sonyahorton
13-03-2007, 11:34 AM
I accredited Autograph Maths last week and was very impressed with how well the software had been adapted for whiteboard use. The menus and toolboxes are all floating and you can use it in whiteboard mode and it adapts the display eg makes the lines in graphs thicker etc.
In their accreditation application they submitted some step by step examples/ideas for using the software with a whiteboard, thought they may be of use to any Autograph users out there:
Vectors and Shapes
1. Open a 2D Graph page.
2. Select No Axes from the toolbar.
3. Right-click on the rectangle at the bottom and select No Key.
4. Select Enter Shape from the toolbar and enter the flag shape.
5. Enter two points using Point Mode.
6. Select both points and right-click > Create Vector.
7. Ask the students where the vector translation of the shape would be. Draw it using the scribble tool.
8. Select the shape and the vector and right-click > Translation
9. Select one of the points which makes up the vector and move it around. Observe how the translated shape changes.
Two Variable Statistics.
1. Open a 2D Graph page.
2. Select Point Mode and enter a number of points by clicking.
3. Right-click > Select All Points
4. Right-click > Convert to Data Set (note you have not needed to use the drop-down menus at all)
5. Ask the students to guess where the centroid is. Maybe mark a few options with the Scribble Tool.
6. Right-click > Centroid. Was the centroid where people predicted? Discuss.
7. Select Point Mode and add another point.
8. Return to Select Mode and select the centroid and this new point.
9. Right-click > Straight Line
10. We are now going to demonstrate to concept of a line of best fit. The teacher could at this point (or earlier) explain the mathematics behind the line of best fit which says it is that line which minimises the sum of the squared residuals.
11. Select the line and the data set and Right-Click > y-on-x Residuals.
12. Drag the free point around to show how the size of the squares changes.
13. Look for the R-Squared value in the status bar. Is it too small? No problem, double-click the status bar to open the status box. The font size in the status box can be increased and the box can be positioned where the teacher wants.
Volume of Revolution and Exploring Surfaces
1. Open a 3D Graph page.
2. Select x-y Orientation (go to the x-y-z Orientation icon on the toolbar and follow the arrow down).
3. Open the onscreen keyboard View > Keyboard.
4. Hit Enter to add an equation, say y = exp(x), using the onscreen keyboard. Select Plot as 2D Equation and click OK.
4. Add two points to the line using Point Mode. (You can see when you are adding points because the mouse cursor will change.)
5. Return to Select Mode and select both points.
6. Right-click > Find Area. Just use the rectangle rule for now.
7. At this point the teacher could demonstrate the idea that area can be thought of as an infinite sum of rectangles by animating the number of divisions using the Animate Object button on the toolbar.
8. Turn on Slow Plot Mode by selecting the icon on the toolbar.
9. Select the area and right-click > Find Volume.
10. The animation will very clearly demonstrate how rectangles "become" discs when revolved around the axis.
11. Select anywhere away from the object and drag with the pen to rotate the scene. Use in conjunction with the Shift or Ctrl keys on the onscreen keyboard for added functionality.
There is a lot of scope for interactivity in this example. The points between which the area has been found can be changed. The teacher can ask the students how they expect the area or volume will change as the number of divisions increases (use the Animate Object button to change the number of divisions).
In their accreditation application they submitted some step by step examples/ideas for using the software with a whiteboard, thought they may be of use to any Autograph users out there:
Vectors and Shapes
1. Open a 2D Graph page.
2. Select No Axes from the toolbar.
3. Right-click on the rectangle at the bottom and select No Key.
4. Select Enter Shape from the toolbar and enter the flag shape.
5. Enter two points using Point Mode.
6. Select both points and right-click > Create Vector.
7. Ask the students where the vector translation of the shape would be. Draw it using the scribble tool.
8. Select the shape and the vector and right-click > Translation
9. Select one of the points which makes up the vector and move it around. Observe how the translated shape changes.
Two Variable Statistics.
1. Open a 2D Graph page.
2. Select Point Mode and enter a number of points by clicking.
3. Right-click > Select All Points
4. Right-click > Convert to Data Set (note you have not needed to use the drop-down menus at all)
5. Ask the students to guess where the centroid is. Maybe mark a few options with the Scribble Tool.
6. Right-click > Centroid. Was the centroid where people predicted? Discuss.
7. Select Point Mode and add another point.
8. Return to Select Mode and select the centroid and this new point.
9. Right-click > Straight Line
10. We are now going to demonstrate to concept of a line of best fit. The teacher could at this point (or earlier) explain the mathematics behind the line of best fit which says it is that line which minimises the sum of the squared residuals.
11. Select the line and the data set and Right-Click > y-on-x Residuals.
12. Drag the free point around to show how the size of the squares changes.
13. Look for the R-Squared value in the status bar. Is it too small? No problem, double-click the status bar to open the status box. The font size in the status box can be increased and the box can be positioned where the teacher wants.
Volume of Revolution and Exploring Surfaces
1. Open a 3D Graph page.
2. Select x-y Orientation (go to the x-y-z Orientation icon on the toolbar and follow the arrow down).
3. Open the onscreen keyboard View > Keyboard.
4. Hit Enter to add an equation, say y = exp(x), using the onscreen keyboard. Select Plot as 2D Equation and click OK.
4. Add two points to the line using Point Mode. (You can see when you are adding points because the mouse cursor will change.)
5. Return to Select Mode and select both points.
6. Right-click > Find Area. Just use the rectangle rule for now.
7. At this point the teacher could demonstrate the idea that area can be thought of as an infinite sum of rectangles by animating the number of divisions using the Animate Object button on the toolbar.
8. Turn on Slow Plot Mode by selecting the icon on the toolbar.
9. Select the area and right-click > Find Volume.
10. The animation will very clearly demonstrate how rectangles "become" discs when revolved around the axis.
11. Select anywhere away from the object and drag with the pen to rotate the scene. Use in conjunction with the Shift or Ctrl keys on the onscreen keyboard for added functionality.
There is a lot of scope for interactivity in this example. The points between which the area has been found can be changed. The teacher can ask the students how they expect the area or volume will change as the number of divisions increases (use the Animate Object button to change the number of divisions).