Replacement Units - with ClassPad support
Each of the following aim to replace a text book chapter(s) and offer a rich and sense making journey through the content.
Describing change (ClassPad)
This is a complete unit to introduce the use of algebraic models (linear and simple exponential) to describe deterministic and stochastic change, as it is seen in the world around us. The unit approaches the fitting of models to bivariate data via the underlying properties of constant additive or multiplicative change and encourages students to critique the ‘fit’ of algebraic models prior to their refinement and use. The unit contains a wealth of data, drawn from a range of aspects of the modern world. Extensive notes are provided on the use of ClassPad technology, to refine a user defined algebraic model as well as to obtain models of best fit. The accompanying .vcp file contains all the data that is used in the unit, in a Spreadsheet and as Statistics variables.
As big as can be? (ClassPad)
This is a complete unit of work to facilitate the study of quadratic functions. The unit starts with a geometric optimisation problem (paper folding) that prompts students to ask the question “is that as big as can be?” This question drives the generation and use of an algebraic model for the geometric system and emphasises the importance of the vertex form of a quadratic function. The unit then focuses on families of quadratic functions, using technology and algebraic techniques to appreciate their graphical and algebraic characteristics.
Below you will see a video of an animation-model of the folded paper that helps students to 'see' 'all' the cases. The animation was made using the Geometry application within the ClassPad II software. The accompanying ClassPad .vcp file contains the animate-able geometric construction to help kick-start this unit.
A 'chapter replacement' booklet, complete with e-tech support and answers to questions can be downloaded below.
The wind in your sails (ClassPad)
This is a complete unit to facilitate the teaching and learning of right-angle triangle trigonometry. The students begin by 'learning' how to sail a boat and then engage with various aspects of sailing and as a result learn about the fundamental trigonometric ratios. The unit comes with pre-made ClassPad Geometry files that enable the students to sail virtual boats, collect data on their sailing and through this learn about trigonometric ratios. The unit includes traditional learning and problems as well as some not so traditional learning.
Seeing double (ClassPad)
This is a complete unit to facilitate the teaching and learning of algebraic identities at an introductory level (approximately Year 9). The unit exploits the world of animation to reinforce student's notion of variable. The unit comes with pre-made CP files that sequentially build up animated paddocks that confront student's notions of equivalence. They are then challenged to express this equivalence symbolically and from this the algebraic identities flow. The unit also includes 'drill' sections to assist students in the automation of these most important algebraic skills.
When studying quadratic functions/calculus, do too many of your students find 'optimisation questions' hard? Have you ever wondered why? The booklet you can download here is the unit of work that supports the ideas presented in a number of workshops during 2011 and 2012 that outlined why students find the ideas hard. Basically, traditional teaching-and-doing approaches fail to focus on what is really happening: the measurement on one dimension and the subsequent calculation of other dimensions. Also, algebraic simplification turns out to be the devil - the patterns in the symbols are lost and so generalisation is not 'seen'! The approach in the booklet supports the idea of each student developing a calculation and then comparing and contrasting to it other's calculations - it is in this that the symbolic patterns appear and the generalisation literally reveals itself. The ClassPad .vcp file features animate-able versions of many of the problems presented in the booklet, offering a reinforcement of generality at work.
A prime experience (ClassPad)
Many students know what a prime number is, but outside of that and perhaps prime factorisation what else do they do (in school) with these amazing creatures? This unit charts a path for students through the prime's landscape along which they discover sexy primes (among others), prove and generally get to behave very much like a mini-mathematician. Workshops on this unit have been offered in a number of states previously. We do not think you will have seen a tried and proven learning sequence like this before.