Specialist Mathematics Yr11 by Texas Instruments

Unit 1 and 2 include the following areas of study: Algebra and Structure; Arithmetic and Number; Discrete Mathematics; Geometry, Measurement and Trigonometry; Graphs of Linear and Non-Linear Relations and Statistics. Each unit includes four or more topics selected from at least three different areas of study and must include two units from number systems and recursion; vectors in the plane; geometry in the plane and proof; and graphs of non-linear relations. Students should be able to apply techniques, routines and processes involving arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations and graph with and without the use of technology.

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.	Download81
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
Arithmetic and Number
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!	Download56
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.	Download56
Seqences and Series Test 3A This assessment resource is suitable for Chapter Three 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.	Download23
Surds 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.	Download19
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.	Download46
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.	Download21
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.	Download21
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.	Download11
Geometry, Measurement and Trigonometry
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.	Download23
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.	Download16
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.	Download31
$Vectors 1 Thumbnail$ 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.	Download140
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.	Download97
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.	Download44
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.	Download53
Graphs of Linear and non Linear Relationships
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.	Download27
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.	Download105
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.	Download35
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.	Download149

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Short Cuts

Nspired Crossword

Pebbling the Chessboard

Squares and Cubes

Seqences and Series Test 3A

Surds Test 1A

Pythagoras is not Real

Imaginary Explosions

Complex Spirals

Complex Numbers Test 1A

Overlapping Squares

Going Around in Circles

Six Trig Functions

Vectors Introduction

Vectors In Component Form

Dot Product

Vector Graphics

Parametric Equations

Advanced String Graphs Part 1

Advanced String Graphs Part 2

Advanced String Graphs Part 3

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