Dogball - a study of bounce
This is Dogball.
Dogball is an enigma.
The bouncy toy exterior hides a rich yet accessible modelling task within; a delicious intersection of maths and physical science, a potential PSMT/Folio Task for Stage 1 Mathematical Methods featuring low floor, high ceiling and room for unique student responses, and just a great bit of maths.
Dogball, and the modelling task he inspires, is introduced via the video below:
The Dogball data is available in the CSV file below:
Instructions on how to import CSV data into a Casio CG50 AU graphics calculator or into the Casio fx-CG Manager Plus are provided below:
CSV on CG50 with PC or Mac.pdf
The content below does not utilise the Dogball data. It consists of four mathematical explorations executed using the Spreadsheet and Graph apps of a Casio CG50 graphics calculators. Some of the functionality and behaviour may or may not be of use in tackling the Dogball modelling task, depending on the approach used.
The video below demonstrates the use of the Spreadsheet app of a Casio CG50 AU graphics calculator as a means of graphing bivariate data and generating functional models for such data. This alternative to the Statistics app is of particular use when the data needs to be manipulated or the graphs of partial data sets is required.
This video demonstrates a range of functionality on the Spreadsheet app of a Casio fx-CG50 AU. This functionality is deployed to hunt for Pythagorean Triads. It includes the entering, copying and pasting of formulae, as well as the editing and saving of a spreadsheet.
The video below demonstrates the use of the Graph app of a Casio CG50 AU graphics calculator to graph 'composite functions', that is, functions that are defined in terms of other functions.
The video below demonstrates the use of the Graph app of a Casio CG50 AU graphics calculator to graph that are defined in terms of a parameter, where this parameter is assigned a range of values, giving rise to a 'family' of functions.
This is a possible task / cover sheet for the use of Dogball as a Folio assessment task for Mathematical Methods Stage 1 (Year 11), as part of the South Australian Certificate of Education (SACE).