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The purpose of Lab 3 is to introduce The Geometer's Sketchpad (Sketchpad), which we will use throughout Math 120. Please follow the instructions and answer the questions below to investigate both Sketchpad and geometry. Something should happen each time a question is asked and each time you are asked for a description. Write answers to all questions. If nothing happens when you try to follow an instruction, try again. Follow the directions carefully! Lab 3 is designed to teach you important basics of Sketchpad use, but feel free to explore!
Part 1: The Free-Hand Tools
These tools are used mostly for drawing, in contrast to the more mathematical constructing. They are good for drawing random points, lines, and circles, but they don't allow you the control that you need to construct a shape that won't get messed up when you drag a point. They do, however, also include the all-important Select tool.
| Open the Sketchpad software. As Sketchpad starts up, you will see a picture with the words "The GEOMETER'S SKETCHPAD" in the center of the screen. | |
Click once anywhere to clear the picture. Once you click, you should get a window something like the image below. |
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Now you are looking at the basic Sketchpad layout, called a sketch. To the left of the sketch you will see six different squares with different objects in them. These object are called tools. The area to the right of the tools is called the sketch plane. To enlarge your window, drag the lower right hand corner. |
| If you make something you don't like, don't worry; just undo it with a 'command+z' command. (While holding down on the command key [control key on a pc], press z.) Repeat this as many times as you like to get rid of objects. |
The Select Tool:
Choose the select tool (the first box). When you press and hold the select tool three pictures appear. In the spaces below, sketch each of the three tools.
1. ________________ 2. _________________ 3. ______________
For now, make sure you are using the first one with the arrow only. Move onto the window and select a circle by moving the arrow close to a circle until the arrow becomes horizontal. When the arrow is horizontal it means the arrow is pointing to something. Try to avoid the point on the circle (called the sizing point); you will need that shortly. With the arrow horizontal, hold down the mouse button and move the mouse around.
4. What happens?
Arrange the circles from smallest to largest so that they look like a snowperson. Now might be a good time to start saving!
| Save the file you are making to your own network space, or to the shared, but unprotected, SummerMath space. For SummerMath, map the network drive to \\ambr\summermath. In the Summermath directory there is a directory named 1ExplorationsInGeometry for your files. |
5. By using the select tool, how can you change
the size of a circle you have already drawn without changing where
its center is? (Hint: see paragraph above)
How do you change the location of the circle you have already
drawn without changing its size?
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The Point Tool: The Segment Tool: |
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6. __________________ 7. _________________ 8. __________________
Off to the side of your snowperson you are going to practice drawing one of each of the three types of straight objects. To draw a straight object, click and hold the mouse button while dragging in the direction you want your object to go. Try drawing one horizontally and one vertically. (Use the shift key as you drag.) Now use segment tool to put arms and hands on your snowperson.
The Labeling Tool:
When you draw anything Sketchpad gives it a label. The label is invisible or visible depending on how the preferences are set (in the Edit menu). Every point, circle, segment you have drawn on your snowperson has a label even if you cannot see it. Let's see what the program labeled your snowperson's nose. Choose the labeling tool from the toolbox on the left of the screen (it looks like an A and the cursor changes to a "hand" when the A is clicked). Move the hand close to the nose of your snowperson. When you are pointing at the nose the hand will turn black. Click once and a letter should appear.
9. What is the label for your snowperson's nose?
Now let's put your name on your snowperson picture. The labeling tool actually serves two purposes: labeling tool and text tool. The text tool allows you to write whatever you want anywhere on the sketch. To put your name on the snowperson, find an empty place on your picture and move the labeling tool there. Double-click and a box should appear. This is called a text box. Type in your name, your partner's name, the date and lab #3.
Printing: (This part will need to wait until you have access, e.g., in 401 Clapp, to a printer.)
10. Once complete choose "Print Preview" under the FILE, click on Scale to Fit Page, and then press the Print button. You should always use Print Preview prior to printing in order to print what you really want printed. (For this reason there is no keyboard command for Print.)
You now need a new, blank sketch to work with. Choose "New Sketch" under the FILE menu.
11. What is the keyboard shortcut for starting
a new sketch? (When you click on any of the menu items, you see
the keyboard shortcuts written to the right of the command names
that have shortcuts.)
