Students and teachers will acquire the ease of using Geometer’s Sketchpad in the classroom.

Introductory lessons will lower frustration levels.

Students will discover the theorems on their own, making the lessons more student centered.

Students will become capable of doing higher-level projects such as transformations in the plane.

This project involves inquiry-based instruction. Both students and teachers will have a variety of resources to utilize, some basic and some more advanced. There are reproducible worksheets for novice to advanced users, which have all been classroom tested. These activities do not have to be done consecutively. There are also websites that offer more lesson plans for use with Sketchpad and a help center.

Cross Content Standards: 2.3, 2.5, 2.7, 2.9

Core Curriculum Standards: 4.2, 4.3, 4.4, 4.5, 4.7, 4.16

Each activity is independent of the others. The amount of time of each activity is listed next to it. The transformations in the plane should be completed in a week covering one topic a day.

Follow the rules that are set by the teacher previously.

Students who have a question are to raise their hand and wait patiently.

Students are to have their own computer or 2 to a computer (depending on class size and number of computers). Each student is responsible for the work. If they work together they are to put both names on the project. Appropriate behavior is expected.

Computer time scheduled

Computer with Internet and Geometer’s Sketchpad

Printer if available

1. Welcome to Sketchpad!! (1-2 days)

Hand out the introductory worksheet. Allow the students to explore for a little bit then have them do the worksheet. Depending on the class’s response to using this program it can be completed in one day. Today is the day for a lot of questions.

Activity 1 <-Make this a hot link to Activity 1

Have the students go to this website for a tutorial. http://forum.swarthmore.edu/sketchpad/intro/gsp.introlab.html

When they are finished they can complete a quiz on this site.

http://forum.swarthmore.edu/sketchpad/intro/gsp.quest.html

2. Constructing quadrilaterals (1 day-this can be done on the same day as the introductory lesson)

In this lab the students are to construct quadrilaterals based on their definitions.

Activity 2 <-Make this a hot link to Activity 2

3. Exterior angles of a triangle (1 day)

In this lab the students will be constructing a triangle with an exterior angle. The students will discover the relationships between the remote interior angles and the remote exterior angle.

Activity 3 <-Make this a hot link to Activity 3

4. Relationships between central and inscribed angles (1 day)

In this lab the students will construct a circle, central angle and an inscribed angle. Students will measure the central angle, inscribed angle and intercepted arc to find the relationship between them.

Activity 3 <-Make this a hot link to Activity 3

5. Translations (Day 1 of 5)

In this lab the students will learn about translating objects along vectors.

Activity 4 <-Make this a hot link to Activity 4

6. Reflections (Day 2 of 5)

This lab focuses on reflecting objects over a line.

Activity 5 <-Make this a hot link to Activity 5

7. Rotations (Day 3 of 5)

The students will learn about rotating objects about a fixed point, a certain amount of degrees.

Activity 6 <-Make this a hot link to Activity 6

8. Glide Reflections (Day 4 of 5)

The students will learn about the composition of a translation and a reflection along the line parallel to the vector.

Activity 7 <-Make this a hot link to Activity 7

9. Tessellations (Day 5 of 5, possibly 2 days)

The students will learn the basics of creating a tessellation. For an extended activity and discussion students can read this web site about M.C. Escher.

Activity 8 <-Make this a hot link to Activity 8

M.C. Escher website:

http://users.erols.com/ziring/escher.htm

10. Tiling (1-2 Days)

The students will explore tiling. They will start out with squares, then progress to hexagons then to octagons.

Activity 9 <-Make this a hot link to Activity 9

Students will be graded on each lab that they hand in. A rubric can be used. One example of a rubric being used: this can be modified; it is to be used just as a guide.

