This task provides a creative way to reinforce linear function algebra with Years 9–10 students land to learn about transformations of sets of such functions. The focus is on the students discovering what effect each parameter in the function (e.g. gradient & yintercept) might have on the shape and location of the set of graphs.




0


What is the difference between simple and compound interest? Visually we can see that simple interest is linear and compound is nonlinear. These visuals can be used to improve student understanding of what a significant difference this can make over time. Dynamic representations illustrate how increasing the number of compounding periods and interest rates dramatically effect the contribution compounding interest has to the overall balance. Recursive techniques, including spreadsheets and formulas help reinforce the concepts numerically. See how you can retire with a million dollars on just $60.00 per week.



 TINspire™ CX CAS
 TINspire™ CX

20


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.



 TINspire™ CX CAS
 TINspire™ CX

28


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




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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).



 TINspire™ CX CAS
 TINspire™ CX

24


Watch Activity Tutorial
Vectors can be used to solve quite complex problems, in this activity students use position vectors in component form to describe points on the Cartesian plane. Students then explore these points, located on the function y = 1/x forming a triangle with some very interesting properties.




10


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.




5


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.




26


Pascal's Triangle goes way beyond coefficients of binominal expansions and combinatorics. In this activity students are introduced to the basics but go on to explore other relationships and patterns such as the triangular and tetrahedral numbers, Fibonacci sequence and even Euler's number. There are so many hidden gems in this amazing triangle.




10


The Golden Ratio and its association with the Fibonacci sequence is well know, but there is much more to explore. Variants of the Fibonacci sequence of the form t(n+2)=t(n)+a.t(n+1) also generate specific ratios. For a = 2 the ratio is referred to as the Silver Ratio, for a = 3, the Bronze Ratio. Collectively these are called the metallic ratios where a = 1 is the specific case and equals the Golden Ratio.




15


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.




5


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.




15


This assessment resource is suitable for Chapter Three of the Jacaranda VCE Year 11 Mathematical Methods textbook. The assessment resource is available as a TINspire file or PDF. The TINspire file provides for automated whole class correction and feedback via the TINavigator system (Exam) or as automated correction for individual review (Self Check). TINspire users can add, delete or edit any of the questions provided.



 TINspire™ CX
 TINspire™ CX CAS

10


Students start with a simple paper folding task that leads to a dynamic geometry approach to the construction of a parabolas. Students gain a better appreciation of a parabola and its properties when they know how it is constructed.



 TINspire™ CX
 TINspire™ CX CAS

15


A very popular probability game, but it is so much more than an end of lesson filler. In this activity students start with the traditional approach of playing and exploring, however they are soon challenged to explore strategies and determine the expected value. In the extension students are challenged to consider a responsive strategy.



 TINspire™ CX
 TINspire™ CX CAS

21

