Mathematical Methods Yr11 by Texas Instruments

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 Activities	Download
Getting Started Resources
$Tips and Tricks Thumbnail$ Short Cuts This activity is intended as a resource to help students navigate the TI-Nspire CX CAS calculator. Three pages of short cuts, tips and tricks are provided in addition to a brief series of instructions designed to show how some of these short cuts can be used. Even if you are familiar with the TI-Nspire CX series calculators and software, you are bound to find some tips and tricks that you didn't know existed.	Download86
Nspired Crossword This activity is designed for students completely new to TI-nspire. No mathematical knowledge is required to complete this task. Students complete a crossword puzzle where the clues relate to application menus and the answers are the menu items. The activity helps students navigate TI-Nspire and become familiar with the menus.	Download43
Functions and Graphs
Understanding Transformations Watch Activity Tutorial 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.	Download19
Reflections Watch Activity Tutorial 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.	Download1
Personal Polynomials Watch Activity Tutorial 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.	Download100
Functions Inverses SFI Watch Activity Tutorial 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.	Download33
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!	Download7
Radians 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.	Download8
Biorhythms 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.	Download1,790
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.	Download155
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.	Download15
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.	Download67
$ACMMM023_domain-range-and-mapping$ 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.	Download121
Circumcircles 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.	Download11
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.	Download51
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).	Download52
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.	Download49
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.	Download15
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.	Download15
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.	Download9
Calculus
Gradient of a function This activity introduces the notion of the gradient of a curve. Initial exploration involves a dynamic tangent where students can use prior knowledge of the gradient of a straight line to determine if the slope is negative, zero or positive. The second stage of the activity goes one step further by quantifying the gradient. The third stage sees the gradient function generated automatically including an opportunity to freely explore the relationship between a parabola and its gradient function. T	Download97
A Special Function Finding the derivative of a polynomial is relatively straight forward, but what about other functions? This activity explores a function with a special property; “the derivative of the function is the same as the original function”! The problem is initially explored using a dynamic line where changes to the line immediately affect the derivative of the line. Manipulating this line provides for instant feedback helping students determine the likely shape of such a function. Calculations involvin	Download55
Take it to the limit Students explore how a regular polygon can be used to approximate the perimeter and area of a circle. The purpose of the activity is to provide a practical, geometric approach to understanding the concept of a limit.	Download54
Triangle Areas A triangle circumscribes a rectangle. The triangle is not unique, so what is the minimum area of the triangle that circumscribes the triangle? Students use the dynamic representation on TI-Nspire, data capture and more to explore this problem with some elegant solutions.	Download10
Fill the Vase Students interpret graphs of empirical data with respect to rate of change of the height of water in vases of different shapes that are being filled at a constant rate. Students are provided with a range of graphs and vases. For each graph they must reshape the vase in order to match the volume – height graph. For each vase they must produce a volume – height graph. Practical ideas including data collection and videos are provided in the teacher notes.	Download99
Paper Folding In this activity students maximize the area of a triangle formed when a piece of A4 paper is folded in a special way. The activity provides an opportunity to explore the problem practically followed by an animated TI-Nspire file that automatically generates data so that students are able to check the validity of their data before proceeding. The unusual general result from this task makes the activity quite intriguing.	Download63
Ladder Problem Maddi the painter needs to work out the longest ladder that she can get around a tight hallway corner. Formulate an expression for the length of the ladder, differentiate and make equal to zero. Then what? Why does the function minimum align with the longest ladder?	Download38
Eye Spy Students use calculus to determine the maximum size of the iris (circle) that just fits inside an outline of the eye defined by two bell shaped curves. The activity uses some basic differential calculus, introduces simple substitutions to eliminate variables and handy techniques for simplifying problems. The problem is much easier than it looks!	Download12
Algebra
Personal Polynomials Watch Activity Tutorial 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.	Download100
Building Rules This activity explores three different ways to generate a rule for a particular interactive and dynamic block pattern. Students use symbolic notation to develop algebraic expressions and represent functions, solve systems of simultaneous equations and produce graphs from data. At the end of the activity students are provided with a powerful visual representation of the same problem that helps them produce the same equation simply and easily.	Download21
