The simplex algorithm, sometimes dubbed the world’s most powerful, sits at the heart of linear programming. Classically the subject of tertiary-level study, Dantzig’s simplex algorithm can be used to solve important problems like how to make a ‘better’ burger patty. …
Dogball is an enigma. The bouncy toy exterior hides a rich yet accessible modelling task within; a delicious intersection of maths and science, a potential PSMT/Folio task for Stage 1 Mathematical Methods featuring low floor, high ceiling and room for …
Below is a video outlining a solution answering the questions posed in the resource “Dogball 2.0 – A Study of Bounce – Part 1“. It is not intended to be the best or only way to answer these questions. It …
The introductory videos introduce students to a complete unit of work, a 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?” …
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.
Find the inverse of a function algebraically using invert and also view the inverse graphically.
Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using a traditional step by step elimination method in Main.
Two methods to restrict the range of solutions returned when solving trig equations in Main.
Use one of the 2D templates to solve systems of equations with 2 or more variables.
How to use sliders in graph and table to explore function transformations.
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 ClassPad technology. A .vcp file contains all unit’s data in a Spreadsheet, and also as Statistics variables.
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 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.
Below you can access: DOGBALL.pdf – a currently-brief but mostly complete summary of the activity you experienced. vdbcgraw.csv – the csv file of the data we used in the activity – which is a subset of the data that was …
This unit uses the context of generosity to introduce a need to have a fractional way of thinking about something.
It develops a way of thinking about fractions – the for-every idea – that is the elusive multiplicative model.
Developed over about 5 years, this approach has been tried and seems to work. 🙂
To students (of all ages):
a short excursion or journey for pleasure
a short mental excursion or mental journey for pleasure, nothing too heavy!
Have a go at mental-jaunt #1 – a wee journey with numbers.
jaunt (noun) a short excursion or journey for pleasure mental-jaunt (noun) a short mental excursion or mental journey for pleasure, nothing too heavy! Mental-jaunts are trails that will evoke certain ways of thinking that are very helpful both in understanding more complex …
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.
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 ClassPad 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.
A selection of test questions and solutions for ACMMG244 (Year 10).
A selection of test questions and solutions for ACMNA240 (Year 10).
A selection of test questions and solutions for ACMNA241 (Year 10).
A selection of test questions and solutions for ACMSP250 (Year 10).
A video introduction presents the mathematics of cup snakes, a hands on phenomena involving additive change that gives rise to a way to think about linear growth. Modeling this phenomena theoretically, with the help of two cups, and through data, with the help of many, many cups, these videos give rise to some of the big ideas around developing and using linear algebraic models to describe additive bi-variate change. These ideas are then unpacked in the accompanying ‘chapter replacement’ booklet.
This video and documents outline a 4 session course that aim to assist students to develop the optimal ways-of-thinking about the ideas that underpin calculus.
A selection of documents that share some nice ideas about exponential functions, trigonometric functions and a lovely context where both concepts come together.
A selection of test questions and solutions for ACMMG242 (Year 10).
A selection of test questions and solutions for ACMMG243 (Year 10).
A selection of test questions and solutions for ACMMG245 (Year 10).
A selection of test questions and solutions for ACMNA229 (Year 10).
A selection of test questions and solutions for ACMNA231 (Year 10).
A selection of test questions and solutions for ACMNA232 (Year 10).
A selection of test questions and solutions for ACMNA233 (Year 10).
A selection of test questions and solutions for ACMNA234 (Year 10).
A selection of test questions and solutions for ACMNA235 (Year 10).
A selection of test questions and solutions for ACMNA236 (Year 10).
A selection of test questions and solutions for ACMNA237 (Year 10).
A selection of test questions and solutions for ACMNA238 (Year 10).
A selection of test questions and solutions for ACMNA239 (Year 10).
A selection of test questions and solutions for ACMSP246 (Year 10).
A selection of test questions and solutions for ACMSP247 (Year 10).
A selection of test questions and solutions for ACMSP248 (Year 10).
A selection of test questions and solutions for ACMSP249 (Year 10).
A selection of test questions and solutions for ACMSP251 (Year 10).
