Replacement Units - with Graphics Calculator 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 (9860)
This replacement unit introduces algebraic models (linear and simple exponential) to describe change in the world around us. The fitting of models to bivariate data is approached via the underlying properties of constant additive or multiplicative change. 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 9860 technology. All of unit's data is provided it g1m files, ready for file transfer.
As big as can be? (9860)
This is replacement unit dealing with quadratic functions. It starts with a geometric optimisation problem 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 9860 technology and algebraic techniques to appreciate their graphical and algebraic characteristics.
The wind in your sails (9860)
This is a replacement 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 9860 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 (9860)
This is a replacement unit introducing algebraic identities including the distributive law, perfect squares and the difference of two squares, general binomial expansion and factorisation and completing the square. The unit exploits the world of animation to reinforce student's notion of variable. The unit comes with pre-made 9860 files that sequentially build up animated paddocks that confront student's notions of equivalence. They are then challenge 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.
Optimisation (9860)
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.
Logarithms - when adding is multiplying (9860)
This unit aims to provide a simple/useful way to thing about logarithms when first meting them. We use two examples of "hard" to graph data (due to the extreme range in the values) to alert students to the idea of thinking about a number as its power, as opposed to its absolute value. The rest of the unit aims to establish a way to think about calculating with logarithms that will set a sound foundation for later on and that builds on their knowledge of 'indices' from previous years.