It is all in the set up: The Waiting Game

It needs to feel authentic

They need to get captured in the intensity of the moment. They need to feel that they are a part of the development of the situation. As much as possible, I need them to ask the questions, not the other way around.

The Waiting Game by Mathalicious

I choose this lesson on Valentine’s day as a preview to our probability unit. The premise of the lesson is to determine how many people a person should seriously date before committing to a partner for the rest of their lives.

The lesson plan as written begins with a very involved handout that lists all of the possible orderings of dating 4 different people: 1234, 1243, 1342, etc… Students are supposed to consider how frequently the end up with their number 1 partner if they choose to commit to their first love compared to if the break up with the first, but then commit to their second person that is a better match than the first, or the third, or wait for mate number 4.

I checked the reflect tab of the Mathalicious lesson to see if there was any thoughts from other teachers:

I thought:

How I adapted the lesson

I did not use the complicated student handout. They need to own this.

I opened the lesson by talking about love. I asked students if they thought they should marry the first person they fell in love with. I showed them some published advice column letters. They debated the advice they would give in each scenario. We talked about the episode of Friends where Rachel and Ross are on a break.

Students had intense opinions.

Quiet students who rarely speak up in math class gave thoughtful reflections.

We invested a good 20 minutes on the buy-in. It got to the point that students were asking; “Is this what we are doing today?” “How is this math?”

Then I asked: “Let’s assume there are 4 people you may fall in love with. If you marry the first person you date, what are the chances that this person is your best match, #1?”

Students replied: 25%

I directed students in small groups to the nearest dry erase board.

What are all of the possible orders that you could date the 4 people? Can you list them?

It started off a complete mess, but eventually groups learned that they needed to organize their thinking.

I followed the rest of this lesson as described in the teacher guide, but using dry erase board and discussion in lieu of a worksheet.

Students calculated the likelihood of committing to their best match if they committed to the first person that was better than their first match. There was some debate and confusion, but eventually students convinced each other that in this case there was a 7/24 chance that you would end up with your best match.

They concluded that the highest probability of ending up with their best match (#1) was if they did not commit to their first love. It was a great Valentines day!

We acknowledged the weaknesses of the initial assumptions and students wrote a reflection on how these assumptions impact our results and weather or not they agree with our conclusions.

 

The great Kahoot workaround

I love getting to learn new teaching strategies through having Eric as an apprentice teacher this semester!

My first period geometry class is very, very quiet. Too quiet. It is a challenge to get any energy and discussion going in that class.

Yesterday, Eric mentioned that he was thinking about trying Kahoot with the class since it can be engaging for students and can increase the energy in the room.  I told him that while I like the program, I dislike that it rewards and encourages speed. I know students are more successful if they take time to think first and don’t just rush to get the best answer.

Here is Eric‘s solution:

1. After logging in to Kahoot, but before the question is presented, tell students to turn their laptops around or put their phones on the table facing down.
2. The question is projected using Kahoot. Students can discuss, but they cannot touch their device while the timer is counting down.
3. Once all students have had enough time to discuss the problem, but before the timer is up, the teacher says GO!
4. Then it is a race to click their solution quickly.
5. Turn devices back around and repeat.

*A modification of this approach using relay races: Have each team place their device along the perimeter of the room, or other side of some line, then have the students stand on the opposite side of the room in their teams. Project the question and once students have had enough time to discuss the solution, yell GO, and a member of each team can race to their device to enter the answer.

So simple and so effective! I am thrilled to be able to use Kahoot again with my students while de-emphsizing speed and increasing student thinking!

School picture day

HEY! YOU – IN THE HOODIE! MOVE TO THE FRONT! YOU’RE SHORT.”

“YOU – GLASSES – MOVE CLOSER TO THE PLAID SHIRT GUY.”

“EVERYONE MOVE IN! IF YOU ARE TO THE RIGHT OF PLAID SHIRT YOU WON’T BE IN THE PICTURE.”

“TAKE YOUR HATS OFF! STOP MESSING AROUND. BE QUIET!”

