Structure

The Structure dimension focuses on developing students’ understanding of set, logic, function and algebra. It is fundamental to the concise and precise nature of mathematics and the generality of its results. Key elements of mathematical structure found in each of the dimensions of Mathematics are membership, operation, closure, identity, inverse, and the commutative, associative and distributive properties as well as other notions such as recursion and periodic behaviour.
While each of these can be considered in its own right, it is in their natural combination as applied to elements of number, space, function, algebra and logic with their characteristic operations that they give rise to the mathematical systems and structures that are embodied in each of these dimensions.
Principal operations for computation with structure include mental, by hand and technology-assisted calculation and symbolic manipulation by calculators, spreadsheets or computer algebra systems, with sets, logic, functions and algebra. (Source: DEECD)

Description

File/Link

Structure: Themes and Progression Points 3-6
This document was derived by organising the progression points for this dimension into logical themes. (sometimes using the DEECD overview categories). Themes are in bold and progression points increase left to right. Could assist whole school planning.

Structure Overview and Progression points 4.25-5.25
This doc is derived from DEECD overview and progression points. Its purpose is to enable teachers to see the big picture (overview) juxtaposed to outcomes in a smaller range (year 7-8)

Structure Online actvities 4.0-6.0
This doc contains screen shots with hyperlinks to a large number of online resources related to structure



Geometric interpretation of pronumerals 4.0-5.0
This doc suggests a way of interpreting algebraic terms as geometric concepts. x=line, x^2=square, x^3=cube

Introduction to Functions and Graphs 4.0-6.0
This powerpoint conatins screenshots that hyperlink to some key online resources that could be used to introduce functions and graphs at year 7-9

4 ways to sketch linear graphs
Animated PPT that demonstrates 4 worked examples

Linear Relations 4.0-6.0
Car Hire Project. An investigation using Excell, Graphmatica, Powerpoint
Car Hire Project
Using Graphmatica 4.0-6.0
For those of you that have this program this doc introduces how to use graphmatica and investigates linear functions. It was written for version 1.5 and should work for later versions.

Linear Graphs Gradient Intercept 4.0-6.0
Pretty standard but weel set out worksheet building knowledge of linear functions in gradient intercept form

Danny's Cartesion Graphs Stuff 4.0-6.0
This links to a wiki developed by Danny Hyndman who has put togther some good stuff on Cartesion Graphs well worth havinga look
Danny's Cartesion Graphs Stuff
Algebraic addition of linear expressions 4.0-6.0
Use conditional formatting to construct a simple puzzle

Algebraic Addition of expressions 4.5-5.5
Drag and drop activity based on Peter Sullivans activity


Quadratic expansions 4.5-6.0
Use formula in a spreadsheet to show the equivalence of expanded and factorised forms

General Quadratic Formula 5.5-year 11
Construct a spreadsheet to find x and y intercepts and turning point

Linear equations Self directed investigation
This task is designed to encourage a self directed learning approach to the task of solving linear equations. It has an accomppanying sheet with progressive examples of linear equations. An a learning capacities self assessment grid can be used to monitor students "Personal Learning".