A selection of test questions and solutions for ACMSP252 (Year 10).
A selection of test questions and solutions for ACMSP253 (Year 10).
A selection of test questions and solutions for ACMNA230 (Year 10).
This document presents an approach or approaches to the 2011 WACE Mathematics 3C3D Examination. These approaches incorporate the use of CAS as well as ‘by hand’ solution methods. At times two alternative methods are presented. The providing of two solutions is intended to encourage a conversation between teachers and students about the most deserning and efficient way to tackle the mathematics presented in this form of assessment.
A ‘how to’ companion book for the Tasmanian General Maths 3 course written by Gary Anderson.
Collect like terms and expand and simplify expressions such as 3(4-2x)^2.
Factorisation of numbers and expressions (eg quadratics)
Use the sequence function in Main to find the defining rule for various sequences
Eliminate one variable from an equation using another equation.
Example: If x=8-2t and y=6t-1 find an expression for y in terms of x.
Create your own user functions.
Examples (i) f(x)=1/x or (ii) Ckh2ms to convert speeds from km/h to m/s
Managing your own user defined functions such as those created in the previous topic.
Create and use a function with many variables. Also edit a user defined function in the program editor.
Solve simultaneously the equations 3y – 2x = 5 and x + 2y – 8 = 0 graphically using both Main and Graph windows.
Draw a line segment between two points A and B and construct its midpoint.
How to update the operating system of your hand-held ClassPad using a Windows PC.
How to download programs, eActivities, csv files, pictures and so on into your handheld ClassPad from a Mac or Windows computer.
Download the programs that accompany the book How Do I CODE on a CASIO fx-CP400.
Examine the growth of money over 10 years using compound interest and also use the difference tool to find individual amounts of interest for any year.
Use sequence to examine the balance of a reducible interest loan, determine total interest paid and find individual monthly interest figures.
Determine the explicit formula for a sequence from a recursive definition using Sequence RUN and the rSolve() function.
An introduction to using NumSolve from the Main menu in the context of the simple interest formula I=PRT/100.
Learn some tips on working efficiently in NumSolve.
Use the built-in probability simulation tool in Main (or eActivity) to simulate throwing one or two dice or selecting items at random from a container.
Calculate simple interest and future values in the Financial application.
Solve compound interest problems in Financial, including finding future values, interest rates and time required.
Solve loan repayment problems in Financial, including payments, time periods and loan amounts.
Use the Verify tool in Main to check steps when manually simplifying expressions.
Smooth time series data in the statistics app with the program mavII. Also fit a regression line and predict future values. mavII is freely available from www.charliewatson.com/classpad/.
Using the program repayII to solve reducible interest problems. repayII is freely available from www.charliewatson.com/classpad/.
A brief look at the Conics app and how it can be used to determine the centre and radius of a circle.
A brief tour of the InterActive DiffCalc app and how it can be used to explore concepts of differential calculus.
A brief overview of picture plot, including the use of sliders to modify function parameters.
Modify the functions assigned to the shift key and save time when using your favourite commands on your Classpad.
How to set a picture as the ending screen – the picture that briefly flashes onto the screen when you turn your ClassPad off.
A brief overview of using the Casio Picture Conversion Engine software to creating a picture for use on ClassPad II for modeling functions in Picture Plot or as an ending screen.
Five examples of small utility programs freely available from the internet are shown.
How to create a small program on your hand held Classpad.
Construct a diameter in a circle and then examine the angle in the semi-circle.
Construct a tangent to a circle and then examine angles in the alternate segment.
Construct 2 angles on the circumference from a common chord and examine.
Construct a cyclic quadrilateral and examine sum of opposite pairs of angles.
Construct 2 tangents to a circle from an external point and examine their lengths.
Examine the angle between a tangent to a circle and a radius.
Construct angles on the circumference and at the centre from a common chord and examine.
How to use sliders in geometry to change lengths and angles.
Find the equation of the line through (2, -1) perpendicular to the line 5x – 2y +6 = 0.
How to change the labels of any Geometry object using the annotation tool – eg change triangle ABC to triangle PQR.
