Plinko: A summer project

This upcoming year, I will be teaching MDM 4U for the first time in quite a while. My ultimate goal is to have students explore most of the concepts through activities before practicing key skills.

After perusing the textbook and doing a quick Internet search, I came up with the idea of building my own Plinko Board to help with some of the probability concepts. This became one of my summer projects.

What you will need (see below for a photo of the final product):

·            2’ by 4’ sheet of peg board

·            2’ by 4’ sheet of plywood

·            5/16^th dowels

o   We purchased 3 feet long dowels and cut them into 3’’ pieces. I did see you could have bought craft dowels that were precut and about the same size.

o   My board has a total of 300 dowels (216 (18 x 12) white dowels and 84 (7 x 12) black dowels). 

·            Wood glue

·            1/2’’ plywood cut 3.5’’ wide for the sides and bottom edges

·            2 hinges to secure the stand

·            stand (2x3’s)

·            hooks to secure the stand when in use

·            ribbon (to create the zig zag walls)

o   I sized out how much ribbon I needed and then sewed loops at each end. I then slipped one loop at one end over a peg in the first row and then looped it down along the sides and slipped the other loop on the last peg in the last row. This was done on both sides.

·            paint

Every summer, I spend a few weeks up in Northern Ontario visiting my parents and I am very fortunate to have a retired father with a creative mind and a workshop that he lets me invade over the summer for a project or two. One of the first days that I was home, I was watching “The Price is Right” with my dad after lunch and I said “Dad, I am going to build a Plinko Board this summer. You can do it using peg board and some dowels.” This now became a joint project – me for education purposes and my dad for interest sake.

Disclaimer: my dad did the building of the board and I did most of the aesthetics of the board. My dad is great at being given a description and he magically creates the idea with the materials he has lying around his workshop. So I know what materials were used but have little details to provide on how all the materials came together (especially with the stand – it seem to magically appear over night and I have no idea how it was created).

Some things I did note during the building process was that it is a great idea to paint the board and the pegs before it is all put together.  Also, you will need to create a barrier along the sides so that the chip doesn’t get stuck in the sides. My first thought was to use elastics but could not find elastics that were wide enough. My final decision was to use ribbon. See the list of materials for more details on how I put that together.

I decided to leave the bottom values blank so that I could adjust them as I saw fit. My idea is to begin the highest score in the middle of the board and working outwards. I would create small paper slips that I would place at the bottom and could replace if need be.

It was now play time and after some trial and error it was discovered a single poker chip was a bit too light and sometimes stopped along the drop. The weight of 2 poker chips seemed like a better tool to drop. I also found foam golf balls and they seem to work the best – they did not get stuck along the way. My current thought is to have a few different items to use to drop in my class.

My thought at the moment is to have the board in my class and use a few minutes each class for the first few weeks to collect data. I would have the students play and record their result on a common chart. They would keep track of what location they dropped from and where it landed. We would then use this data to drive the discussion in a future lesson.

Stay tuned for how this all unfolds in my class in the upcoming school year.

My year in review

As we approach the end of another school year, I take this opportunity to reflect on my teaching over the past 10 months. Though this was my 12th year of teaching, I realized that I had many firsts in the 2015-16 school year.

Primarily, this year I
1. Tweeted for the first time (I'm sure this isn't the correct terminology - I'm still learning this Twitter world)
2. Created my first blog post.
3. Attended my first EdCamp in Windsor (I found out about this on Twitter)
4. Used 2 Truths and 1 Lie thinking activity (again, a Twitter find)
5. Used VNPS
6. Participated in my first TwitterChat

Yes, I guess you could summarize this by saying I finally discovered Twitter this year (Though I created my account in the last school year, I became a more active user of Twitter this year - not just reading items but also posting and using what I read). I'm still amazed at Twitter's power to universally connect teachers to collaborate and easily share ideas.

Though I may not always walk away from browsing Twitter (yup, pretty sure all the Twitter pros are laughing at my incorrect terminology) with an activity that I can use in my classroom, I readily find statements or articles that make me think - my bookmarks have grown greatly this year. This thinking often leads to a discussion within my department. I know I have greatly appreciated these department discussions - they can sometimes be lengthy but passing ideas back and forth and having colleagues that challenge my ideas has been extremely valuable.

I'm not exactly sure what my specific teaching goals will be for next year but I know that Twitter will continue to be part of my daily routine! Looking forward to more learning and more discussions next year.

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:

 

Questions????

Recently, I read a post by Jon Orr where he used "2 Truths and 1 Lie" as a review tool for the exam in grade 10 math and it made me think about how I could use it in my classroom. Here's my account on using "2 truths and 1 lie" in Grade 12 Calculus - what worked, what I would modify, what it showed me about my students' understanding.

