Intel® Teach Program
Essentials Course
Maths on Track: What Makes for
Success?
Unit Overview
Unit Title
Maths on Track: What Makes for Success?
Unit Summary
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 in Australia 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 Links
Mathematics
Year Level
Victorian Certificate of Education Unit 1 (Year 11) Mathematical Methods (This theme could be easily adapted
for other year levels.)
Approximate Time Needed
12 x 50 minute class periods plus 5 hours out of class/home based work.
Unit Foundation
Standards/Syllabus Outcomes
Year 11 Standards as specified by the Victorian Curriculum Assessment Authority (V.C.A.A.)
Area of Study: Rates of change: This area of study covers constant and average rates of change and an
informal treatment of instantaneous rate of change of a function in familiar contexts, including graphical and
numerical approaches to the measurement of constant, average and instantaneous rates of change.
Outcome 1
On completion of this unit the student will be able to define and apply a range of related mathematical routines
and procedures including:
– constant rate of change (linear functions), use of gradient as a measure of rate of change;
– average rate of change, practical examples of average rates of change such as average speed;
- use of gradient of a tangent at a point on the curve to describe instantaneous rate of change of y = ƒ(x) with
respect to x, practical examples of instantaneous rates of change, such as speedometer readings
- motion graphs, construction and interpretation of displacement–time and velocity–time graphs and informal
treatment of the relationship between displacement–time and velocity–time graphs.
Outcome 2
On the completion of this unit the student will be able to apply mathematical processes in non-routine contexts,
and analyse and discuss these applications of mathematics including the ability to:
• specify the relevance of key mathematical content from Rates of Change area of study relating to motion of
an F1 car on the Australian Grand Prix track in the investigation of the curriculum framing questions;
• make inferences from analysis and use these to draw valid conclusions related to this investigation;
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• communicate conclusions using both mathematical expression and everyday language, in particular,
interpretation of mathematics with respect to this investigation.
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Curriculum-Framing Questions
What Makes for Success?
Essential Question
 What skills are important?
Unit Questions
 Why are teams important?
(Questions to be investigated by student teams 1 to 4)
Questions of the Australian Formula 1 Grand Prix circuit
 What is the average speed around the Australian Grand Prix track?
 What are the fastest and 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 an F1
car?
 How would an “acceleration” pattern look like for an F1* car on the Australian
Grand Prix circuit?
(Questions to be investigated by student team 5
Content Questions
Questions on the F1 Team
 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?
(Questions to be investigated by optional special needs student team 6)
Questions on F1 racing teams to be negotiated with students and appropriate
to their abilities
 Questions may be modifications of the questions Teams 1 to 5 are considering
 Questions may investigate areas of interest to the student.
(Questions to be investigated by optional gifted student team 7)
Questions on Acceleration and Weight
 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?)
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Assessment Plan
Assessment Timeline
Before learning activities
begin
Group K-W-H-L
Chart using
Interactive
Whiteboard
Team
Organisation
and Roles
Checklist
Progress checks
with teacher
While students work on
learning activities
After learning activities end
Final Seeing
Reason Tool
Teacher feedback Causal Map
on Problem
Blog Posts: Self
Solving
Evaluation
Analysis Task
Rubric
Causal Map
(min of 5 edits) (see rubric at
end of this
using Seeing
Blog Posts
Reason Tool and document)
Evaluation
peer feedback.
Guide (teacher
Blog posts- Self evaluation)
Evaluation
Rubric
H.O.T. & 21st
Century Skills
Evaluation (by
team & teacher)
Video
interviewAdult & peer
feedback on EQ
reflections
Assessment Summary
Group K-W-H-L Chart
using interactive
whiteboard
A what do you Know- What do we need to find out-How do we find this outwhat did we LEARN chart reveals the knowledge already held by the group and
clarifies the task for students. They complete the K-W-H-L using an interactive
whiteboard and use this discussion as a launching point. The teacher uses the group KW-H-L initially to gauge group needs and to help them make connections between what
they already know and what they will be learning.
Team Organisation
and Roles Checklist
Students are provided with a checklist, partially completed by the teacher, that they will
complete and present for discussion with their teacher. The purpose of this support
document is to aid students to clarify important tasks, develop a reasonable timeline for
these to be completed by for the teacher to use to monitor progress.
Problem Solving
Analysis Task
(Teacher feedback
using rubric)
Causal Map using
Seeing Reason Tool
-minimum of 5 edits
A Problem Solving Analysis task in which they use the mathematical skills they have
developed from their texts (Rates of Change) is evaluated using a rubric provided at the
same time students are given their question booklets. The teacher uses the rubric to
assess student’s responses to the questions. This task assists students to view the race
through the eyes of the driver and the teams that support him thus providing valuable
insights into the Unit Questions What skills are important? and Why are teams
important?
Using the Seeing Reason Tool, students develop a cause and effect map that links how
the many teams involved in Formula One contribute to success in the race. Students list
as many of teams as they can and state how these teams impact upon the performance
of the car and driver. They make a minimum of 5 edits throughout the project. Edits
should be a team effort. Their first map will basically represent their initial opinions with
subsequent maps representing what they have learned about Formula One teams as
they progress through their research.