Create a triangle in Geometry, apply a matrix transformation to the vertices in Main and view the image back in Geometry.
Use an object and its transformed image in Geometry to determine the equivalent transformation matrix in Main.
Fast track your animation skills by animating a tangent line around a circle.
Examine the angle in the semi-circle using a slider.
Examine the angle in the semi-circle using the Animation tool.
Examine sum of opposite pairs of angles using the Expression tool.
Basic settings in the Sequence application.
Create the sequence of Triangle Numbers using an explicit definition, and graph the first 12 terms.
Create an arithmetic sequence, then a geometric sequence, also finding the sums of the GP.
Create the Fibonacci Sequence, graph the first 10 terms and find the ratio of conscutive terms.
Simulate throwing 120 six-sided dice in a spreadsheet and display the resulting distribution as a histogram.
How to import external data in comma separated variable (csv) file format into the Spreadsheet app and then into the Statistics app.
Store and solve all your commonly used formulae as strips in eActivities.
Lock, Unlock, Delete, Move Folder and Rename eActivities. Also create a new folder.
Strip Help is a great way to add hints on what to do within any strip in an eActivity.
Many multiple-step math problems can be programmed into an eActivity. This example uses Herons method to find the area of a triangle given three side lengths.
Some tips on working within eActivities including working with text or calculation rows, deleting strips and adding strip help.
Examples of ways to deal with the ambiguous case of the sine rule when solving obtuse triangles.
Create and save an eActivity to calculate the average rate of change of any function over a given interval.
Create and save an eActivity to calculate ANY of the parameters (eg mean, sd, etc) involved in a normal probability question.
A Geometry Link in an eActivity is used to investigate translations applied to a parabola. Other possibilities are also hinted at.
Setting up the geometry window, including scales, displaying axes, integer grid and saving.
Draw a line segment, measure its properties of length, gradient, equation.
Draw a line segment between two points A and B and determine its length.
Draw a simple triangle and learn how to measure angles, sides, area and perimeter.
Construct a right triangle and measure angles, sides, area and perimeter.
Construct and solve triangle ABC given two sides and the included angle.
Construct and solve triangle ABC given two sides and a non-included angle.
Construct and solve triangle ABC given all three sides.
Draw a circle and construct a diameter.
Create a histogram from a frequency table.
Calculate two variable statistics from paired data.
Create a scatterplot and then calculate and plot the least squares linear regression line through the data.
Create an xyLine of time series data.
Vary the class intervals when summarising data with a histogram. Also shows use of the randList() command to create a list of random numbers.
Substitute a value into a recently calculated regression line to determine a predicted value.
After finding a linear regression model for a bivariate data set, residuals are calculated and plotted to check suitability of linear model.
Calculate inverse normal probabilities in Statistics using the Calc menu and Inverse Normal CD tool.
Calculate a confidence interval for a mean from supplied summary data in the statistics application.
Calculate a confidence interval for a proportion from supplied summary data in the statistics application.
A quick introduction to the common data types – text, number and formula – and some useful spreadsheet tools.
Create a simple sequence and then extend the spreadsheet using Cut and Paste technique.
Create the Fibonacci sequence, adjust columns widths, use the Fill Range command to extend the sequence and display very long integers.
Create a geometric sequence including the sum of terms and extend using Tap and Drag technique.
Create a pie chart, determine the percentages represented by each sector and dynamically modify.
Create a flexible Simple Interest spreadsheet using Absolute and Relative cell references and extend by copying and pasting multiple columns.
Create a flexible Compound Interest spreadsheet using Absolute and Relative cell references and format cells to 2dp.
Use a spreadsheet to examine the balance of a reducible interest loan.
Use a spreadsheet to examine the balance of an annuity.
Smooth time series data in a spreadsheet using moving averages, fit a regression line and calculate residuals.
Graph y = 4^x using the Graph & Table application, including use of Zoom facility.
Solve y = 3x – 4 and y = 6 – 2x graphically by first drawing the functions and then finding the points of intersection.
Solve y = 2 – 5x and y = -3x^2 + 4x + 2 graphically by first drawing the functions and then finding the points of intersection.
Jump to any exact coordinate whilst tracing along one of several functions in graph.
