# Lesson 8: Dinosaurs and Non-Euclidean Geometry

Amazingly, this Saturday will be our last lesson.  Time flies when you’re having fun with Sketchpad!  This coming Saturday, students will be involved in a number of investigations:

1.Students will start with a classic warmup puzzle:  How can you use two containers (one 5 quarts and the other 3 quarts) to measure 4 quarts of water?  Hopefully the Three Jug Problem applet will work on their iPads.

2. We will revisit our dinosaur that was plunged in water and has since grown over the week.  Students will answer questions on the handout regarding scale factor in higher dimensions.

3. Students will investigate weird geometries including Mobius Strips on the handout and Taxicab geometry on the iPad.

Here are the the materials students need for the lesson:
iPad file in DropBox, copy of student handout in DropBox, scissors, tape, and a few sheets of blank paper to use for Mobius Strips.

It’s been a blast working with you or your students.  We’ll see each other soon for the upcoming summer workshop!

# Lesson 7: More with Similarity

For this Saturday’s lesson, we will build on previously studied concepts related to similarity.  Students will be involved in the following activities:
1. Warmup Problem on iPad: The goal is to find the number of rectangles in the shape below and then are challenged to see how many are similar and congruent to emphasize vocabulary.

2. Donald in Mathemagic Land Video: I have attached a quicktime movie of a video clip that talks about the Golden Ratio that you can watch at your site.  There are questions students should be ready to answer on the iPad.
3. Golden Shape Activity: Students will need a meter stick for this activity.  They will investigate human ratios in pairs.  Students will need the activity sheet copied for them that is available on DropBox.
4. Rabbits: On the iPad, students will generate the first few terms of the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, …
5. Lastly, students will look at different fractals constructed on the iPad.

I look forward to working with you and your students this Saturday!

# Lesson 6: Area (Part 2) & Similarity

This Saturday, students will conclude using the iPads to investigate Pick’s Theorem.  I have posted the GSP file to the dropbox (entitled Area(Part 2) and Similarity) as well as a new handout for students.  I also included a solution guide that has sample answers as well as additional questions you can ask.  I spent some time trying to debug the issue we had on the past warmup last time so I hope the warmup can be easily manipulated this week.

I have also included the handout and sample answers here for you to print:
Investigating Area (Part 2) and Similarity (student handout)
Investigating Area (Part 2) and Similarity Key (sample answers)

I hope your students are enjoying the lessons!

# Lesson 5: Area Investigation

While the plan was to continue more with reflections with students golf course ideas, I did not receive any emails with other students’ designs.  This is not a problem as we can continue this further in other lessons as we see fit.

For this Saturday, students will be investigating concepts of area.  The Geometer’s Sketchpad file has been uploaded to the YSP Dropbox.  Students will investigate a warmup problem dealing with an area paradox.  They then will be engaged in using animations in Sketchpad to understand various geometric formulas.  They will also work together to discover and apply a formula called Pick’s Theorem.

To get a feel for some of the questions, you can check out the Investigating Area Student HandoutPlease copy this handout for your students prior to the lesson.

Please let me know if you have any questions.  I look forward to working with all of you this Saturday.

# Lesson 4 Update

Robert and I have been discussing the prospect of students using the iPad to design their own golf course hole.  While there are some decent applications for the iPad that allow drawing basic geometric objects, we felt implementation of this problem for Saturday is a bit too late.  We will keep looking at possible apps for students to use on the iPad for constructions beyond Sketchpad Explorer.

For this Saturday, please have students design their golf course hole using more traditional methods (paper, compass, ruler, protractor, etc.).  If you have scanning capabilities, please scan these and email them to cbolognese@uaschools.org.  I will compile the golf course holes for our next videoconference session and organize them where students can solve one another’s design using reflection techniques.

Let me know if you have any questions for this Saturday!

# Lesson 4: More Minimum Distance and Golf Course Design

For week 4, I’d like to continue the minimizing distance problems from the iPads.  Azita told me that students only went through the first two problems in Sketchpad, so I would like to continue their investigation of these problems to fully understand the benefit of using reflection to solve minimum distance problems.  This should require about the first hour of the session.  Have students pick up where you left off (which I believe is the Flag Pole problem) and have them investigate the remainder of problems in small groups, having a concluding discussion as a full class about what they learned.

To apply these reflection ideas, I would like to have students generate their own aerial representation of a putt put golf course.  I have attached a sample of a putt putt hole that students can use as a guide.  Students should then work in small groups to design their own golf course hole.  It would be best if they did not draw how to find the hole in one shot using reflections since other groups will do this with their design next week.  Encourage students to not only draw the design, but challenge them to see if they can determine the area and perimeter of their design.  Students will need the following materials to draw their own hole:

-Blank Paper to draw their design (the larger the better)
-Protractors
-Rulers
-Compass (if possible)
-Colored markers (if available)

Update: Robert is looking into a DIGITAL way for students to make and share their golf course design instead of doing it by hand.  I will let you know in a few days if we are able to do this.

For the next videoconference session on March 31, I thought the students could share their holes to other sites and have the sites determine a solution applying the reflection techniques that they learned.  This will take some careful planning on our part as ideally I would like to digitally share these designs.  Perhaps each site leader could scan the designs and email them to me to prepare for sharing for March 31st.

Please email me at cbolognese@uaschools if you have any questions.

# Lesson 3: Minimizing Distance (w/ iPads!)

This coming week’s videoconference lesson will involve the Geometer’s Sketchpad Explorer on the iPad!  I’m very excited for students to use GSP to make lessons more hands on. If you have never used GSP, you should be able to follow along and assist students as the Explorer version that they will have on the iPad has limited functionality.  Check out this YouTube clip to see an example of how Sketchpad can be used to make a kaleidoscope.

I will be posting the GSP file to the YSP Drop Box folder that was created.  The file should then be uploaded to student’s iPads before the next session.  There is no handout that will need to be prepared beforehand to give to students as the lesson will be entirely contained on the iPad.  The only thing that may help would be for students to have a calculator handy, but of course they could just use the calculator on the iPad.

Finally, here is a link that showcases some of the problems that students will be investigating.  I suggest you check it out to familiarize yourself with the problems.

For Saturday, OSU professor Azita Manouchehri will be leading the lesson as I will be predisposed grading math contests for OCTM.  She is a passionate and energetic teacher so I know she will do a wonderful job!  I look forward to your comments about how the lesson was designed and how your students were engaged.