A grading rubric can be found at http://school.discovery.com/schockguide/assess.html

The Geometer’s Sketchpad Math Forum Classroom Resources

This is a great resource for Sketchpad ideas.

http://mathforum.com/dynamic/sketchpad.links.html

A great source for discussion groups, classroom resources, archives of labs, help center, etc.

http://forum.swarthmore.edu/dynamic

This is the home page for Key Curriculum Press, which produces The Geometer’s Sketchpad. On this site there is a demo version of Sketchpad, project ideas, a help center and product information.

http://www.keypress.com/sketchpad/index.html

1. Move your mouse to the left hand side of the screen. Click on the 1^st box and hold down. What do you see?

 

 

2. Hold down the segment key. What three things come out when you hold the mouse down?

1. Make three points (in a triangle form) on your screen, then click on the arrow.
2. Hold the shift key down, while clicking on each of the points. Do not let up on the shift key, until you are done clicking on all three points. All points will be highlighted.
3. Go to the construct menu and click on segment. (Make sure that on your tool bar on the left, the segment is showing, not the ray or line.
4. Click on the hand with the pointer finger. Click on each of the points on the triangle. What happens?

 

5. Now click on the arrow. Click on the side of the triangle then go to measure and click length. Do this for each side.

Record the three lengths he

a)

b)

c)

6. Now click on one of the points (with the arrow) , hold down and drag. What happens?
7. Drag the points until two of the side measures equal. (isosceles triangle)
8. Now click on the three sides of the triangle while holding down the shift key. Click on construct on point on midpoint.
9. Now highlight the three new points and go up to construct and segment.
10. Click the hand again. Hold the left mouse key down and drag on the white area of the screen. A blinking box appears. Type your name.
11. Now click on the arrow and then click on your name. Drag it to a different place on the screen.
12. What are some of the things that Sketchpad can do?

Construct the following based on their definition.

1. To construct a pair of parallel lines, construct a line and a point somewhere above that line.

2. Highlight the line and the point (not on that line), then go to construct parallel line.

3. To construct a perpendicular line (perpendicular lines form 90 degree angles) construct a line and a point somewhere above that line.

4. Highlight the line and the point (not on that line) and go to construct perpendicular line.

Make sure BEFORE you print, go to print preview and select scale to fit page.

Use these constructions to help you create the following figures.

Trapezoid- a quadrilateral with exactly one pair of parallel sides

Parallelogram- a quadrilateral with two pairs of opposite parallel sides

Rhombus- a parallelogram with four sides congruent

Rectangle- a parallelogram with four right angles

Square- a parallelogram that is both a rectangle and a rhombus

1. Construct a ray
2. Construct a triangle ABC on ray AD.
3. Measure Ð BAC, Ð ABC and Ð BCD.
4. What is the relationship between the remote interior angles and the remote exterior angles?

 

 

 

 

5. Drag any point around to change the size of the triangle. Does the relationship remain true? Why is this so?

 

 

 

 

6. What is the relationship between Ð BCA and Ð BCD?

1. Construct a circle
2. Construct CA and CB to create central angle ACB
3. Construct DA and DB to create inscribed angle ADB.
4. Measure Ð ADB, Ð ACB and arc AB.

What is the relationship between Ð ADB and arc AB?

 

 

What is the relationship between Ð ACB and arc AB?

 

 

A translation is a slide (up, down, left or right) along a marked vector.

In this lab we will practice translating figures.

1. Construct any polygon.

2. Highlight the points and construct the polygon interior.

(To construct polygon interior highlight ONLY the points then go to construct polygon interior)

3. Now hold the shift key down a highlight two consecutive points. Either left to right or right to left) (Do not highlight more than two points because doing so will not work) Go to the Transform menu and click, Mark vector " -> ".

4. Take the arrow and highlight the entire figure, go to the Transform menu and click Translate. (a window will pop up and just click OKAY) to Marked Vector. (it will be highlighted already)

Your polygon will now be translated.

5. Highlight your picture again and translate the figure.

6. Next, mark another vector, (different) and translate the figure up or down. 7. Repeat this three times.

Mark vector CD

Highlight entire picture

Translate twice

Then mark vector BC

Highlight JUST polygon interior

Translate twice.

2. Construct a 6 sided polygon and

translate to the left 4 times

and down 2 times.