3D Equations Equations of 3 variables can be visualised in three dimensions. In this activity students are provided with 5 sets of three equations. Supporting the understanding and development is a 3D graph for each equation set. Students can see how pairs of graphs interact or all three. An estimate for the point of intersection is gained from the 3D graph. Students are then provided with a scaffolded learning environment and resources where they progressively eliminate a variable. What does it mean graphically when a variable is removed?	Download31
Discrimination of Parabolas Students manipulate progressively more flexible parabolas whilst a ‘special number’ is displayed on the screen. The problem for students to solve is ‘what is so special about this number’. Students continually review their conjectures as the parabola becomes more and more flexible.	Download65
Factor and Remainder Division of numerical quantities is a great way to start exploring and understanding division of polynomials. In this activity students start with what they know about division of numerical quantities and then apply this to division of polynomials. This assists with some of the terminology and also developing a deeper understanding. Polynomials can be regenerated dynamically and rapidly including the resultant quotient and, where applicable, the remainder, this helps students identify and explain patterns. The visual representation of polynomial division also helps students understand the factor and remainder theorem, particularly expressing a polynomial as a product of its linear factors.	Download69
Linear Equations Review Test 1A Assessment resource for Chapter One of the Cambridge VCE Year 11 Mathematical Methods textbook. The resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided. The companion PDF provides the same questions in a printed format.	Download27
Lines and Linear RelationshipsTest1A This assessment resource is suitable for Chapter One of the Jacaranda VCE Year 11 Mathematical Methods textbook. The assessment resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided.	Download28
Algebraic Functions Test 2A This assessment resource is suitable for Chapter Two of the Jacaranda VCE Year 11 Mathematical Methods textbook. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided. The companion PDF provides the same questions in a printed format. Whichever option you chose, this free assessment resource will save you time.	Download18
Quadratic Relations Test 3A This assessment resource is suitable for Chapter Three of the Jacaranda VCE Year 11 Mathematical Methods textbook. The assessment resource is available as a TI-Nspire file or PDF. The TI-Nspire file provides for automated whole class correction and feedback via the TI-Navigator system (Exam) or as automated correction for individual review (Self Check). TI-Nspire users can add, delete or edit any of the questions provided.	Download21
Probability and Statistics
Pascals Triangle Hidden Gems Pascal’s Triangle goes way beyond coefficients of binomial expansions and combinatorics. In this activity students are introduced to these basics but go on to explore other relationships and patterns such as the triangular and tetrahedral numbers, the Fibonacci sequence and even Euler’s number. There are so many hidden gems in this amazing triangle.	Download45
Great Expectations This activity uses a combination of simulation and simple probability tree diagrams to explore a set of dice with some very unusual characteristics. Grime Dice, created by Dr. James Grime are used in the initial investigation, however Efron dice and other non-transitive dice can be explored in the extension section of the investigation.	Download26
Simulating randomness Randomness and chance affect events that have a major impact on our lives. In this task we explore methods for simulation randomness, and how the mathematics of chance can be used to analyse events affected by random factors.	Download28
Sampling With and Without Replacement Students simulate drawing random samples of 3 marbles, selected with and without replacement, from an urn containing 10 marbles. Comparisons are made between the results obtained for these selection methods. The effect of increasing the number of trials in the simulations is explored. Finally, comparisons are made between the simulation results and the theoretical probability distributions of the random variables associated with these random processes.	Download41
Circular Probability A triangle is formed such that two vertices are on the base of a unit square and the third vertex somewhere within the square. What is the probability that the angle at this third vertex will be greater than 90 degrees? A diagram helps to provide a visual, the interactive nature of the TI-nspire file makes it easy for students to explore, estimate the probability and determine a geometrical approach to solving the problem.	Download9
Investigations
Personal Poly Investigation Turn your name into a Polynomial. Are there any two names that share the same polynomial? Students explore names and polynomials, including what happens to palindromic names, what degree is their polynomial? This investigation is provided as a Word document for teachers to edit and customise for their students. A PowerPoint slide show is ready to go, suggested answers and TI-nspire files, this investigation has it all wrapped up!	Download21

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Short Cuts

Nspired Crossword

Understanding Transformations

Reflections

Personal Polynomials

Functions Inverses SFI

Exponential Decay

Radians

Biorhythms

Unit Circle Sine

The Movie Contract

Pendulum Swing – Part 1

Domain, Range and Function Mapping

Circumcircles

Transformation Game

Function Transformations

Learning Exponentially

Transformations 1 - Translations, a graphical approach

Transformation 2 - Dilations, a graphical approach

Transformations 3 - Reflections and Revision

Gradient of a function

A Special Function

Take it to the limit

Triangle Areas

Fill the Vase

Paper Folding

Ladder Problem

Eye Spy

Personal Polynomials

Building Rules

3D Equations

Discrimination of Parabolas

Factor and Remainder

Linear Equations Review Test 1A

Lines and Linear RelationshipsTest1A

Algebraic Functions Test 2A

Quadratic Relations Test 3A

Pascals Triangle Hidden Gems

Great Expectations

Simulating randomness

Sampling With and Without Replacement

Circular Probability

Personal Poly Investigation

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