“TAKE YOUR HOOD OFF! WHAT ARE YOU DOING?!”

I cringe

These are human beings. Stop talking to them like that!

Do I say something to him? Do I leave the room because it is making me so uncomfortable and let it continue?

He is just trying to make our school photo as good as possible. He wants to do the best job he can. He probably works hard.

Do I ever do this?

I might.

We can get so focused on doing our job that we forget that we are working with independent, beautiful, thoughtful, individuals – each with their own stressors and needs and dreams.

This disregard for our humanity happens at every level. We have all been subjected to this and we all have done this to people we care about.

It hurts all of us.

“What you feed us as seeds, grows, and blows up in your face” – Tupac Shakur

Threatening them with a good time

I am terrible at moderation. Terrible.

I’m not sure I even want to be good at moderating.

When I find something I like, I indulge until there is no more.

An example: I tried to make a little geometric art with a compass and straightedge. The next day I was investing too much money and all of my time in compasses, pencils, fancy markers, watercolor paints, brushes…etc. I barely slept for weeks obsessed with making increasingly complex designs.

I teach at a public alternative school. A school where many of my students have struggled with some type of addiction and/or anxiety. My students also struggle with moderation. Impulse control is a challenge for teens because it is a part of a developing teen brain. How can I use this to my advantage?

Why do I need to give them headaches and aspirin in order to generate student buy-in to learning mathematics?

Why not instead make learning math so satisfying that we all want more? Like my experience with Islamic geometric design? Let’s find ways to give learners and their teachers so much satisfaction in making connections and understanding that we all want more.

I propose that we shift our thinking away from, “If Math Is The Aspirin, Then How Do You Create The Headache?” and move towards, “If making connections and discovering is exciting that how do you maximize these opportunities for learners to get them hooked?”

I know it is possible. I have experienced it with my students.

I want to shift perspectives on teaching and learning from headaches and aspirin to connections, discoveries, beauty and excitement.

I need to remember to always invest the time and effort in finding the beauty in a concept for myself and then develop my lessons from this perspective.

Requiring all math to have simple, commercial applications is like requiring all reading and writing to be nonfiction or marketing. Sometimes we want and need fiction and poetry. Sometimes math is just pretty (until you’re ready to do physics with it).

— Jenn Broekman (@jsb16) January 30, 2018

Geometry Right Triangles unit project: Barbie Zipline Day 3

This is the conclusion of a three day lesson applying right triangles. Here is day 1 and day 2.  Eric is my apprentice teacher and he initiated this discussion:

Eric: Yesterday we prepared to go outside, what information did we collect?

student: How much rope we need and what angle.

Eric: Where is the angle? Here or here? What else did we find?

student: The height of the flagpole.

student: The distance away from the flagpole

Eric: One person from each group come up to the board and write your angle and distance from the flagpole on the board.

Eric: Let’s make a plan before we go outside.

We then discussed and agreed that we should actually measure the height of the flagpole  when we put barbie on the pole. We also decided to find the exact ground distance to create a 30 degree angle, but that it looks like it should be approximately 45 feet from the base of the flagpole. Students also agreed that they would like to confirm their thinking that this angle will result in a safe speed for Barbie to zipline down from the top of the flagpole.

 

The Wrap Up

Eric made a sheet for students to reflect on the lesson.

Geometry Right Triangles unit project: Barbie Zipline Day 2

Students sat with their partners from Barbie zipline day 1 and we begin by reviewing the scenario and their calculated flagpole height.

Next we discussed how this zipline will work. I used a string and a binder clip to make a model zipline, using a very steep slope for the zipline and I asked students to predict what would happen if Barbie came down a zipline like this.  They agreed that she would fall too fast and get hurt. Next, I held the string almost horizontal and asked how this zipline would work – and students agreed that she would get stuck or mover too slowly.

I explained that the goal for this day is to use a model in class to determine a plan for Barbie to zipline down safely from the top of the flagpole. By the end of class, students had to know what angle of elevation they planned to use and how far from the base of the flagpole they needed to place the end of the zipline.

