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Units 1 & 2 provide an introductory study of simple elementary functions of a single real variable, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts. The focus of Unit 1 is the study of simple algebraic functions. Unit 2 students focus on the study of simple transcendental functions and the calculus of simple algebraic functions. The areas of study covered in each unit include Functions and Graphs, Algebra, Calculus, Probability and Statistics. For more information on the Mathematical Methods course visit the VCAA website.

VIC: Mathematical Methods Yr11 Classroom ActivitiesDownload
Functions and Graphs
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Understanding Transformations

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Understanding transformations looks at how points are translated and dilated (towards and away from the axis) and what this means for the equation. The new point tool makes this very intuitive. The extension content naturally blends this approach into matrices and helps students understand rather than blindly applying rules.
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Reflections in the x and y axes, the line y = x and also x = n and y = m, they're all here. The companion video helps students understand reflections and how they can be performed on the calculator. This activity includes a range of extension questions that are more conceptually demanding.
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Personal Polynomials

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If A = 1, B = 2 ... your name could be converted into numbers and described as a function, your Personal Polynomial. What does your polynomial look like? Students find their own personal polynomial and then study its properties. They set up and use simultaneous equations to find their polynomial, the bisection method to locate x-axis intercepts and transformations to compare others. Palindromic names create polynomials with an axis of symmetry. Is it possible for two names to generate the same polynomial, Alex(x) compared with Alexander(x)? A guided exploration task that will run over several lessons.

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Functions Inverses SFI

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Students explore a range of functions and determine their inverses, explore points of intersection, domain and range. The investigation aims to dispel some myths with regards to points of intersection.


Exponential Decay

Students run a simulation using M&M'S® whereby they eat each of the M&M'S with the M facing upward. Each time approximately half the remaining M&M'S get consumed. The result is exponential decay. A truly memorable and satisfying mathematics investigation!
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This activity introduces Radians as the arc length around a circle of radius one unit and the equivalent angle measurement. Students are then provided with a unit circle on the Cartesian plane to see how the arc length relates to the distance to the x axis (sine). Students are provided with interactive content to help explore this relationship. 


Students use trigonometric functions to model biorhythmic activity. Whilst the psuedo science of biorhythms equates approximately to astrology, the activity content is applicable to graphing simple trigonometric functions involving only transformations. The alignment of days helps students understand the period of the function.


Unit Circle Sine

Students explore an animated unit circle, looking for patterns. The interactive content allows students to control the level of assistance when answering questions. To understand relationships such as –sin(x)=sin(-x) switch the hint on to see a triangle with its corresponding reflection. The graph of sin(x) is broken into four parts to align with each quadrant of the unit circle and finally, exact angles are reviewed.

The Movie Contract

This task is designed to compare exponential function behaviour relative to linear function behaviour. It uses the context of payment schemes to look at how simple rules for constant change and constant multiplier impact the payments from each scheme over time.

Pendulum Swing – Part 1

Students use a motion detector (CBR) and pendulum (fishing float) to collect data for the motion of a pendulum. The quality of the data never ceases to amaze students and teachers. Students align practical knowledge, logic and familiarity with the various parameters to transform a basic trigonometric function into a model for a pendulum.

Domain, Range and Function Mapping

Students explore the concept of domain, range and function mapping through a variety of visual representations. Interactive sets, ordered pairs and graphs provide for opportunities for students to explore, the idea is then flipped as students build a function to match the domain and range supplied.
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A circumcircle is a unique circle that passes through all three of a triangle's vertices. In this activity students start with the geometrical entity and then transfer this to the Cartesian plane where they determine equations to lines (given two points), equations to lines (given point and gradient), intersection of two lines and finally the equation to a circle. Once students have completed the prescribed points they are required to come up with their own three points, a TI-nspire teacher file generates all the required equations given three starting points.

Transformation Game

The classroom activity associated with this task is a ‘whole class’ guessing game, where a random member from a predefined family of curves is drawn on the Cartesian plane by the calculator, and students must write down the associated function rule. It requires an IWB or data projector so that students may easily view the calculator screen (i.e. via TI-Nspire CAS software). There is a student worksheet in which students can record their answers.
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Function Transformations

A collection of data from bouncing balls to pendulum swings, discharging capacitors and Olympic rings are included in this activity for students to model. In each example the original function is presented and students determine the appropriate transformations of f(x) so that it models the data (or rings).
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Learning Exponentially

How and why are transformations of exponential function different from polynomials? What is a dilation away from the x or y axis? This activity provides a series of questions, explorations and dynamic visuals that will help students understand transformations of exponential functions, including a selection of homomorphic representations.
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Transformations 1 - Translations, a graphical approach

Beyond sliders and memorising, students need a good understanding of the reasoning behind transformations. This activity focuses on the algebra behind translations, starting with the discrete analysis, a single point, building to a family of points and finally an equation. 
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Transformation 2 - Dilations, a graphical approach

Beyond sliders and memorising, students need a good understanding of the reasoning behind transformations. This activity is the second part of three, focusing on the algebra behind dilations, starting with the discrete analysis, a single point, building to a family of points and finally an equation.
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Transformations 3 - Reflections and Revision

Beyond sliders and memorising, students  need a good understanding of the reasoning behind transformations. This activity is the third part in the series, focusing on the algebra behind reflections, plus a review of parts one and two.