Day 4: Thursday, February 9th, 2012
Fill out the Tessellations Activity Form while you complete the activity.
Objective: Use Geometer's Sketchpad to create tessellations with triangles. Doing the construction on the computer allows you to change the shape of your original triangle and see how the tessellation changes.
  1. Run Geometer's Sketchpad (GSP). You should have an Untitled window for sketching. If you don't, go to the file menu and choose "New Sketch".
  2. Use the line segment tool to draw a segment. Then draw two more segments to make a triangle.
  3. Construct the interior of the triangle: First, use the select tool (the arrow) to select all three corners of the triangle. Selected things are outlined in red, or have red checkers. To select nothing, click on any empty area of the sketchpad. Choose "Triangle interior" from the Construct menu to construct the interior.
With the interior selected, you can change its color and shading (using the Display menu) if you want by right clicking on the shape, selecting properties, then color.
  1. Construct the midpoint of one side of the triangle. To do this, select a side of the triangle. Then choose "Midpoint" from the Construct menu.
  2. Rotate the triangle around the midpoint you just made. To do this, select the midpoint and choose "Mark Center" from the Transform menu. The rotation center will flash. Now select the triangle and choose "Rotate" from the Transform menu. You want to rotate by 180°. Make the new triangle a different color than the first.
Q1: What shape do you have now?

  1. Try moving the original triangle's corners. Q2: What is different about the shape when you move the original triangle's corners? Q3: What stays the same when you move the original triangle's corners? You probably want to save your work at this point.
  2. Use translations to finish the tessellation. To do a translation, you first need to specify the length and direction, which is called a "vector". Select one corner of your triangle, and then select a second corner. Now choose "Mark Vector" on the transform menu. The translation direction and length should flash. Select both triangles and choose "Translate" from the Transform menu. You should get another shape, translated over from the first.
  3. Keep making copies (use different translation vectors when you need to), until you fill out a good-sized piece of the plane: Q4: If you were to keep doing translations, will you ever be able to fully cover the window? Why or Why not?

Move the corners of the original triangle. Q5: What is different about the tessellation when you move the original triangle's corners? Q6: What stays the same when you move the original triangle's corners?
  1. Answer the following questions:
    • Q7: For a random triangle, what symmetries (reflectional and rotational) does the picture have?
    • Q8: Make the triangle a 45°-45°-90° triangle. Now what symmetries does the picture have?
    • Q9: Make an equilateral triangle. Now what symmetries does the picture have?

Q10. Call Ms. Riggins' over so that she can see your tessellation.
Extra Credit:
11. Create a new sketch.
12. Construct a parallelogram, using Parallel Line in the Construct menu.
13. Construct a random shape attached to the left side of the parallelogram by using points and line segments. Label all the points.
14. Select D and then C, and click Mark Vector "D->C" in the Transform menu. Then select all of the random shape and Translate it By Marked Vector using the Transform menu. (Vector is the name for a segment with a given length and a given direction.)
15. Construct a 2nd random shape attached to the top of the parallelogram by using points and line segments.
16. Mark D to A as a vector, and translate the 2nd random shape.
17. Select the vertices of your polygon in consecutive order and Construct Polygon Interior
18. Translate the whole polygon (vertices, sides and interior) by a vector DC and then by a vector DA to create a tessellation. Use different colors for adjacent polygons. Drag any point to change your tessellation.
19. Call Ms. Riggins' over so that she can see your tessellation.

Day 3: Thursdsay, October 14th and Friday, October 15th, 2010
1. We will complete the activity Lines, Triangles and Intersections that requires you to use the Geometer's Sketchpad (GSP) program.
2. You can also answer the questions by entering your answers into the form .

Day 2: Thursday, September 30th and Friday, October 1st, 2010

Computer Lab activity
1. Use the Manga High User ID and Password to Login to Manga High.
2. Complete the three lessons assigned. You have one week to complete.
3. If you finish early, you can play the game for the challenge.

Day 1: Thursday, September 2nd and Friday, September 3rd, 2010

  1. If you haven't already, create your gmail account and fill out the form.
  2. If you don't have a twitter account, create one by clicking on the link at the top right that says 'Join Twitter'.
  3. Fill in the appropriate information and click Create My Account.
  4. On the next page don't fill in anything, Click "Skip This Step" at the bottom of the page.
  5. On the next page, don't click anything except the link that says "Settings" at the top of the page.
  6. Click where it says "Mobile" and follow the steps to get it set up on your phone.
  7. Go back to and click "Follow" (underneath the pi sign).
  8. If successful, the word "Following" will replace the word "Follow". If you have unlimited texting on your phone, make sure both images are green so the updates can be sent to your cell phone.
  9. Go to and follow them.