Golden Ratio & Apple Cores

@BHSGeomety students recently studied the Golden Ratio and Golden Rectangles with a number of different activities.  For example, in one activity students found lengths on different measurements on their face and bodies and calculated to see if any of their ratios were "golden".

The activity I want to share about goes a little something like this...

1.  Give each student (or group of students) an apple.  Have the student cut the apple horizontally so that the cross section is a circle and it exposes the core.

2.  As you can see, the inside of the core has a pentagram shape.  This is one of many instances of the golden ratio found in the natural world.  We had students take a picture of their apple cores and import them into Geometer's Sketchpad.  Our document camera was extremely efficient at doing this.

3.  Using a regular pentagon custom tool in GSP, students constructed the pentagon around their apple core.

4.  Students then compared each other's apple core to see which had the most "golden" core.

This is a fun 10-minute activity that integrates technology and is very hands-on and student centered.  Students were interested to see what each other's cores looked like.  We actually used four different types of apples in our experiment.  No one type of apple seemed to be any more or less golden than the others.

Here are a few more examples:

Mr. Ott: Finding His Way

Mr. Ott (@iteach_kidsmath) was a student teacher in my classroom this past fall semester.  He was great with the students, very receptive to feedback, and open to new ideas.

Now that he has his own classroom, it's cool to see him continue to grow as an educator.  He has fully embraced the power of twitter as a tool for professional development and collaboration.  He has also begun to blog about his experiences in the classroom.

Keep up the great work, Mr. Ott.  We're glad you're going strong!

Student Created Videos

New year, new goals.

While doing some planning for our new semester, Mr. Huntimer found an activity on myOER that we decided to use to begin the second semester with our geometry classes.

Working in groups of two or three, students were given the task of finding real world objects that model a variety of 2-D and 3-D shapes.  Students were to either take a picture or a video clip of the object.  Then they were to create a video that fused all of the pictures or videos together.  As part of the video, students were required to define the object that they had found.

We allowed students to make a lot of decisions regarding their videos.  Students could define their objects using a number of different methods.  They could define objects as they recorded the video clips, they could record voice narration and align it to their pictures, or they could insert text into the video.  We had students use all three methods.

Students could create their videos around theme or concept.  We had one group use the theme of "shape hunters" and another use the theme of "mathletes".

We also allowed students to use whatever type of video editing software they'd like.  Our laptops have MovieMaker installed, so that served as our default video editor for those who had no preference.  Mr. Huntimer and I were rookies working with the software and found it very user friendly and easy to implement.  Some groups chose to use their iPhones and iMovie.  Another group used a third video editing software that we had never heard of before.  Our only stipulation was that students needed to submit their videos in mp4 or mov format so that we could view them from any computer (via Edmodo).

Overall, the task went very well.  We had some bumps in the road the first time through.  The biggest challenge was we had a number of groups submit their MovieMaker projects before they had converted them to mp4 format.  We simply had to ask those groups to convert and re-submit the videos.  A majority of the videos were similar in that they contained the minimum amount of effort / work needed to complete the task.  A few groups forgot to include all of the required information, thus costing them a few points.  Meanwhile, a few groups produced excellent videos that really caught our attention.

The content of the geometry in the task was really quite elementary, but the task did align to a CCSS ( G-MG.1).  The bigger skill that students practiced was collaboration and technology use.  We asked students to reflect on what they had learned in doing this project and many said they had never or rarely used software to create a video.  We were very happy with the technology application component.

I leave you with two links.  The first is a link to the task via myOER and Mr. Zachary Feldman (click here).

The second is a link to one of our best student videos.   The three gentlemen who created this video have agreed to share it.
Student Video