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

New Year's Resolutions

A couple of quick New Year's Resolutions for my classroom and @BHSGeometry...

1.  Focus on highlighting the standards of mathematical practice.  We use many of them every day in class.  Are the students aware of this?


2.  Less telling, more doing.  Force the students to do the heavy lifting in class.  This is always a goal of mine, and always a challenge to meet.


3.  More student self-reflection.  The more students reflect, the more that gets transferring into long-term memory.  Google forms, exit tickets, possibly student blogs... we'll see where 2015 takes us!

Google Earth in Geometry

We recently finished our unit on triangle centers in geometry.  Students were asked to do a lot of discovery / investigative learning with Geometer's Sketchpad (GSP).  

One activity we had students do was get into groups of three and using Google Earth and GSP, find the location that is equidistant to all three of their houses.

For most, this was a great way to have students collaborate and have direct meaning to the geometry involved in the lessons.  We saw some excellent sketches, such as the example below.

Google Earth is a very useful tool for this type of task.  We found it more user friendly than Google maps since Earth allows the user to pin more than two locations at a time.

4-State Math Collaboration Conclusion

Today the first of two 4-State Math Teacher Leader conferences wrapped up.  I had a 400 mile drive across the state to let my brain stew about things I took away from the conference.

Here's a brief summary of our two days of work.

• Students need to be engaged in tasks in which they are required to use higher-order thinking skills.  The best tasks are accessible to all students and allow multiple entry points.
• These types of tasks call for teachers to be less helpful and allow students to wrestle with the concepts involved.  Often times teachers assist students too much which can cause a potential higher-level task to lose its value.
• Equity in education is something that needs some attention.

Other thoughts and ideas from the conference...

• State leaders are trying to find the best way to get more PD to classroom teachers, especially in the grades of 6-12.  
• It was really motivating to be around a group of people as passionate and invested in improving math instruction as I am. I met some great classroom teachers who are doing great things.  I plan to continue to collaborate with those folks as we move along.

I feel as though we could classify a majority of 9-12 math teachers into one of four categories.

Category 1: Leave me alone

Teachers in this category love the walls that protect them and their students from outside influences.  They prefer to be left alone and have no interest in changing the way they do business.  These are the teachers I have no time for.

Category 2: Mild intrigue

Teachers in this category make frequent visits to category 1, but may be interested in what else is out there.  These teachers have no real interest in hunting for activities and lessons, nor for taking risks.  They are intrigued by seeing how well something worked in another classroom and would consider implementing some changes in their classroom activities as long as the new activity come pre-packaged and usable upon opening.

Category 3: Looking for the light switch

Teachers in this category are open and willing to change, but aren't sure where to begin.  They are typically overwhelmed by the volume of resources available online.  If we can channel the best materials into one place for these teachers to hunt through, then there is serious potential for improvement.

Category 4: Figuring it out

Teachers in this category have already begun to refine their lessons to include deep, engaging tasks that require higher-level thinking.  These teachers typically know where to find the best resources and are aware when more are born.  These teachers are the ones we need in the front line, fighting the battle and swinging the war.  

Last thought:

There is already a movement to try to corral the best resources in one place.  The South Dakota DOE has worked on developing myOER, which is designed to align great lessons with CCSS.  This is a start.  However, I fear if too many resources fall into any one given place, category 2 and 3 teachers lose confidence in their ability to hunt.   

I have worked with Smarter Balance these past 15 months developing the Smarter Balanced Digital Library.  Again, great concept, but with over 1500 resources available to teachers, it too is overwhelming for many teachers to browse through.  

I'm looking forward to part 2 of the 4-state collaboration coming this spring.  

4-State Math Collaboration

I've arrived at Rapid City to take part in a two day Cross-State Mathematics Teacher Leader Conference.  I'm excited to see what I'll learn from fellow math teachers and teacher leaders.  I'll post a summary at the conclusion of the conference, with potential twitter updates (@kreiem).