John Napier created logarithms to help speed up multiplication, he achieved this by turning multiplication into addition via logarithms. Understanding how this works can help students understand why logarithms were created, how and why we use them. A combination of a virtual slide rule, graphs and tables help students understand logarithms.



 TINspire™ CX
 TINspire™ CX CAS

1


Students learn basic programming commands to drive the TIRover, drawing shapes such as squares, circles, regular triangles and stars. In addition to the coding skills, students also learn to be persistent and resilient problem solvers. Through trial and error, students use the results of their program to refine and improve their result.



 TINspire™ CX CAS
 TINspire™ CX

2


This is a basic activity designed to introduce students to coding with the TIRover. The activity is a great precursor to Rover Geometry.A complementary outcome is student persistence for irresolution. If at first they don't succeed, students simply try and try again; each time learning from their previous efforts.




2


Consul the Educated Monkey was a mechanical toy from 1916. The toy relied on geometric properties to perform the multiplication tables. In this activity students use a virtual representation of the toy to analyse and explain how the geometry works and apply new ideas for other applications.



 TINspire™ CX
 TINspire™ CX CAS

2


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 TInspire teacher file generates all the required equations given three starting points.



 TINspire™ CX
 TINspire™ CX CAS

2


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 TInspire file makes it easy for students to explore, estimate the probability and determine a geometrical approach to solving the problem.



 TINspire™ CX
 TINspire™ CX CAS

3


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!



 TINspire™ CX CAS
 TINspire™ CX

2


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?




15


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.



 TINspire™ CX
 TINspire™ CX CAS

4


Students collect data for a bouncing ball using a CBR connected to their calculator. Consecutive ball bounces are modelled using combinations of translational, intercept and standard form of a quadratic equation. Each student has their own data so each student’s working and answers will be unique making it the ideal assessment task!



 TINspire™ CX CAS
 TINspire™ CX

9


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

31


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

35


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

32

