8A: Barbie Bungee Jump - Explore More

As introduced in the post, Snapshot: 8A Barbie Bungee Jump, the eighth grade applied their knowledge of linear functions to a Barbie bungee jump challenge. The intent of the project was to provide a real world application of linear functions to ground student understanding.  Students were divided into groups of two or three to do some introductory experimentation with a Barbie, up to three rubber bands, and a meter stick.  Here are all the bungee jump groups with their test Barbie and company name.

Groups plotted their data two ways: by hand and using the an online regression tool. Using their math skills they drew a line of best fit and did their best to estimate the slope of the line. Once they had their calculations figured out, they plotted their data on regression tool and it gave them a linear equation. They had to figure out what the slope and y-intercepts represented in this scenario and use these data points to decide how many rubber bands to add to their bungee rope.

We had to wait patiently for a dry day to perform our bungee jumps. Jump day was thrilling. They students made their initial jumps and then modified their numbers one last time.  Here are some photos from jump day.

We experimented with filming and photography of the event.  There were a couple of GoPros and lots of iPhone footage. Our favorites were the slow-motion jumps taken from the ground.For our final jump, we had all Barbies jump simultaneously.  It was a great way to make a direct comparison of all the bungee cords.

 Student reflection and feedback gave me insights into how to improve upon this activity. Fun was had by all and we made math come to life! 

Thank you to all the people who shared their Barbies for us to use and to B. Hansen for the great video clips. 

Snapshot: 8A Barbie Bungee Jump

Students are always asking,"When will I ever use this?" in math class. I do my best to give them real world contexts for the skills they are learning. In the 8th grade, we began the year learning about linear functions and figuring out how to graph them. To help make these skills real, the students did an activity where they had to use linear functions to figure out how many rubber bands a Barbie required to get the most thrilling bungee jump off QLab 201's balcony (16 feet).  Thrilling was defined as getting as close to the ground without actually touching the ground.  Here is a compilation of shots from our jump day. 

Thank you to Blake Hansen for the video footage and editing.


If you wish to read more about this adventure or see more photos and video, check out: 8A Barbie Bungee Jump: Explore More.

6C : Four Digit Challenge

Students in 6th grade are working on solidifying their understanding of the order of operations in mathematics. The class explored why it might be important for a mathematical phrase or sentence to have only one solution. They came to realize that without a set of universal rules to follow, communication would be flawed. It would be impossible ensure that the information you are trying to communicate would not be misinterpreted. 

To extend their understanding, the class was given the "Four-Digit Challenge." They were asked make equations that equaled 0 to 50. The requirements were:

• the digits 1, 2, 3, and 4 were required to be in each equation
• each digit could only be used once
• they could use addition, subtraction, and multiplication (no division)
• they could use parenthesis and other grouping symbols
• they could use exponents and square roots

The class was challenged to see if as a group they were able to complete all of the equations from 0 to 50. They broke into groups and set to work. 

I wish you could have been in the room to hear all of the wonderful mathematical thinking that was happening. Here is a small glimpse into the type of collaboration that was happening.

Check back for more on the Four-Digit Challenge!

7 Math and Art Connection: M.C. Escher Tessellations

Today, we began exploring how to translate a figure in geometry. We have already looked at line symmetry, rotational symmetry, and reflections. In the course of our discussion, I casually mentioned M.C. Escher's tessellations. I was startled to discover that most of the class had no idea of who M.C.Escher was. I promised the class that I would post a few links so they could explore his work further. 

Resources
M.C. Escher (official site)
Artsy.net: Maurits Cornelius Escher
The Mathematical Art of M.C. Escher
Tessellations.org - Escher Gallery 

Video: 9.999...reasons 0.9999...=1 by ViHart

As we explore the world of fractions, decimals, and percents, the sixth graders have stumbled into the annual debate about whether 0.9999...repeating is equal to one. I enjoy hearing their reasons for both sides and how passionate they get about their point of view.  To wrap up the debate, I share this definitive video about why 0.999.... is equal to one. It is the work of one of my favorite YouTube stars, ViHart.  If you have not had the pleasure of experiencing ViHart, enjoy. I recommend just letting the experience wash over you first, then go back for a closer look on the second time round. Or third....

Does she convince you? 

Population Growth

In 6C, we ended up on a tangent discussing population and population growth. I shared this video with the class because I thought it was a nice illustration of why the population on the planet earth has grown so much. It unearthed questions about history, and where are we headed. They asked that I share this with them, so here it is!

Event: Julia Robinson Mathematics Festival in San Mateo on Nov. 21, 2015

Registration has just opened for the November 21, 2015 Julia Robinson Math Festival in San Mateo. Two years ago, I took a group of BPC students to this event and we had a terrific time exploring math in a collaborative environment. I highly recommend this event if you have the time to check it out!

Register here. 

Video: The Great Math Mystery (NOVA)

Thanks to EB2018 for sharing this video with me. We discussed the Fibonacci sequence when we were studying arithmetic sequences. Through that discussion, EB recalled this program he saw and shared it with me. The sixth graders have watched the first 6:30 minutes related to math and nature. I highly recommend the video as it ask the question, "Is math part of the natural world, or is math a construct of our mind?"

Video: TED-Ed How Folding Paper Can Get You to the Moon

This is a great illustration of how exponential growth is different than multiplication. How realistic is this example? 

8A: The Banach-Tarski Parody

My classes quickly learn that I am easily side-tracked by interesting math ideas and conversations. This VSauce video was sent to me by a student and I felt compelled to share it with the rest of the class. In the last two years, we have tackled the concept of infinite, on multiple occasions. This video does a tremendous job of simplifying this abstract and complex idea. Our brains were stretched and I loved the interesting ideas it generated in class. I hope if you are interested in learning more, you will check out the links on the YouTube page and the many books referenced at the end of the video.

Thank you to JP for sharing this video with me and the rest of the class!

OP's Pi Day video

I am delighted to share this video made by OP2017 to celebrate Pi Day 2015.