Lab 2
In this lab, there are several places where you will need to ask the teacher to fill in a number for you before you can do the problem. Put your name on the list if you are waiting for a number.
1) Ask your teacher to help you set up a short cut to the Tranz program on your computer.
· From Shape Library on the top menu, choose Non-Convex Polygon
· From the Transformations menu, check Translation.
· Go to Current Shape, and choose Transform.
You should now see the non-convex polygon on a black coordinate
grid.
2) Get a piece of graph paper and set it up for plotting points. Write “Lab 2, #2” on your graph paper. You will make a copy of the Non-Convex Polygon that you see on the screen. The shape has four vertices, labeled here as A, B, C and D. The screen is set up so that each little dot is worth 1 unit, like a square on the graph paper. From the screen, count the (x, y) coordinates of each vertex and then plot the points on your graph paper.
3) Now go back to the computer screen and type in these parameter values:
x translation: -6
y translation: 3
After you hit Transform, you will see a new version of the shape. When a shape changes in this way, we say that the shape has been “translated.” Write the new (x, y) coordinates for vertex C here:
After translating, vertex C is now at ( , )
4) Now try translating the shape so that vertex C is at (______, ______) ¬ Ask teacher to fill in #s
You will need to try many different numbers for the x translation and y translation until you get the shape to move to the correct location. When you get it to work, write down the x translation and y translation numbers that you used to put vertex C in the right place.
x translation: ______
y translation: ______
Teacher Initials: ______à
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5) Clear the screen by hitting Clear Screen. It will ask if you are sure you want to clear the screen, and you should say “Yes”.
Now, you will use translation to relocate vertex B instead of vertex C. Put vertex B at the location (____, ____) ¬ Ask teacher to fill in #s
Again, you will have to try different numbers in order to get the shape to move where it needs to be. Be sure you are looking at vertex B (top of the shape). When you get it to work, write down the x translation and y translation that you used to put vertex B in the right place.
x translation: ______
y translation: ______
6) Go to your graph paper where you have a copy of the Non-Convex Polygon. Draw a Measuring Box around the shape. Count blocks to find width ↔ and height ↕ of this shape.
width:______
height:______
7) You will now design a new shape. Get a new piece of graph paper and set it up. Write “Lab 2 #7” on the graph paper. Here is what your shape needs to do:
· it’s a polygon
· all of the vertices are in Quadrant 3
· it has 6 edges
· it does not have rotational symmetry
· it does not have reflection symmetry
Mark the vertices A, B, C, D, E, and F in order around the shape. Ask the teacher to check it.
8) Then follow these steps to get to put your shape into the computer:
· From the top menu bar, select Create New Shape à Start Fresh
· Type in vertex A of your shape like this: 3,2 and hit Enter. Repeat for each vertex.
· After you enter vertex F, check the Close Shape box.
· Hit Finish to finish your list of points.
· Go to the right side of the screen and click Save Design. Give your shape the name “Hexagon”. That shape will now appear in your shape library.
9) You will now use translation on your hexagon shape.
· From the top menu, choose Current Shape à Transform
Now your goal is to move your shape so that one of its vertices touches the point (7,6). It can be any vertex. When you get it to work, write down the x translation and y translation that you used to put that vertex at (7, 6). Show your teacher that it works.
x translation: ______
y translation: ______
Teacher Initials: ______
Clear the screen. Choose Current Shape à Transform again.
10) Now use translation to create a new version of your hexagon shape so that one vertex of the new version touches one vertex of your original (white) version. Don’t let any other parts of the shape touch. There are many different ways to do this. When you get it to work, write down the numbers that you used:
x translation: ______
y translation: ______
11) How do negative ( - ) translation numbers change your shape? Be careful about how x translation is different from y translation.
Negative x translation numbers change the shape by:
Negative y translation numbers change the shape by:
12) Suppose Sofia used these translation numbers but did not like where her shape ended up.
x translation: -4
y translation: -6
She really wanted her shape to be more to the left ¬ and just a little bit higher up on the screen. What should she use for her translations?
x translation: ______
y translation: ______
13) Go to your Shape Library and select Non-Convex Polygon.
· Then choose Current Shape à Transform
· Choose Transformations and make sure only the “Rotation” box is checked.
As you are working through the rotation problems, you may need to try several sets of numbers before you get your actual answer. Keep track of what you try by taking notes. This will be especially important if you don’t finish a problem on a given day and have to pick up where you left off the next day.
14) Experiment with a variety of angles of rotation. The angle is measured in degrees, so if you type 12 for your angle of rotation, the shape will rotate by 12 degrees (12°).
Teacher Initials: ______à
15) Do you think the rotation is noticeable when you use an angle of 1°? What's the smallest number you can use for your angle and still be able to see that it rotated?