Show the gradient of a function on screen when tracing along its graph.
Use the Modify tool when graphing to vary the parameters of a graph. In this example we vary a and b when y = ( x + a )^2 + b.
Find the equation of the tangent to a curve in Graph and Table using the Analysis, Sketch, Tangent function.
Evaluate and illustrate definite integrals in Graph and Table using Analysis, G-Solve tools.
Solve a linear programming problem with 4 constraints in Graph and Table.
Draw the graph of a function in y1 and automatically draw the graph of its first (and second if required) derivatives.
Evaluate and illustrate area trapped between x-axis and function in Graph and Table using Analysis, G-Solve tools.
Evaluate and illustrate trapped areas in Graph and Table using Analysis, G-Solve tools.
Graph a polar function using r=Type, adjust basic view window settings and become aware of some limitations.
Graph parametric functions using ParamType, adjust basic view window settings and become aware of some limitations.
Calculate one variable statistics from a single list of scores.
Calculate one variable statistics from a frequency table.
Create a boxplot from a single list of scores.
Create a boxplot from a frequency table.
Create several boxplots in a single graph to compare their distributions.
Create a histogram from a single list of scores.
Learn how to over-ride the selected angle setting when working with trig functions in Main.
Generate random numbers and simulate throwing dice using the rand() and randlist() functions in Main.
Temporarily and permanently assign and delete values to variables in Main. Useful for substitution.
Differentiation basics in Main using either Interactive, diff or the 2D template. Also higher orders and any variable.
Find the equation of the tangent to a curve in Main using the tanLine function.
Find indefinite and definite integrals in Main using either Interactive, S or the 2D template.
Find a volume of revolution in Main and graphically.
Find the gradient at a point of an implicitly defined function in Main.
Important actions that should be taken in Main before trying any of the activities in this section.
Solve the equation 7x – 3 = 2x + 4 using a traditional step by step approach in Main.
Solve the equation 7x – 3 = 2x + 4 using the solve command in Main.
Solving the quadratic equation x^2 + 6x + 5 = 0 with the solve command in Main.
Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using the 2D simultaneous template in Main.
Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using the Solve command in Main.
How to express a as the subject of the equation t = 2a + 3b in Main.
Use the differential equation solver with a simple growth and decay question.
Important settings that should be taken in Graph & Table before trying any of the activities in this section.
Graph y = 2x + 3 using the Graph & Table application, including setting the View Window.
Graph 3x + 2y =12 using the Main application, including use of Resize.
Graph y = x^2 + 3x – 4 using the Graph & Table application, including setting the View Window.
A brief welcome to ClassPad II Help Series and a preview of some of the new features and apps that come with OS2
Settings in Main we recommend you should make to ensure your initial experience of Classpad and these help sheets is hassle free.
A guided tour of the most commonly used areas of the Classpad keyboard.
Some basic editing methods in Main, including drag, cut, copy and paste.
Some basic calculation techniques including evaluation of expressions and substitution.
Simplification and addition of algebraic fractions
Determine the Highest Common Factor or Lowest Common Multiple of two numbers.
Rounding to a given number of decimal places or significant figures.
Create your own cis function for making complex number entry simpler.
Basic complex number entry and calculations, including finding magnitude, argument and conversion between forms.
Use the toPol and toRect functions to convert between polar and rectangular coordinates with vectors or complex numbers.
Calculate normal probabilities in Main using the Interactive menu and normCDF function.
Draw a random sample from X~N(60,144) in Main and calculate mean and SD. Also analyse in Statistics.
Calculate binomial probabilities in Main using the Interactive menu and BinomialPDF function.
Draw a random sample from X~Bin(24,1/6) in Main and calculate mean and SD. Also analyse in Statistics.
Enter and graph piecewise defined functions in Graph and Table.
Calculate normal probabilities in Statistics using the Calc menu and Normal CD tool.
Calculate a confidence interval for a mean when sample data has been entered in the statistics application.
Calculate binomial probabilities in Statistics using the Calc menu and Binomial PD tool.
Create and reflect a triangle in the line y=-x in Geometry. Also, tips on using other transformations.
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