I posted the function  on the board and asked my class to create 2 truths and 1 lie about the derivative of that function. My goal was to see the depth of their understanding of derivatives as well as the product rule, quotient rule and chain rule. (We has spent the previous two classes on the product rule and the quotient rule and we had covered the chain rule in this class).

I had them write their 2 truths and a lie on post-it notes and hand them in (I asked for their names on the back of the post-it and to also identify their lie on the back). My hope was to then, at the beginning of the next class, display all their post-it notes and have them as a class sort through them into truths and lies.

As I read through their responses, I didn't think the activity went that well (I did this activity in 2 classes on the same day and got the same type of results in both sections). Here are some of their answers:

One of the reasons that I thought it didn't go well was that I was not getting very detailed responses or their responses were very surface level. Most of their responses were also very similar. After debriefing the activity with a colleague, I realize that perhaps their responses showed their understanding of derivatives at that moment was only surface level. It made me reflect upon my practice - had I only focused on the algorithm and not so much on the meaning of a derivative? Was what they were producing a reflection of what I had shown them in class? If I repeated this activity as exam review at the end of the course, would I get more detailed responses?

I then questioned if this was the right type of question to ask and where might I use it to get more detailed responses. As we start the curve sketching unit in calculus, this activity may be more appropriate if when shown the equation or graph of a functions, they were asked "Determine 2 truths and 1 lie about the graph of a given function." Students would have more aspects to reflect upon and be able to create more detailed truths and lies. Would I get better responses if students were shown the equation? the graph? or both?

I also pondered using this activity as part of a conversation with students. What if I created a list of truths and lies and asked each student to identify, from the list, 2 truths and 1 lie about a function or graph and describe why they know it is a truth or a lie.

Though I was not completely satisfied with the results of the first attempt at this activity, I definitely plan on using "2 Truths and 1 Lie" again in the upcoming weeks in Calculus. The students were engaged and each student did have an opportunity to participate and demonstrate their current level of understanding.

My favourite

What is one thing that I couldn't live without in my classroom or that greatly improves student learning in my classroom? Though there are many things that I think I could choose, the one that comes to mind is Vertical Non-Permanent Surfaces (VNPS).

I discovered VNPS through Twitter near the end of the last school year.  After hearing about them from a colleague again at the beginning of this school year, I decided to try them in my Advanced Functions course and quickly discovered their usefulness and power they have on learning. I'll admit that I am a fan of reading about something (usually on Twitter) in the morning and attempting it in my classroom later that day. Some of these attempts are successful, some require some thought and reconsideration before attempting again. Using VNPS was one of these events that was extremely successful.

I usually use VNPS during a lesson that is very skill based. I have used them with polynomial long division, factoring polynomials, and basic derivatives. What normally happens is that I introduce the concept, work through some examples with the student and then have them show me their understanding using the VNPS (or I have also used them during review periods).

I begin by randomly organizing my students into small groups (usually 2 - 3) and have them move to a VNPS. I ask that each group have one white board marker for the group. The first person takes the marker and answers the question posed to the class. The group works together to solve the problem but the person with the marker is considered the lead for that question. Once each group has answered the question, the white board marker is passed to another student and another question is revealed. This continues until each member of the group has had a chance to write a solution on the board. I usually have as many questions prepared as there are members of the group.

Why do I like VNPS?
- They offer another opportunity for me to formatively see their work as well as their form in questions in a less formal setting.
- They encourages conversations between students in small groups on the concepts that we are learning.
- They allow each student to demonstrate their knowledge to the group and get peer feedback on their knowledge.
- They allow me to showcase student work within the class.

Positive thoughts and positive results.

Teaching can be pretty chaotic and stressful. Even if I have taught a course before, I'm always looking to improve a lesson and adapt it to the students in my class. There is always something that needs to be done (planning a lesson; creating an assessment; developing an activity; meeting with colleagues to plan an activity, assessment, lesson; giving extra-help; coaching; etc.) And each day is different - you never know what might come across my desk on a given day. This busy work day can be draining and very tiring but being able to stay positive can make even the busiest day a good one.

Keeping a positive mind frame can be challenging on some days but by focusing on the small things can make a huge difference. Here is a list of some of my small good moments that can occur any day:

1. Getting out for a morning walk.
2. Getting a parking spot in the closest lot.
3. Finishing my coffee while it's still hot.
4. Having a student ask a really good question during the lesson - especially one that makes me have to really think about the answer.
5. Finding a new gem of a lesson or an activity to try out in my classroom (usually from someone I follow on Twitter). My latest one is probably "Polygraphs" from Desmos.
6. Having my team already have set up the volleyball nets before I arrive at practice.
7. Laughing at least once (usually at myself for something that I said or did).
8. Hearing a student say "Wow, math was fun today!"
9. Getting out for a walk after dinner for some fresh air and thinking time.
10. Getting to bed before 11 pm!

Always looking for the positive ++++++++