This classic problem challenges many students. What better way to explore it than a simulation? Once students work through the simulation, they are more open to working through the logic of the unexpected outcome. The Monty Hall problem is a must for all Methods students as they learn to dig deeper when it comes to investigating probabilities.



 TINspire™ CX CAS
 TINspire™ CX

5


A probability function may be represented as a formula (usually an equation), a table or a graph. In this activity, you will use interactive graphs in TINspire CAS to explore the effect that changing the value of a parameter (a number describing some characteristic of the distribution) has on the graph of that probability function.




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Students approximate the gradient of a function using the Central Difference method and approximate area under a curve using a series of trapeziums.




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This activity focuses on graphs of probability density functions for continuous random variables, including the normal and standard normal distributions.




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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.




2


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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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.




8


Introduction to Leslie Matrices. The TInspire activity file includes interactive Leslie Matrices and data extraction to monitor the different age groups associated with the Dung Beetle population. The student question sheet includes a range of questions to help students develop an understanding of each row and column in the matrix in addition to population variation and stabilisation.



 TINspire™ CX CAS
 TINspire™ CX

10


The aim of this activity is for students to use a table of values to compare two linear functions through the context of taxi and rideshare fares. After obtaining an estimate from the table of values, students then proceed to the algebraic solution.




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In this activity students determine the approximate area under a curve using a variety of shapes including squares, rectangles (inner and outer rectangles), triangles and trapezia. An optional extension includes the use of the midpoint and Simpson's rule(s).
This activity includes a video tutorial.




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Students use the two function definition tools on the TI30XPlus MathPrint calculator to neatly define the function f(x) and then g(x) for the gradient function using differentiation from first principles. By repeatedly decreasing the distance between the two points (limit) students can see the gradient also approaches a limit. This tool is then used to generate a list of gradient estimates with a view to establishing the rule for the gradient.
This activity includes a video tutorial.




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Students explore three different ways to generate a sequence on their calculator: recursively, using the sequence command (lists) and finally using the function editor. The memory locations a and d work nicely with the formula for an arithmetic sequence and make for a more dynamic and userfriendly environment.
This activity includes a video tutorial.




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Students review probability as a measure of likely chance to occur, perform simulations of experiments using technology including the identification of factors that could complicate the simulation of real events, create and use a sample space to determine theoretical probabilities and expected values, all through the context of the popular board game Monopoly™.




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Two popular word games in one activity. Students use a program to extract letter frequencies from text and uses the data to analyse two of the most popular word games: Scrabble and Wordle. Students develop strategies for the second game and test them using the program: TIgram.



 TINspire™ CX
 TINspire™ CX CAS

4


Watch Paul discusses the kick, we discuss the calculus and more.
There is no doubt, a kick directly in front of goals is more likely to be successful, but where is the best place if you are near the boundary line? This activity starts with shooting for goals in soccer before heading out to the MCG and a magnificent kick from the boundary by AFL great, Paul Salmon. Did he find the best spot from where to launch his kick?



 TINspire™ CX CAS
 TINspire™ CAS

5

