Introduce Ti-nspire

http://web.hku.hk/~amslee/nspire.pdf

TI-Nspire CAS (software)

http://www.ti-nspire.com/tools/nspire/index.html

References written by Bernard Kutzler http://b.kutzler.com/src/download.htm

Introduction to TI-Nspire CAS (Software) (2007) this is a 269 pages comprehensive guide to the use of the software

Algebraic Calculators as Pedagogical Tools for Teaching Mathematics (2000) What Math Should We Teach When We Teach Math with CAS? (2001)

TI-Nspire CAS Software Guidebook http://education.ti.com/educationportal/downloadcenter/SoftwareDetail.do?website=US&tabId=2&appId=6687

TI-Nspire CAS is a powerful mathematics tool suited for teaching and learning. It combines several applications under one roof... TI-Nspire CAS enables new approaches in teaching, learning, and understanding mathematics by providing seamless integration of numeric, algebraic, graphic, geometric, and statistic capabilities enhanced with the support of data collection.

Kutzler (2007) p.5

Calculator

Calculator

Calculator

Calculator

Calculator

Graphs and Geometry change window settings - drag the entire graphing area

Kutzler (2007) p.76

Graphs and Geometry change window settings - edit the range

Kutzler (2007) p.76-77

Graphs and Geometry change window settings - drag the tick marks

Kutzler (2007) p.77

Graphs and Geometry When you have graphed a function, you can use the Pointer tool to translate, stretch and/or rotate it by grabbing its graph. As you maneuver the graph, its symbolic representation also changes.

The graph starts blinking and the mouse pointer now has the shape of a diagonal dash with a double-headed arrow perpendicular to it.

When you see this shape, click and hold the left mouse button, and then drag the mouse pointer down and to the right. Finally release the left mouse button.

Kutzler (2007) p.78

Graphs and Geometry When you have graphed a function, you can use the Pointer tool to translate, stretch and/or rotate it by grabbing its graph. As you maneuver the graph, its symbolic representation also changes.

The mouse pointer takes the shape of a four-headed arrow. This indicates that now you can translate the curve.

When you see the four-headed arrow, click and hold the left mouse button, and then drag the mouse pointer up and to the left. Finally release the left mouse button.

Kutzler (2007) p.79

Lists and Spreadsheet

Data and Statistics Move dots in the graph to see how the mean and median change.

Graph and Calculator

Graph and Calculator variables p, q and k are linked to coordinates of certain points in the graph

Graph and Spreadsheet r and s are defined in the graph while p and a are defined in the spreadsheet

Graph and Spreadsheet

Graph and Spreadsheet study area function with data capturing and plotting

Activity: circumference and area of circle start with a graphing and geometry application; choose the Plane Geometry View

draw a circle and measure its circumference (length) and area

Activity: circumference and area of circle create a variable ● click the measurement to highlight it ● click the var button ● select Store Var

Activity: circumference and area of circle ● type the name of the variable and press enter ● if it is named successfully, the name should appear in bold ● do the same for the area

Activity: circumference and area of circle ● after creating the variables, split the page into two subpages and add a spreadsheet application ● choose a suitable layout ● select Lists & Spreadsheet ● we'll record the values of the variables (cc and ar) in some cells of the spreadsheet

Activity: circumference and area of circle name the column A as 'plotx'

enter the variable cc in cell A1; type the equal sign before cc

press enter and the current value of cc will be displayed

Activity: circumference and area of circle When both variables are recorded in the first cell of each column A and B, we can add them as a scatter plot back in the graphing application. Click inside the geometry subpage, show Analytic Window from the toolbar, a small graph appears.

Activity: circumference and area of circle Switch to Scatter Plot, the entry field below changes so that you can select the available list names previously set (i.e. plotx and ploty). You may not see the point yet if it is outside the graphing range. Right click to zoom data to get the appropriate range.

Activity: circumference and area of circle When the point (plotx, ploty) appears, drag the circle (not the center) to change its measurements, you should then see the point in the graph and values in the spreadsheet updated automatically.

To display the change in area against circumference, right click the point in the scatter plot and activate Geometry Trace. Vary the circle again to see the effect.

Activity: circumference and area of circle We can plot a quadratic function to compare with the scatter plot. Switch to Function graphing in the toolbar. You can then enter a formula for a function. Type x^2 and press enter.

Activity: circumference and area of circle

● Put the pointer on the graph of f1. ● Drag to change the parameter to make the quadratic graph gradually approach the scatter plot.

Activity: circumference and area of circle

Choose another layout to add another application (Calculator) in the same page.

We'll try some calculations for further understanding the coefficient of f1.

Activity: circumference and area of circle insider the calculator, enter ar or cc to display their current values

calculate the ratio by entering "ar/cc^2", the result is close to the coefficient of f1

find the ratio again with a symbolic calculation, enter "(pi*r^2)/(2*pi*r)^2"

turn the last result into an approximation, choose from toolbar "Convert to Decimal"

press enter

the same numerical answer is shown

Activity: circumference and area of circle In the previous steps, although we set up a scatter plot based on column A and B, there is only on point in the graph with its change displayed as a geometry trace. We can really collect a set of values corresponding to a variable by using data capture. To do so, right click the cell directly above cell A1. Choose Manual or Automatic data capture. [Use Ctrl . (period) to trigger each manual capture.] 'var' should be replaced with the name of the variable to be captured

enter 'cc' to indicate the variable

press enter