Eggstreme bungee

We summarize our linear relations unit with an "eggstremely" fun activity - one of my favorite days of the year!

Based on the "Barbie Bungee" activity, our goal is to have an egg have the best bungee jump experience possible (i.e. get as close to the ground as possible without hitting the ground). An elastic band is taped to the egg and a bungee cord is created using elastic bands. We use three different sizes of elastic bands so that each pair of students had to do their own calculations and couldn't just rely on the first group's answer. By the time we do this activity, students are familiar with finding the slope of a line using two points, graphing lines, and determining the equation of a line given two points.

At the beginning of the activity, students (working in pairs) are given an egg and 10 elastic bands and told the following as the main idea:
 
Using their 10 elastic bands, they create a table of values with number of rubber bands and length of drop. Because the drop happens so quickly, we have them film each drop with a camera that has a slow motion option so that they can get more accurate drop lengths.

Students then determine an equation to represent the drop length based on the number of rubber bands. Because this activity was done over two days, this was what students were expected to complete by the end of day 1. We ensured each student left that class with their data collected and their homework was to graph their data and determine the equation, if not done in class.

Class #2 began with partners comparing equations. We then headed outside to the drop zone.

We measured the drop zone and then students were to use their equation to determine how many elastics they needed for their egg to have a safe jump. They then tested their predictions. To speed things up, we had created chains of 20 elastics for each type of elastic. Once a group has tested their prediction, they would then pass along the chain of 20 elastics. Each egg was then dropped and some were successes, other were not. Here is a video of one of the very successful drops.

We do have prizes (fruit snacks) for the winning team so there is an extra incentive on getting the drop closest to the ground. In order to help them determine how low their egg goes, we have them film their drop and having the background board with the different colours, allows them to distinguish how close their got to the ground.

Finally, after the activity is complete, we have the student complete a reflection piece. We use this reflection piece as part of their summative evaluation of these skills (finding the equation of line, interpreting the meaning of slope and y-intercept, extrapolating using an equation). 

Why I like this activity:
Most of the math that students experience has one right answer and usually has "nice" numbers to deal with. Because the weight of eggs varies slightly and the amount of stretch in elastics also varies, there is no definite correct answer for this activity. Because the height of the drop also varies from year to year, an answer can't be passed down from year to year. Students must work out their own prediction using their data.

It was interesting to see students question their answers when its based on a real world example. Students will trust their mathematical solution (they know the steps to find an equation and solve for a variable) but will doubt that the number they found is correct. They then watch their peers egg drop and then start to question their solutions even more. Some groups often take one elastic off just to be sure their egg won't hit the ground.

2 Truths and 1 Lie - Encore

I had the chance to re-try the activity "2 Truths and 1 Lie" in my Grade 12 Calculus (MCV4U) course today and had very positive results. When I did this activity before, I did not get the depth of answers I was hoping for (you can see my previous post on my first attempt and what the activity is about) and so I modified the delivery of the activity slightly. I don't think I could have envisioned the amazing outcome that I got today.

Just to give context of what my students know, we are just finishing up the calculus section of the course and will be starting Vectors next week. The final Calculus test is at the end of this week and covers the derivative of all functions (polynomials, trigonometric functions, exponential functions, logarithmic functions), and problem solving.


I started the activity by displaying this image to the class and told them 2 of these were true and 1 was a lie.

I gave them 1 minute to individually determine which of the statements was the lie (they didn't have to write anything down, just think and come up with an answer they could justify). After the one minute, they worked in pairs with the person sitting beside them and came up with a group decision on which one was the lie. I then asked them to justify why the other two options were true.

As they did this, I walked around the room and listened to some of their thinking. I checked in with each group and asked some sort of follow question. We then came together as a big group and I asked, by a show of hands, who thought each was the lie. At this point, I would ask certain students why they thought it was a lie (it was interesting that some chose the left-most option as the lie as it was the one they least understood and thought it must just be wrong). It was then revealed that the middle option was the lie and that the other two were truths (we also spent a few minutes explaining what the first option meant).

Now the students got to be creative. Similar to my first attempt, I gave each student three pieces of paper and asked them to create 2 truths and 1 lie based on some calculus concept we covered in the course. I also asked that the statements could not be direct facts, they each had to require some thinking to decide if it was a truth or a lie (It could not be "the derivative of y=sinx is y'=cosx but could be finding the derivative of a y=sin(ln(x-3))). They were allowed to look through their notes for inspiration. All their contributions were then posted on the front board (they were asked to put their initials on the back so I could see what they came up with).

I now asked each student to go up to the board and select one of the notes (as long as it wasn't their own) and return to their desk. We then went around the room and each student read their note and stated whether it was a truth or a lie and how they figured it out. The truths were collected in one part of the room and the lies were in a separate location.

I ended the activity here. We had many more contributions to still sort through and my plan is to continue sorting through them as a class before the final exam in June. I'm not sure if I will have each of them pick another note and justify if its a truth or a lie or if I will collate the remaining options and have the class sort through them electronically (not sure how I would do this yet).

Why I am thrilled with the outcome:
- their answers all required some thinking to figure out
- each student willingly participated
- because they had access to their notes, each student had an entry point to the activity
- I was able to further see their understanding when they chose someone else's note and had to determine if it was a truth or a lie.

My next steps:
As we start to think about end of year exams and making productive use of review time, my current plan is to try this again with my class by assigning each student a certain unit and asking them to create 2 truths and 1 lie for that particular unit. I would then use this list as part of their overall review in some way.

A selection of student answers: