Students reflecting on their learning

In order to take the emphasis off of the final mark on the unit test, my colleagues and I decided to try something new in our last grade 9 unit. We were going to have the students reflect on their learning before seeing their final grade on the test.

The day the students wrote the test, we photocopied their completed test before grading it. On Friday, students were provided with the photocopy of their own test and a sheet that looked like this:

They then spent the class time working through each question identifying what content of the unit was assessed in that question along with a reflection of how prepared they felt for the question. 

At the end of the period, students were provided with their graded test. 

Some of my take aways from the activity:

-  Students focused more on their own solutions and not just the number of marks they got. Often students who do well on the test only focus on the few questions that contain mistakes and do not take the time to reflect on what they also did well. 

- The conversations between students were focused on learning and not just on marks. If two students got different answers, they worked together to determine where the mistakes arose.

- When the marked tests were returned, there were no surprises or emotional responses to lower than expected marks. And as mentioned above, the students who did well looked through their test with a critical eye as opposed to seeing a good mark and filing it away in their binders. 

I'll admit that this was in reaction to students writing the test and identifying that they felt it was a challenging test. In the future, it would be beneficial to have students go through this reflection activity before the test (even before the review period) so that they can focus their studying on the content of the unit where they feel least prepared. It is definitely something that I would consider doing before the final exam. 

Finally, we did have the benefit of having time to use a class to go through this process. In other units, I hope to use this same reflection activity but may have to assign it for homework the day before I return the test. I could envision students going through this process at home and arriving to class with an educated guess as to how they think they did on the test. 

A sweet 3-Act Math Task

The other day we had the opportunity to host our Grade 8 students in the Senior School to showcase what Grade 9 math is all about. To give them a taste of linear systems, John Doma (@Domanator19) and I created a sweet 3-Act Math Task.

Act 1:
Act 2:
Act 3:

Though I have used several 3-Act Math tasks in my MPM1D class, this seems to have been one that created the most opportunities for different solutions. Though unintentional, the data that we provided in Act 2 allowed for multiple solutions. This lead to the majority of students being engaged in the activity and willing to contribute their ideas (maybe it was also because we gave them a small box of Smarties to use in their problem solving!).

Here are some of the ideas that students brought forward:

a) 2 cm = 215 Smarties. Therefore 1 cm = 107.5 and so 15 cm = 15(107.5) = 1612.5 Smarties
b) 5 cm = 485 Smarties. Therefore 15 cm = 3(485) = 1455 Smarties
c) 11 cm = 1147 Smarties. Therefore 15 cm = 11 cm + 2 cm + 2 cm = 1577 Smarties

My take away from this activity was making sure to truly think about what data to provided. Going forward, I will definitely be reconsidering the data I do provide in Act 2 taking into consideration multiple pathways to creating an answer.

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.