Highlighting/Selecting:
An essential function in Sketchpad is highlighting or selecting
objects, using the Select tool you used to drag circles around
when you created your snowperson. When you click on an object
with the Select tool, you are telling the computer, "I am
talking about this object." The computer tells you a straight
object or a circle is selected by surrounding the object with
a red outline. A point is selected when it looks like a bulls-eye.
On your new sketch, draw several points. Notice that the last
point drawn is selected. Draw a circle and two segments that start
outside the circle and pass through it. Use the Select tool to
move the circle just a little bit but still intersecting the segments.
Now select the circle and one of the segments. Move them away
from the second segment so that the second segment and the circle
no longer intersect.
Constructing the Interior of a Circle:
Select only the circle (If both the circle and a segment are selected,
click on the segment to de-select it.), and from the Construct
menu choose Circle Interior. The interior of the circle should
now be shaded and "cross-hatched," which shows that
the interior is selected. Without clicking anywhere, follow the
instructions in the next paragraph. (If you inadvertently click,
just click on the interior to select it again.
Using Color:
With the interior of the circle selected, choose from the Display
menu "Color," and from its menu of choices pick a color.
Hiding Objects:
You should seldom delete objects, but you can hide them if you
don't want to see them. (There are two reasons for not deleting:
Deleting takes up more space on a saved file than hiding does,
and when you delete an object, you also delete all the other objects
that were constructed based on the object you deleted.) Look through
the menus to find the "Hide" command.
12. What menu was it under?
13. What is the keyboard shortcut?
Select the interior of the circle and hide it using either the menu or keyboard shortcut. The interior should disappear. To bring it back you need to use the "Show All Hidden" command under DISPLAY menu.
Changing Labels:
There will be a time where you will want to change the label the
computer gave to an object in your sketch. Click once on the circle
with the Labeling tool.
14. What label did the computer give your circle?
Let's change the label of your circle to "Anna the Circle." As you move the Labeling tool close to the circle it turns black. As you move the Labeling tool close to the actual label a small capital "A" should appear on the little white hand. When this happens double-click the mouse button. This may take some practice. If you double-clicked properly, a screen should appear. Type "Anna the Circle" and click "OK." As above, change the label of the endpoint of the segments to W, X, Y, Z in any order.
Animation:
Select the circle, and from the Construct menu choose "Point
On Circle." Label the object "Butterfly." Now select
the point Butterfly, and from the Edit menu choose Action Buttons
and from its choices Animation. A dialog box should appear. Click
on Object within the Animation dialog box. You should get information
saying, "This button animates one point." When you get
that information, click on OK. A button labeled Animate Point
should appear on the sketch plane. Try clicking on the Animate
Point button.
15. What happens when you click on the Animate Point button? _________ What happens when you click on the Animate Point button again? _________
Exploration
Three-Dimensional Effects:
Carefully construct an additional circle with Butterfly as its
center by doing the following: With the mouse, move the Circle
tool towards Butterfly; when the tool is centered at Butterfly,
the Circle tool turns Butterfly large and red, which means that
point will be the center of the circle if you click and drag.
(And if you look at the very bottom right of the sketch window
the message will change from Construct Circle to one that says
...from Point ....) Make this new circle a little smaller than
Anna the Circle. With this new circle selected, from the Construct
menu choose Point On Circle. Label the point you just constructed
"Bee," and hide the "sizing point" on this
circle.
Construct the line segment joining the points Butterfly and Bee, and label the segment "Sonia." Finally, with Anna the Circle, Butterfly, and Sonia selected, from the Construct menu choose Locus. Hide the circle that Bee is on.
16. Describe the locus you just constructed.
17. Try dragging Bee around. What is the effect of dragging Bee around its circle?
18. Label and print results of your exploration.
Constructing VS. Drawing
19. We'll make a distinction between drawing and constructing when we use Sketchpad. Drawing uses the free-hand toolbar tools, but doesn't build in any relationships among the objects drawn. In this sense, the figures drawn can be 'messed up' by dragging the live points. When we construct, on the other hand, we do build in relationships, which are maintained when points are dragged.
As an example, take a look at SQUARES, (http://www.mtholyoke.edu/courses/jmorrow/lab_03.html and click on the link on page 4 SQUARES)
and try dragging the live points of the three squares.
a. Which figure is so mess-upable that no relationships are maintained as you drag points? (Well, maybe some relationships are maintained.)
b. Each of the other two figures maintain some relationships as you drag points. For each of the other two figures state some relationships that are maintained as you drag points.