Student Guide for Blog Posts (doc) will support students as they develop their contributions to the blog, and a self assessment rubric will assist students to reflect upon the quality of their posts. Using their learnings from previous activities, a key task will be for each student to post their response to each of the unit questions What skills are important? and Why are teams important? These responses will be self assessed and then teacher assessed using a scoring guide that is based upon the self assessment rubric students had been using. The rubric and scoring guide will be available on the class blog.
10. All students: Class will discuss the Essential Question What Makes for Success? and make connections to what they have learned regarding teams. They will also consider what teams contribute to supporting them in their lives. Following this discussion, each student will make a videoed interview (about 2 to 3 minutes) on their response to the EQ. The interviews will be edited into one video, representing the collective class response to the EQ. This video is then posted to the blog as a resource for others. Students will receive final feedback from one invited adult and one peer who will view their interview online and provide feedback as a blog post.
Accommodations for Diverse Needs
Students with Special Needs
These students form a separate team (optional Team 6) and investigate a set of content questions that are appropriate to their abilities that they negotiate with the teacher. Members of other teams may be assigned to mentor students in Team 7. Assessments will also be negotiated appropriate to the learning activities. Instructions and supports will be provided as podcasts as well as in written form.
English as a Second Language (ESL) Students
Appropriate support personnel if available, including parents and other community members, Internet resources including language tools, alternative ways to demonstrate their learning that does not require advanced language skills (eg Photostories, art work and other visuals)
These students form a separate team (optional Team 7) and investigate a more challenging set of content questions requiring deeper analysis and collaboration with the other groups.
Appropriate support personnel if available, including parents and other appropriate community groups/ individuals (for in class support or for consultation).
© State of Victoria 2008
Alan Thwaites is involved in the Intel Teach Program and developed this portfolio, in collaboration with other teachers.
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