Blog Posts (self and
teacher assessed)
Students will use the blog to support each other and deal with issues that they face.
Regular posts (at least weekly) are expected. In particular each student is expected to
respond to the Unit Questions What skills are important? and Why are teams
important?, which will individually be posted by the teacher once sufficient
investigations have taken place.
Completed Causal
Map
This final causal map is based upon the maps students have been making throughout the
unit using the Seeing Reason Tool. This final map answers the question: Why are teams
important in a Formula One Grand Prix?
Blog posts – blog post
Individual student responses to the Unit Questions ,What skills are important? and
Why are teams important?, will be assessed by the teacher using a scoring guide that
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scoring guide
is based upon the self assessment rubric that students have been using for their blog
posts. Each student should have been using a self-assessment rubric, to assess their
own blog posts, so it is expected that they will understand well what constitutes an
effective blog post. Each student should present their self assessment of their posts to
their teacher, after which the student and teacher then compare and discuss their
assessments.
HOT & 21st Century
Skills Evaluation (by
team & teacher)
Using the guide provided, the depth to which each student has thought about and
responded to the CFQs (H.O.T.) is evaluated by their team and by the teacher. The
demonstration of 21st century skills (specifically Interpersonal and Collaborative
Skills, Critical Thinking and Communication Skills) is also assessed.
Video interviewAdult & peer feedback
on EQ reflections
Following the completion of all other activities, and after students have received
feedback on their work, the class will discuss the Essential Question What Makes for
Success? Following this discussion each student will give a brief interview giving their
response to the Essential Question. These interviews will be videoed, collated and edited
into one video representing the collective class response to the EQ. This video will
become part of the blog as a resource for other classes who might undertake this unit.
Students are to invite one adult and one of their peers to view their interview online and
to post feedback.
Unit Details
Prerequisite Skills
Students Prior
Knowledge
Teachers’
Professional
Learning
Some students have knowledge (and interest) in the Grand Prix. These
students become a resource for the class.
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
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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
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Setting the Scene/Introductory Activity
Teacher reviews Unit Implementation Plan 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 (link to http://www.grandprix.com.au/) . 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 (link to http://athwaites.globalteacher.org.au/maths-ontrack) 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 (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 Questions appropriate 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 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 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 (http://athwaites.globalteacher.org.au/maths-on-track/ ) to share findings, resources or ask questions.
The Student Guide for Blog Posts 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
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feedback
one invited
adultReserved.
and one peer who will view their interview online and providePage
feedback
blog post.
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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)
Gifted Students
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.
Indigenous Groups
Appropriate support personnel if available, including parents and other appropriate
community groups/ individuals (for in class support or for consultation).
Materials and Resources Required for Unit
Technology – Hardware
Camera
Laser Disk
 Computer(s)
 Printer
 Digital Camera
 Projection System
DVD Player
Scanner
 Internet Connection
Television
VCR
 Video Camera
Video Conferencing Equip.
 Interactive Whiteboard
Technology – Software
 Database/Spreadsheet
 Image Processing
 Desktop Publishing
 Internet Web Browser
 E-mail Software
 Multimedia
 Web Page Development
 Word Processing
Other
Encyclopedia on CD-ROM
Student mathematics text books on rates of change for mathematics skills that are
Printed Materials
applied investigations.
Race merchandise (purchased or created by students) adds to the F1 atmosphere of this
Supplies
unit.
Blog (support material and for blog postings) http://athwaites.globalteacher.org.au
Internet Resources/
Communication Tools
Other Resources
Blog (support material for postings) http://athwaites.globalteacher.org.au/mathson-track
Excellent scaled map and other Australian Grand Prix information and race statistics
http://www.grandprix.com.au/
Intel Thinking Tool which facilitates causal mapping and the visualising of cause and
effect: www.intel.com.au/education/au/seeingreason
See separate Resources document for additional resources for this unit of work.
Local car racing clubs, while not F1, may provide guest speakers who can discuss racing
strategies with students. Also some F1 drivers run websites with discussion forums and
do reply to posts by students. In some areasa visit to a race meeting may be posssible.
© State of Victoria 2008
Alan Thwaites is involved in the Intel Teach Program and developed this portfolio, in collaboration with other teachers.
Copyright is owned by the Crown in right of the State of Victoria. It may be reproduced in whole or in part for study or
training purposes, subject to the inclusion of an acknowledgment of the source and no commercial usage or sale.
Reproduction for the purposes other than those indicated above requires the written permission of the Department of
Education and Early Childhood Development. Requests and enquiries concerning reproduction and copyright should be
addressed to the Liability Management Manager, Department of Education and Early Childhood Development, 2 Treasury
Place, Melbourne, VIC, 3002
The State of Victoria accepts no responsibility for the accuracy of any part of this material and bears no responsibility for any
modifications made.
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* Other names and brands may be claimed as the property of others.
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