Median smoothing, more interesting than your average graph. While most median smoothing questions relate to graphs, this activity focuses on an application embedded in digital image enhancement. Students are supplied with a digital image of an old photograph. The original photograph has deteriorated but can be automatically improved by applying various levels of median smoothing. Check it out!



 TINspire™ CX CAS
 TINspire™ CX

4


Have you ever wondered how a car reverse sensor works? In this activity you will build a reverse sensor that provides audible and visual signals when an object becomes too close.



 TINspire™ CX
 TINspire™ CX CAS

0


What is a Stem and Leaf plot and how can you generate them on your TInspire? This activity includes a range of data that can be plotted on Stem and Leaf plots. Students are required to extract a range of information from the plot and discuss the benefits of this representation and also the limitations.



 TINspire™ CX CAS
 TINspire™ CX

15


You won't believe your eyes. How is this possible. This is an amazing sequence. Students use some basic coding to generate a sequence in order to expedite calculations. The result is really cool. You have to try the activity to see the result.



 TINspire™ CX CAS
 TINspire™ CX

13


An interesting question, so many ways to solve it. The question sheet (provided) includes scaffolding to help students solve the problem, however teachers are also encouraged to let students explore the problem. A simple geometric solution exists, but the problem is equally solvable using calculus. Students studying Specialist Mathematics also may like to use implicit differentiation, alternatively, some simple geometry can again be applied. So many ways to solve it.




7


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

6


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

11


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.




3


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

10


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

4


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

6


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

5


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?




22


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

11


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

16

