Maddi the painter needs to work out the longest ladder that she can get around a tight hallway corner. Formulate an expression for the length of the ladder, differentiate and make equal to zero. Then what? Why does the function minimum align with the longest ladder?




6


In this activity students maximize the area of a triangle formed when a piece of A4 paper is folded in a special way. The activity provides an opportunity to explore the problem practically followed by an animated TINspire file that automatically generates data so that students are able to check the validity of their data before proceeding. The unusual general result from this task makes the activity quite intriguing.




1


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.




66


Students simulate drawing random samples of 3 marbles, selected with and without replacement, from an urn containing 10 marbles. Comparisons are made between the results obtained for these selection methods. The effect of increasing the number of trials in the simulations is explored. Finally, comparisons are made between the simulation results and the theoretical probability distributions of the random variables associated with these random processes.



 TINspire™ CX CAS
 TINspire™ CX

5


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.




0


First principles approach to loan amortisation as a recursive relationship, and then further use of a program to model the process over the life of a loan.



 TINspire™ CX
 TINspire™ CX CAS

11


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.



 TINspire™ CX
 TINspire™ CAS
 TINspire™ Apps for iPad®

0


This task asks students to create a template for ongoing use in attempting smoothing problems. The data is saved and able to be plotted for further analysis.



 TINspire™
 TINspire™ CX
 TINspire™ Apps for iPad®

2


The classroom activity associated with this task is a ‘whole class’ guessing game, where a random member from a predefined family of curves is drawn on the Cartesian plane by the calculator, and students must write down the associated function rule. It requires an IWB or data projector so that students may easily view the calculator screen (i.e. via TINspire CAS software). There is a student worksheet in which students can record their answers.



 TINspire™ CX
 TINspire™ CX CAS

2


To investigate the idea of transformations of numerical variables to aid in the assessment of goodness of fit, using residual plots, transformed plots and associated statistics.



 TINspire™ CX
 TINspire™ CAS

2


In this activity, simulated random sampling is used to develop the concept of the sample proportion as an estimator of the population proportion. Simulation will allow us to investigate how a sample proportion varies from sample to sample.



 TINspire™
 TINspire™ CAS
 TINspire™ Navigator™
 TINspire™ Apps for iPad®

4


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.




20


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.



 TINspire™ CX
 TINspire™ CX CAS

1


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.



 TINspire™ CX
 TINspire™ CX CAS
 TINspire™ Apps for iPad®

1


Which statistics really count towards a football team's success? Football commentators often refer to the over use of handballs. Is there any correlation between a team's success and the frequency that players use handball to maintain possession or move the ball forward? This activity comes preloaded with all the relevant statistics from the 2016 AFL home and away season so that students can focus on searching and exploring for correlations rather than data entry. See which statistics really count.



 TINspire™ CX CAS
 TINspire™ CX

4

