A few years ago, one of our local elementary schools had a 50th anniversary celebration. The principal of the school contacted me regarding an anniversary photo the school wished to take with students and staff. The principal asked our Math Theory & Problem Solving class to come up with the "most aesthetically" pleasing dimensions for the photo. Our class was tasked with using mathematical methods to systematically design the dimensions of both digits.
Here's a quote from the newspaper article about the photo before it was taken:
Browning, who has taught at the school since 1976, starting as a music instructor and then principal in 1998, said Friday would begin with the weekly assembly in the gym.
“Each class will perform a song from each decade, starting with the 1960s,” she said. Browning added the day-long celebration for students would also include special drawings for prizes, carnival games and the group photograph – if it’s not raining. The students and staff will form a “5-0” and have their picture taken by Downey’s Photography from the Scottsbluff Fire Department’s aerial ladder truck.
The principal emailed some information about how many students and staff would be involved in the photo, the approximate height of the aerial ladder, and that the photo would be taken in a field adjacent to the elementary school.
Our class used mathematics to figure out the size of the viewing field of the camera (based on conservative estimates regarding the camera lens viewing angle). The students did some research and found information on the Golden Ratio, a number that appears over and over again in artwork.
The students wrote instructions for the staff members to utilize when organizing the photograph. We discussed the challenge of keeping that many students organized and engaged for a sufficient period of time in which the photographer could take the photo.
Below is a screenshot of the photo taken to celebrate the 50th anniversary of Westmoor Elementary.
(photo by Downey Photography)
After the photo was taken, I asked my students, "If we compute the ratio of the width of each number to the height of each number, how close is the actual value to our recommendation of the golden ratio (approximately 1.618)?"
Below are screenshots from the Geogebra worksheet examining how close the dimensions are to the target value of 1.618.
Screenshot with the initial question. Students can use measurement tools to judge whether or not the 5 and 0 in the photo meet the desired dimensions.
Clicking on the checkbox in the Geogebra sheet (Show / Hide Measurements and Ratios) reveals the details in evaluating how close the ratio of height to width for each digit is to the Golden Ratio.
Here are the details to the Geogebra sheet. If you would like to download the Geogebra sheet and mess with the values to see what happens, you can find the Geogebra sheet here.
I have been in Washington. DC for the past few days at the Teaching & Learning 2014 conference in our nation's Capitol.
When I stood at this podium, our meeting and session with policy makers had just ended. No audience occupied the opposite side of the podium. I began thinking, however, about the opportunity for positive change an educator could bring to a public office. Towards the end of the conference, we had the privilege to hear Angela McLean. Here is an article about Angela.
Below are some of the resources and knowledge from the conference sessions I attended.
Ralph Smith's Grade Level Reading Campaign
Myself, Deborah Ball, and colleague Dan Schaben after Deborah's outstanding presentation.
Deborah Ball on "Safe to Practice"
Linda Darling-Hammond's Getting Teacher Evaluation Right
Sarah Brown Wessling, featured on the site Teaching Channel, helping teachers connect with great instructional examples
One thing I hope my students learn in school is how a person can unlock their creative potential and pursue their passions into adulthood. To this end, our Math Theory & Problem Solving (MTPS) class took a field trip to do some data collection. I would like to give special thanks to Daryl Payne for allowing our MTPS class to enjoy data collection (racing cars). Daryl's creativity and passion for racing inspired the students to re-imagine what is possible in the world outside school. The video below shows the electric car race track where students raced.
We spent our lunch period having a pizza party prior to racing cars as a reward for the work students have been doing in class. My original motivation in this trip was collecting data and trying to determine how a person could use statistics to potentially detect cheating through exceptional lap times. However, there are also many other mathematical and statistical ideas we can explore with what we learned on this trip.
Here are some things that students wondered about and could lead to mathematical investigations:
- How much longer is the outside lane than the inside lane?
- How does the electronic timing system work?
- How much voltage/current is being supplied to each car?
- What would a person have to know about electronics and circuitry in order to build such a track?
- What is the difference between cars with magnets and cars without? (Cars with magnets can maintain higher speeds around the turns, for example)
- What amount of voltage causes a car to fly off the track?
- How should we determine the best racer? The fastest lap time? The best median lap time?
- Is there a difference between the performance of the blue guest car and the silver guest car? If so, how could we detect this difference numerically?
- How does the "KILL POWER" switch work?
Below, Mr. Payne gives the students some guidelines to follow while they practice racing on the race track.
This short video shows the beginning of a head-to-head race between students.
I am interested to see the types of mathematical investigations that spring up from our field trip. We will take our race data and use it to determine the best racers.
This video segment is phenomenal. Mathematics and engineering can empower anyone to overcome any challenge.