16) What angle do you type if you simply want the original version of the shape in the same place as it started in? There is more than one way to do this. Find at least two numbers that bring the shape back exactly to its original position. One of the numbers should be bigger than 100.
17) Refresh the screen. Now work on using several rotated versions of the shape to make a five-pointed star. Include the original version as one of the five elements of your design. (Remember that you need to specifically request the original version in order for the machine to know that you want it to be included as part of the final design.) Keep reworking your star until you get it evenly spaced all the way around. Use a ruler to make sure the star is evenly spaced out. Then write down a list of the 5 angles you used to make the star. Keep the shape on the screen.
______, ______, ______, ______, ______
18) Look at your list of numbers in #17. Do the numbers get bigger in a steady pattern? If not, adjust them a little so that they do. What is the pattern? To find a pattern it is often helpful to use a calculator to see how to get from one number to the next number.
19) What would be the next number in your pattern for #18? Try typing that in as a rotation number on the computer and see where your shape goes. Does the new shape land on top of one of existing shapes? If you made a good choice of angles, each one of the new shapes should land on one of the existing shapes. If that doesn’t happen, you need to readjust your numbers.
20) Try continuing your number pattern from Problem #19 a few more times and list the angles you used below.
______, ______, ______, ______, ______
Teacher Initials: ______à
21) Refresh the screen. Ask your teacher to give you a number to use for your first version. Starting from there, make a five-pointed star that is still evenly spaced. The white original version will not be part of this star. Once you have the star evenly-spaced, write down your angles in the blanks below. Then click Save Design to save the shape. Name the shape “Five”.
Ask teacher to fill in the 1st # here à______, ______, ______, ______, ______
22) What is your pattern of angles in Problem 21?
23) Look at the pattern of angles you used in Problem #17 and the pattern in Problem #21. What is the similarity in the two patterns? Why is that happening?
24) Choose Current Shape à Transform. Find an angle to use that will make Five land on itself exactly. Your angle should be between 10 degrees and 100 degrees. This is a good way to check to see if the star really is evenly spaced. Does the new version of the shape cover up the original version? It should.
angle of rotation: ______
25) Clear the screen. From the Shape Library, select Golden Rectangle as your shape. You will be using rotation with this shape also. Find out what happens when you use negative ( - ) numbers for the angle of rotation. For instance, what's the difference between 30° and -30°? Use the curved arrows to show the difference between negative rotation and positive rotation.
26) Now you will do the same experiment with a different shape. Clear the screen. Choose Aztec
from the Shape Library. Again, find out what happens when you use negative numbers for the
angle of rotation. What does that do to the shape? How is negative rotation different from
positive rotation?
Teacher Initials: ______à
27) You will make yet another five-pointed star, with the Non-Convex Polygon from the shape library as your starting shape. For this star, use only negative ( - ) numbers for your angles of rotation.
______, ______, ______, ______, ______
28) What pattern do you notice with the angles of rotation in Problem #27?
29) You will need your teacher to fill in the blanks in order for you to do this problem. Clear the screen. Try an angle of _____° and then an angle of _____°. They come out looking the same! Why does that happen?
30) Now look for three more numbers to use for angle of rotation, where the shape will come out looking the same as _____°. ß Have the teacher fill in the blank.
angle of rotation: ______
angle of rotation: ______
angle of rotation: ______
31) This time, look for a negative number to use for angle of rotation that comes out looking the same as _____°. ß Have the teacher fill in the blank.
angle of rotation: ______
32) Here is a practice test question that you should be able answer without using Tranz. Suppose you start out with Non-Convex Polygon rotated 50°. That is your green shape. Then you need to find another angle of rotation that would land right on top of the green shape. What angle could you use?
angle of rotation: ______
33) This is another practice test question to do without using Tranz. If you rotated Non-Convex Polygon 30º, what angles of rotation would you use to make a five-pointed star? The white original version will not be part of this star.
30 , ______, ______, ______, ______
Teacher Initials: ______à
34) Using Non-Convex Polygon and rotation, work on making an evenly spaced 8-pointed star. Write down a list of the 8 angles you used to make the star. Save the star as EIGHT. To check to make sure the points are evenly spaced out, follow the pattern of your angles and add one more angle of rotation. This ninth angle of rotation should land perfectly on your star.
______, ______, ______, ______, ______, ______, ______, ______
What is the pattern for making an 8-pointed star?
35) Here is another practice test question that you should try to answer without using the computer. What 8 angles would you use to make an 8 pointed star starting with an angle of rotation of 13º? Think about your answer to Problem #34. Check your answer on the computer.
13 , ______, ______, ______, ______, ______, ______, ______
36) Ask your teacher for a protractor. Measure each of the following angles. Write the measurements inside of the angles.