STEM Education Conference, Linz
Using dynamic worksheets to support functional thinking in lower secondary school
Table of Contents
- Rolling ball
- Hill
- Valley
- Billiard
- Billiard
- Billiard dynagraph
- Triangle
- Triangle
- Triangle dynagraph
- Geoboard
- Geoboard picture
- Throw of a ball
- Throwing a ball
Hill
(a) Click on [b]START[/b] and watch the animation several times. Describe in words how the speed of the ball changes on its path! Draw the corresponding graph in a coordinate system![br][br](b) Click on the check box "speed". Play the animation. What is displayed in the coordinate system? [br][br](c) Does the representation in the coordinate system approximately match with your solution from exercise (a)? [br][br](d) Solve using the representation in the coordinate system: At which position do you find the maximum speed? At which position do you find the minimum speed?[br][br](e) How does the speed change while the ball is moving? Can you read the solution off the graph?
Billiard
From point P, a red billiard ball is shot along the indicated path. Here, d is the distance of the ball from the upper boundary of the billiard table.
(a) Play the animation. Describe, how the distance of the ball from the upper boundary of the billiard table changes with time![br][br](b) Click on the check box "distance d" and play the animation. Compare your results of task (a) to the displayed numerical value of the distance d. Discuss your observations and record your results![br][br](c) How would a corresponding graph in the coordinate system look like? Reason your decision![br][br](d) Click on the check box "graphical representation" in the right graphics window and play the animation. What is displayed in the coordinate system? When has the distance its greatest value, when its smallest? Compare the graphical representation with your own conjecture (task (c))!
Triangle
The dashed line can be moved left and right. F indicates the area of the blue shaded figure.
(a) Move the yellow point to the right and observe the shaded figure. Describe in detail how the area of this figure changes![br][br](b) Click on the check box "area" in the left graphics window. Move the yellow point again and observe how the value changes. Compare your observations to those of task (a)![br][br](c) How would the corresponding graph in the coordinate system look like? Reason your decision![br][br](d) Activate the check box "graphical representation" in the right graphics window. What is displayed in the coordinate system? Compare this representation with your solution of task (c)![br][br](e) Solve by observing the graphical representation in the coordinate system:[br]• What happens when the dashed line reaches point C?[br]• What happens the yellow dot is right of point B?
Geoboard picture
Click the check box "show picture". By moving the yellow point you can change the size of the square.
Tim is a painter. He has to paint a picture of an 8 dm high bear (with santa claus hat) on a window. For testing, he already painted a 2 dm high picture; he needed 5 ml of color for it. How much color will Tim need for the big bear?
Throwing a ball
A ball is thrown vertically upwards from a height of 2 meters at a speed of 20 m/s. In the left graphics window the motion of the ball is displayed; the right graphics window shows the corresponding graphical representation.