ack in 2004, at the end of my first year of teaching, I went on a trip to New Zealand. During that trip I visited Queenstown and decided that I would have a go at bungee jumping. Given my experience on my first bungee jump, that first year of teaching could have been my last. The jump was quite a substantial one and before the jump the first thing they did was to weigh everyone, and to write the weight on your hand, in this way the jump operators could ensure that you got the right bungee cord for you, to make sure the jump is both safe and thrilling. This is where my issue arose, they weighed me, wrote my weight on my hand and I waited as they did the same with the others, as I sat there I looked down at my hand and saw the weight that was written there and saw that they had gotten it wrong, the weight they had written was about 20 kg below my actual weight at the time. If I had left it, and they had thought I was lighter than I actually was, then the rope would stretch much more than intended and my safe but thrilling ride, would no longer be safe. Luckily I noticed it and had them reweigh and change the weight on my hand.
At he start of 2019 a new STEM centre opened at my school. Early in the planning stages for the implementation of programs in this centre was that all students in the school needed the opportunity to be involved in STEM learning experiences. In years 8 and 9 was to take the form of a 5 week unit of work in their maths lessons and also 5 weeks in their science lessons. As the head of mathematics at my school I was tasked with developing those learning experiences for maths, learning experiences that all teachers would deliver at some point during the year.
In my initial thinking for the year 9 task I really wanted mathematical modelling to play a strong role. I really wanted students to see the power of mathematics in being able to accurately model a situation and to test and refine that model over time. I also wanted their model to be robust, to be able to handle anything we threw at it, so that it could deal with uncertainty. Finally I wanted them to be able to communicate that model clearly, not just to me as a mathematics teacher, but to any audience. I wanted them to take all the complexity of the situation being investigated and to synthesise it into something really clear to anyone, regardless of their level of mathematical confidence.
In the years I have been keeping an eye on the #mtbos, Barbie bungee has always seemed to be a popular activity, throughout the year there are numerous posts showing the excitement that students bring to the problem and it provides a good opportunity for some mathematical modelling. It was a task that I had always wanted to try, but never had the opportunity to since I did not teach in those year levels. However after reading a number of blog posts on the activity I could see that for many, this activity lasted a few lessons, or maybe a week or two, I was trying to make this into a 5 week task. This is where I started thinking back to my experience with the bungee jump. The other activities that I had seen, they had just considered the number of rubber bands as a variable that determines how far the Barbie drops, and that works brilliantly as a shorter unit of work. However in my own jump, weight was the variable that almost sealed my fate. I needed to bring more variables, not less, to the problem, I needed to introduce more uncertainty. As I thought about it more I knew I wanted to incorporate weight but I also thought the height of the jumper would also be a factor that I could get students to investigate.
As I reflected on my thinking I realised that I was asking students to consider how many rubber band sections would be needed for any jump height (up to 8 meters), any jumper weight (up to 200 g) and any jumper height whilst still maintaining the criteria of a safe but thrilling jump. I began to wonder if it was possible and whether I was asking too much. From looking at other posts I knew that the fall distance scaled approximately linearly with the number of rubber bands, the stretch of a rubber band being the slope, and the height of the Barbie being the y-intercept. However the addition of weight as a variable also meant that the slope of the model, the stretch of the rubber band, would also be a variable as less weight would mean less stretch and more weight would mean more stretch. In further research it was revealed that the stretch of a spring scaled linearly with the force applied (Hooke's Law) and therefore I hypothesised that a rubber band would behave in a similar way and that the stretch would be directly proportional to the weight, but to be honest, I wasn't sure.
I was amazed with what they came up with in this task. Some used different numbers of rubber bands and looked how far the Barbie fell and then repeated the same numbers of rubber bands with differing weights. Others decided to determine how many rubber bands would be required to fall to set distances and then looked at how weight would effect the number of bands needed.The third and probably most intriguing approach involved not dropping the doll to collect data at all. They researched the physics of bungee jumping and attempted to use all of the physics formulas to determine the best approach, they only dropped the Barbie enough times to verify some of their numbers.
It wasn't until the day of the final jump that they were told how high the jump was, hot tall their doll was and how heaving it was going to be. They had 15 mins to calculate the number of bands needed, and construct their bungee cord before the drop this is why the jump calculator tool became so important. They had three opportunities to drop their Barbie, the video below only shows the first attempt. It is clear from this that many of the drops are not as close to the ground as ones I have seen online, however given they are having to adjust according to more variables this is a great result. and as you can see some of them are quite close and did very well as a predictive model
Overall I feel that this activity has been very successful and as more classes complete this task I will have more information about what changes I might make. All the resources that I used to run this activity can be found here.
Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
Opinions in this blog are my own and do not necessarily represent the views of my employer.