Specialist Mathematics Yr11 by Texas Instruments

The areas of study for Specialist Mathematics Units 1 and 2 are ‘Algebra, number and structure’, ‘Data analysis, probability and statistics’, ‘Discrete mathematics’, ‘Functions, relations and graphs’ and ‘Space and measurement. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.

For more information on the Specialist Mathematics course, visit the VCAA website.

VIC: Specialist Mathematics 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.	Download87
TI-nspire CX II CAS 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
Arithmetic, Number and Structure
Amazing Chords Students produce three relatively simple proofs relating to randomly generated chords in a cirlce. The problem is that the three proofs produce three different results. Can you solve this chord conundrum?	Download24
Squares and Cubes How much mathematics can be generated from a single image? This activity looks at two different number sequences that can be identified directly from the diagram. The challenge is to then prove that this relationship holds true for all positive integers.	Download69
Pythagoras is not Real Students manipulate the location of z on the Argand plane and observe the location of z squared on a second Argand plane. The coefficients of z squared form the two shorter sides of a right angled Pythagorean triangle. Students explore this relationship then prove it. The extension activity includes the opportunity to explore the polar form of a complex number in an informal manner.	Download52
Imaginary Explosions What happens when you square an imaginary number? Does it get bigger or smaller? How can you tell if the number will get bigger or smaller? This seems straight forward enough, but a really surprising result occurs if you add something after you square, then repeat, square and add, square and add. While the activity involves only adding, squaring and graphing complex numbers, the results are truly amazing.	Download22
Complex Spirals In this short focused investigation students explore what happens when a complex number is repeatedly raised to a power. Students then move onto Partial Sums and some of the geometry involved.	Download26
Complex Numbers Test 1A This assessment resource is suitable for Chapter One of the Jacaranda VCE Year 11 Specialist Mathematics 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.	Download17
Discrete Mathematics
Pebbling the Chessboard It’s amazing how often sequences and series pop up in problem solving. In this deceptively challenging problem three discs are placed on a chessboard in a bounded region. The task is to move the pieces out of this region with the only complication being that pieces double when moved. After you’ve struggled to find the solution a geometric sequence comes to the rescue!	Download77
Functions, Relations and Graphs
Parametric Equations What is the difference between a parameter and a variable? This activity introduces the notion of a parameter through two pairs of parametric equations that result in the same Cartesian equation, highlighting the additional information provided by the parameter. Variable isolation and animation support visual and conceptual development models for understanding the mathematics concepts in this activity.	Download30
Advanced String Graphs Part 1 The famous designs of Santiago Calatrava represent beautiful examples of the synergy between mathematics, engineering and architecture. In this activity students model the cables of the “Bridge of Stings” in Jerusalem using a family of straight lines. The envelope formed by these straight lines can also be modelled by a single equation defining the curve. Students determine equations to straight lines, solve simultaneous equations, generate parametric equations and finally a single equation to model the resulting curve.	Download109
Advanced String Graphs Part 2 This is an extension of String Graphs Part 1 but can be done independently. In this activity students stitch points on the lines y = x and y = -x. The family of straight lines form an envelope which can be modelled by finding successive points of intersection. The points of intersection can be modelled by a parabola. A range of extension questions are provided including generalising the parabola for stitching points on the lines y = mx and y = -mx.	Download38
Advanced String Graphs Part 3 This activity brings together a range of ideas from Activity 1 and 2 using a combination of rotation and dilation matrices and a very powerful visual and algebraic approach. The activity gives function to the use of matrices and highlights how relatively complicated expressions can be determined very easily. Students connect many aspects of the Specialist Mathematics course in a single activity that is sure to engage students.	Download151
Space and Measurement
The Matrix Part 1 The focus of this activity is to help build conceptual understanding of transformations. This activity includes three video tutorial links, an interactive TI-nspire file, student questions, teacher answers, notes and recommendations. Students build an intuitive understanding of transforming points, a plane and ultimately simple functions all through a very visual and numeric environment. Students then use matrices and build understanding of the importance of the determinant.	Download24
Six Trig Functions The six trigonometric functions: sine, cosine, tangent, secant, cosecant and cotangent are all inter-connected. In this activity students use a dynamic representation of the unit circle with each trigonometric function to identify relationships. They see why co-sine, co-tangent and co-secant are so named and where the identities come from, including the opportunity to build their own.	Download44
Overlapping Squares This activity is designed as a teacher demonstration tool to introduce students to the notion of ‘proof’ as it applies to geometry. Initially the diagram looks complicated, however, add a couple of lines and it’s obvious! Then students have to go beyond what is obvious in an illustration to mathematical proof.	Download27
Going Around in Circles This activity includes a collection of circle - angle relationship for students to explore and prove. Scaffolded instructions are included in the TI-Nspire file to help students build confidence and develop structure to their proof.	Download17
$Vectors 1 Thumbnail$ Vectors Introduction An introduction to vectors visually, conceptually and numerically. Students manipulate vectors to show addition (head to tail) and the parallelogram rule. Students use a column matrix to represent a vector and explore scalar multiples and the magnitude of a vector.	Download158
Vectors In Component Form Students experiment with an interactive 2 dimensional vector and observe the corresponding changes to its representation in i and j component form.	Download113
Dot Product Students manipulate two vectors as the corresponding dot product of the vectors is displayed graphically on the same page. By exploration students are able to explore the factors that affect the dot product, the conditions for which it is positive, zero and negative.	Download59
Vector Graphics Vectors can be used to solve quite complex problems, in this activity students use position vectors to describe points on the Cartesian plane. Students explore three points located on the function y = 1/x forming a triangle with interesting properties.	Download61
Data Analysis, Probability and Statistics
Calculator BlackJack In the game of Blackjack, players continually draw cards until they can gain a score as close to 21 as possible, without going bust. In Calculator-Blackjack the random number generator is used to produce numbers between 0 and 1, these numbers are summed with the aim to keep this sum less than 1. On average how many cards do you think a player might have drawn to end up bust? This question is explored through statistics and sampling distributions. The answer to the question may surprise you!	Download57
Investigations
Six Trig Investigation Students use interactive content to investigate the six trigonometric functions: sine, cosine, tangent, secant, cosecant, cotangent, including relationships between each. The unit circle animation helps build the relationships, which they derive and prove. The second stage of the investigation has students building relationships for double angle formulas, thanks to a series of visual prompts. The Word document can be edited to suit your needs, so too the companion TI-Nspire file.	Download18

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Short Cuts

TI-nspire CX II CAS Crossword

Amazing Chords

Squares and Cubes

Pythagoras is not Real

Imaginary Explosions

Complex Spirals

Complex Numbers Test 1A

Pebbling the Chessboard

Parametric Equations

Advanced String Graphs Part 1

Advanced String Graphs Part 2

Advanced String Graphs Part 3

The Matrix Part 1

Six Trig Functions

Overlapping Squares

Going Around in Circles

Vectors Introduction

Vectors In Component Form

Dot Product

Vector Graphics

Calculator BlackJack

Six Trig Investigation

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