Dissertation
Using dynamic worksheets to support functional thinking in lower secondary education
Table of Contents
- Rolling ball
- Hill
- Valley
- Billiard
- Billiard 1
- Billiard 2
- Billiard dynagraph
- Triangle
- Triangle 1
- Triangle 2
- Triangle dynagraph
- Geoboard
- Geoboard 1
- Geoboard 2
- Geoboard picture
- Motion problems
- Linear motion - Meeting vehicles
- Linear motion - Overtaking process
- Throwing 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 1
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 the corresponding graph in the coordinate system look like? Reason your decision![br]
Triangle 1
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]
Geoboard 1
On a 10x10-Geoboard, a square is spanned with red rubber bands - its [br]area is highlighted in blue. By moving the yellow point you can change [br]the side length of the square.
(1) Move the yellow point and observe the representation. What do you observe? [br](2) Describe how the perimeter of the square changes as you increase or decrease the side length Examine how the area of the square changes when you change the side length Determine perimeter and area for following side lengths a: 0 cm, 1 cm , 2 cm, 5 cm, 8 cm, and 10 cm!
Linear motion - Meeting vehicles
A car starts on the motorway in Linz and drives with 110 km/h in the direction of Vienna, which is 170 km from Linz. At the same time, a truck starts in Vienna on its way to Linz with 80 km/h.
(a) Play the animation in the upper window and describe your observations.[br](b) Click on "show" in the graphics window below and play the animation. Discuss the representation in the path-time diagram. The following questions may be helpful:[br]• What happens at the intersection point of the two straight lines?[br]• How can you read the distance traveled by both vehicles off the diagram?[br]• How can you read the speed of both vehicles off the diagram?[br](c) Change the speed of the car and the truck. How does the representation in the path-time diagram change? When and where will the two vehicles meet now?
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.
[size=85][size=100]a) Play the animation and describe your observations![br][br](b) Activate the check box "graphical representation" and play the animation. What is displayed in the coordinate system?[br][br](c) Solve by using the graphical representation and compare your solution to the the situation presented on the left side.[br]• At which position and when do you find the ball's maximum height? [br]• At which position and when do you find the ball's minimum height?[br]• What is the height of the ball after 3 seconds?[br]• When is the height of the ball 12 meters?[br]• How far has the ball flown?[br]• What happens with the ball after 4.2 seconds?[br][br](d) Find a solution, explain and reason your considerations.[br]• How does the height change over time? Can you read this off the graphical representation?[br]• Determine the changes in height when the ball moves twice as long![/size][/size]