This day felt a little chaotic, but students did end up finding errors in their measurements by verifying their calculations in a variety of ways. The worksheet below incorporated a range of geometry topics including:

• Pythagorean Theorem
• right triangle trigonometry to calculate lengths
• inverse trigonometric functions to determine angles
• similar triangles

Tomorrow, we test our calculations outside on the the flagpole.

Barbie is harnessed and ready!

 

Geometry Right Triangles unit project: Barbie Zipline Day 1

I have seen posts about Barbie zipline on occasion over the past few years. I’ve avoided the lesson because it seemed like a lot of advance prep work and typically I don’t allow enough time plan this far ahead and work through constructing a zip line trial run to make sure it all works in advance. To keep it completely real, I also hadn’t seen any description or resources that I thought would fit my classes well. But I found myself approaching the end of a right triangle unit in geometry with 2 full block periods mapped on my unit plan labeled “Right triangle synthesis project – need to create.”

This is my first semester with a full time apprentice teacher, Eric, so I have help and some new motivation to make this a fun project for everyone this time too. This time of the school year, with short days, cold temperatures and no end in sight, it seems a lot of students appear pretty bored with school and many of the staff here are also struggling. I really just needed to lighten things up for the students and myself. The next logical thought: Queue Barbie and high quality pulleys.

Day 1 (80 minutes): How tall is the flagpole?

The set up

Randomly assign teams (I used pairs)

Introduce the activity with this fantastic video from Jed Butler:

We leaned heavily on Jed’s blog post and started with the activity guides included in his post, modifying them a little to incorporate his thoughts on how the lesson could be improved and our learning goals.

1. I like having students select a team name because it forces them to talk to each other before they being working with content. It increases collaboration and breaks down barriers with a safe opening topic for conversation.
2. Given the image below, use Mr. R to estimate the height of the flagpole. This led to students getting rulers and measuring on the image and a rich discussion on whether 4 inches is the same as 0.4 feet. 
   

   

3.   Discussion

1. • Eric: What are some ways we could find the height of the flagpole?
     • student: climb up the flagpole?
     • student: find the angle?
   • Eric: What angle?
     • student: The angle of elevation?
   • Eric: Where does the angle of elevation go (sketches diagram)?
     • student: Do we know how tall Ken is?
     • student: Are we Ken in this situation?
   • Eric: What can we measure?
     • student: You could measure the distance from the flagpole to the person.
     • student: We could use that angle tool thing that Mrs. B carries around.
     • student: oooohhhhhh. yeah.
   • Eric: How could we use that? What else would we need to measure? Would we all have the same measurements?
     • student: The adjacent!
     • student: The hypotenuse!
     • student: oh! So we could use tangent.
   • Eric: I want you to measure two different times, switching roles. Why do you think we should do it twice?
     • student: To see if we get the same answer?
   • Eric: Will we all get the same answer?
     • Student:  No.
   • Eric Why not?
     • student: Because it is not exact, but they should be really close.
   • Eric: Work with your group and make a plan before we go outside.

4.  Measure & Calculate

Outside measurements, then back in for calculations, using this sheet from Jed Butler’s description as a guide.

Favorite question while measuring angles outside:

• student: Is it possible to get the same angle of elevation if may partner and I are different heights?
• Eric: What do you think?

 

5. Enter both of your calculated flagpole heights into the google form (accessed using a bit.ly address from their cell phones).

6.  Justify flagpole height

Project the spreadsheet from the google form as students enter their flagpole heights.

• Eric: We don’t know the actual height of the flagpole. Here are all of your calculated heights. We need to determine what number to use as the height of the flagpole. What are some was to analyze data?
• students: average, mean, median, outliers, graphs, range…..
• Eric:  Determine what height you believe the flagpole is and use one or more of these measures to justify your conclusion.

 

 

Day 2: Design a model and calculate angle of elevation, zipline length, and ground distance.