GeoGebra. Before we begin. Dynamic Mathematics for Schools

Transcription

1 Before we begin Start your favorite internet browser If is not installed: Go to Click WebStart (third item down in the menu on the left) Click the WebStart button ( is installed automatically) Go to teach.lanecc.edu/~gettyst Start Microsoft Word (OK to take notes!) Dynamic Mathematics for Schools Tom Gettys Fall 2008 In-service Lane Community College

2 What is? Dynamic Mathematics software built by and for Mathematics instructors Open Source, meaning It s free! It s supported by a community of likeminded people Why? In the Principles & Standards for School Mathematics published by the NCTM, one of the principles states that: Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Students can learn more mathematics more deeply with the appropriate and responsible use of technology. For more go to:

3 is Innovative Combination of elements of dynamic geometry software (Sketchpad, Cabri) computer algebra systems (Derive, Maple) High technical portability is fully platfom independent (Windows, MacOS, Solaris, Linux) dynamic worksheets (html) as a Pedagogical Tool Drawing Tool Geometric drawings for handouts & activities Graphs for worksheets, quizzes & tests In-class Presentation Tool Dynamically show relationships Visualization of abstract concepts Authoring Tool (Web Export) Interactive virtual manipulatives Exploratory mathemathics

4 Start up Click Help to get access to the : Home page User Forum Wiki User Forum

5 Wiki Free Materials = Geometry + Algebra Algebra Window Geometry Window

6 Getting to know the user interface The Move tool the most important tool on the menu! Help for the selected tool Tool bar Toolboxes group Similar tools Input field Input field assists Let s get busy! Select the Line through two points tool (notice the tool tips!) Move the cursor into the geometry window (AKA the drawing pad) Hold the mouse button down and notice that coordinates are displayed; release to set point Symbolic Geometric Create a second point to complete the action Observe that the points and line also appear in the algebra window! Extra credit: On the menu bar Select View, then Grid

7 Adding a Drawing to a Document Click on File, Export, Drawing Pad to Clipboard Start Word, then Edit, Paste You re done! Resize and position as desired Context Menu Right-click any object in either window Notice the Properties item at the bottom Context menu

8 Properties Dialog object customization The Properties dialog is accessed via the context menu (or the Edit menu) Notice that this is a tabbed dialog; each tab contains a set of related properties Try this: Change the color of your line (Color tab) Change the style of your line (Style tab) Extra credit: Modify the labeling of point A to Value Activity construct a rhombus (a rhombus is a quadrilateral with all sides equal in length) METHOD 1 (delete all objects and turn off the grid & axes) Begin by drawing a circle (center A and point B) Create a point C on the circle Draw a 2 nd circle centered at B out to point A Draw a 3 rd circle centered at C out to point A Create a point D at the intersection of these two circles ABCD are the vertices of the rhombus Finish by hiding the circles and drawing the line segments Manipulate your rhombus and observe the behavior Tools Used:

9 Activity construct a rhombus (a rhombus is a quadrilateral with all sides equal in length) METHOD 2 (delete all objects and turn off the grid & axes) Begin by drawing a circle (center A and point B) Create a point C on the circle Draw line segments AB and AC Construct a line through B parallel the AC Construct a line through C parallel the AB Create a point D at the intersection of these two lines ABCD are the vertices of the rhombus Finish by hiding the lines and drawing the line segments Manipulate your rhombus and observe the behavior Tools Used: Activity construct a rectangle (a rectangle is a quadrilateral with all interior angles 90 ) Begin by drawing a line segment AB Draw a line through A and perpendicular to AB Draw a line through B and perpendicular to AB Create a point C on the line through A Draw a line through C perpendicular to AC Create a point D at the intersection of these two lines ABCD are the vertices of the rectangle Finish by hiding the lines and drawing the line segments Manipulate your rhombus and observe the behavior Tools Used:

10 Activity - The Pythagorean Theorem Draw a right triangle Draw a line segment AB Draw perpendicular to AB at A Point C on perpendicular Draw line segment CB Hide perpendicular line Construct squares Use Regular polygon tool (Notice the polygon areas are shown in the algebra window) Label each square with its area Properties - Show label - Value Tools Used: Area of a Triangle Create 2 horizontal lines Input: y=0 and y=6 Create a triangle ABC Make 3 points on these lines Connect using line segments Create the altitude Line thru C and perpendicular Make intersection point D Hide line; make line segment Create text Label & Value of height & base Text showing computed area Now the fun part! Move point C and what (doesn t) happen?

11 Tools & Commands Two ways of doing things Input y=x^2 (parabola c is created) Create point A on c Use the New Point tool or Input Point[c] Create the tangent to c at A Use the Tangents tool or Input Tangent[A,c] Create a Slope object Use the Slope tool or Input Slope[a] Parameters & Animation A Slider is a graphical representation of a number Input a=2 Input y=a*x^2 Note in the algebra window that a is off Right click on a, then Show object The variable a has become a graphical object! Manipulate the slider and observe its effect Extra credit: set a to -5 and then right-click on the parabola & turn trace on, then sweep the slider from -5 to 5; a family of curves!

12 Riemann Approximations - part 1 Type the following into the Input field: f(x)=4x-x^2 a=0 b=4 Area=Integral[f,a,b] Type the following into the Input field: n=10 UpperSum=UpperSum[f,a,b,n] LowerSum=LowerSum[f,a,b,n] Adjust the colors of Upper & LowerSum Riemann Approximations - part 2 Right click on a and select Show object The variable has become a graphical object! Manipulate the slider and observe its effect Repeat for the variables b and n n should take only positive integer values Access the Slider properties for n Set min, max and increment appropriately

13 s Web Export Every Construction can be exported as a Web Page (html), also known as a Dynamic Worksheet Try it with your current drawing File, Export, Dynamic Worksheet as Webpage Examples Go to Click on Demonstrations Example 1: Graphing Linear Equations Example 2: Basic Construction Kit Dynamic Worksheet Example: Graphing Linear Equations was used to create this page Access to the internet is all that is needed to interact with it! User is limited to just the actions you design in

14 Dynamic Worksheet Example: Basic Construction Kit A limited subset of the construction tools are available The algebra and input windows are turned off The menu bar is on so students can save their work! Other Features to Mention Booleans Check boxes, used to reveal/hide parts Vectors u=(1,2); v=(2,1); w=u+v Polar Coordinates a=0; r=1; P=(r;a) Parametric Equations c=curve[2cos(3t), sin(4t), t, 0, 2 pi]