Save both projects #1 + #2, print preview first and

"scale to fit page" then print.

A reflection reverses the orientation of an object and is isometric.

A. Part 1

1. Construct any polygon with a polygon interior.
2. Construct a line next to the polygon.
3. Highlight the line
4. Go to the Transform menu and select "Mark Mirror"
5. Highlight the entire polygon
6. Go to the Transform menu and select "Reflect"
7. Print preview and scale to fit page.
8. Print out with name.

Example

The darker polygon (on the left) is

my original picture.

I marked the line my mirror,

selected the entire original polygon

and reflected. The picture on the right is

the reflection.

B. Try again with a different polygon.

 

Activity #7

Rotations

A rotation moves a figure around a set point a certain number of degrees. The resulting figure is congruent to the original (isometric).

A. Part 1

9. Construct any polygon.
10. Highlight any point on the figure.
11. Go to the Transform menu and click on "mark center".
12. Highlight the entire picture and click the Transform menu.
13. Highlight rotate.
14. A window will pop up and ask for a degree measure.
15. Try 60 degrees and see how it rotates. If there is an overlap undo the rotation and try a higher degree measures like 75.
16. Continue this until you go around 360 degrees.
17. Print preview and scale to fit page.
18. Print out with name.

The center marked C is the center point. The "petal" was highlighted and rotated 45 degrees seven more time to create a flower.

2. Try again with a different polygon and different degree measure.

A glide reflection is a transformation that consists of a translation by a vector, followed by a reflection in a line that is parallel to the vector.

1. Construct a polygon and polygon interior. (Draw something odd so that you can obviously see the reflection.
2. Construct a line
3. Select the line and go to transform-mark mirror
4. Highlight the polygon and go to transform-reflect
5. Hold down the shift key and select the two points on the line-go to transform and mark vector
6. Highlight the new reflection (image) and go to transform-translate

A tessellation is an arrangement of congruent figures that completely covers a plane without gaps or overlapping. In a tessellation what is added to one side is taken away from the other.

Construct a square with the script.

(c://sketch/samples/scripts/polygons/4byedge.gss)

Construct a random point, E, next to segment AC

Construct segments AE and CE

Highlight points C and D go to transform and mark vector

Highlight segments AC and BD, go to display and hide segments

Highlight segments AE, CE and point E

Go to transform and translate

Highlight all points go to construct polygon interior

Highlight entire picture then go to transform and translate

Repeat this four times

Highlight points A and C go to transform and mark vector

Highlight entire picture then translate.

Construct another one of your own.

Here is an example of a translation tessellation. Points were made on the side and the top of the square.

Tiling is a repeating pattern of figures that completely covers a plane without gaps.

1. Open the square script (c://sketch/samples/scripts/polygons/4byedge.gss)
2. Construct the square using the given
3. Now pick two points on the square
4. Highlight and go to script and click Fast (you may have to choose the points in different orders so the square will tile)

Your tile should look similar to this.

5. After you have tiled about 6 quadrilaterals, type your name and print out.

1. Open the hexagon script (c://sketch/samples/scripts/polygons/6byedge.gss)
2. Construct the hexagon
3. Tile the hexagons as you did the quadrilaterals.

1. Open the octagon script (c://sketch/samples/scripts/polygons/8byedge.gss)
2. Construct the octagon
3. Highlight ONE side of the octagon.
4. Go to the Transform menu and click on Mark Mirror
5. The highlighted segment will pulse
6. Now go to the Edit menu and click on Select All
7. Go to Transform and click on reflect
8. You should now have two connected octagons
9. Now go clockwise, skip the adjacent side and then highlight the segment. (Every other segment you will highlight-one at a time)
10. Repeat steps 4-7 on every other side.

1. How do the quadrilaterals tile?
2. How do the hexagons tile?
3. How do the octagons tile?
4. What is the difference between tiling the hexagon and octagon?
5. Why do you think there is a difference between tiling the two?
6. How do you think a regular pentagon will tile?

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