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Syllabus Reference
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Download zip
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Steve Arnold
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Representing and Analysing Data: Birthday Buddies
Download Student Worksheet file (PDF)
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(Suitable for CAS extension)
What is the chance of sharing a birthday with someone in your class? This simple question offers a rich context for mathematical modeling, which is potentially accessible to students from the early years of secondary school to seniors. Using TI-Nspire CAS, students are offered the tools by which they can investigate the problem and build a meaningful model, which will deepen their understanding of the problem, and help them to further appreciate the applications of mathematics to their world.
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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Rex Boggs and Steve Arnold
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Representing and Analysing Data: Bar of Soap
Download Student Worksheet file (PDF)
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Do you use up the same amount of the soap in the shower each morning, or does it depend on the size of the bar of soap?
This data was collected by Rex Boggs of Glenmore State High School in Rockhampton, Queensland.
"I had a hypothesis that the daily weight of my bar of soap in my shower wasn't a linear function, the reason being that the tiny little bar of soap at the end of its life seemed to hang around for just about ever. I wanted to throw it out, but I felt I shouldn't do so until it became unusable. And that seemed to take weeks."
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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Steve Arnold
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Areas and PaperFolds
Download Student Worksheet file (PDF)
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Who would have thought that there could be so much mathematics in simply folding a piece of paper? This activity spans the years of secondary school, beginning with measurement, data collection and interpreting scatter plots in the early years, through linear functions, Pythagoras' Theorem and trigonometry, right through to calculus in the senior years.
The mathematical focus at each level is different - from finding the largest area to discovering functional relationships between the sides of a right-angled triangle, and on to optimisation. While algebra and calculus can be used to prove this result, it actually takes some geometry to understand why the final result is true.
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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Steve Arnold
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The Falling Ladder
Download Student Worksheet file (PDF)
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What does it feel like to be at the top of a ladder as the bottom begins to slide away? Do you fall at a steady rate? If not, then what is the nature of your motion - and when are you falling fastest?
This modelling problem is suitable for students across the secondary school, from consolidation of work on Pythagoras' Theorem in the early years, to optimization using differential calculus in the senior years. At all levels, it is a realistic and valuable task, which links a variety of mathematical skills and understandings with a practical real-world context.
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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Steve Arnold
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The Beach Race
Download Student Worksheet file (PDF)
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This beach race begins from a point 4 kilometres out to sea from one end of a 6 kilometre beach, and finishes at the opposite end. Contestants must swim to a point along the beach, and then run to reach the finish line first. I can swim at 4 km/h and run at 10 km/h - where should I aim to land on the beach so as to minimize my total time for the race?
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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Bjorn Felsager
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Random Rectangles
Download Student Worksheet file (PDF)
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What variables characterize a rectangle? What kind of relationships exists between these variables?
In this activity you will explore this, examining patterns and forms using tables, graphs and equations.
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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Ian Edwards
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Environmental Mathematics: Black Bear Cubs
Download Student Worksheet file (PDF)
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The data in this activity was collected in order to better understand the health and growth patterns of black bear cubs in the wild. In their first year of life, these cubs grow from 225 grams to between 22.5 and 31.5 kilograms.
Analysis of this data involves curve fitting and some introductory calculus from first principles.
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AM1: Basic algebraic skills
AM2: Modelling linear relationships
AM3: Algebraic skills and techniques
AM4: Modelling linear and non- linear relationships
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