Do you roll your eyes at traditional icebreakers? Do you worry about developing a community in your digital class? Then let's talk about ONLINE ICEBREAKERS! On Monday, August 24th, we invite you to submit, participate, and vote for your favourite icebreaker. A public repository of icebreakers will be hosted on www.firstyearmath.ca and the University of Toronto Mississauga website.

Email your activity to Tyler Holden (tyler.holden@utoronto.ca) by Friday, August 14th, and you will be entered to win one of three $20 Starbucks gift cards. The community will vote on their favourite icebreaker starting on Saturday, August 15th, and our meet up on Monday, August 24th will consist of participants engaging in the top N activities. A final vote will be held at the end of the meet up, with the top icebreaker receiving a$50 Amazon.ca gift card. Sweet deal, eh?

We hope you will share your brilliant ideas with the community!

The session has now completed. Thank you for all of our contributors and participators.

Top Three Candidates:

1. Winner! Alfonso Gracia-Saz.
3. Timothy Yusun
Our draw winners were Asia Matthews, Timothy Yusun, and Xinli Wang.

1. From Burcu Karabina:

During the first week, we will host a Meet Your Instructor and Learning Assistants event.

We will use the virtual classroom Bongo for this event. During this event, I will share a world-map on the screen and ask students about their location (if they feel comfortable with sharing this information.) In the chat, they will also tell us what they like the most about the city they live in. I will tell students that this information will be useful because we hope to identify students from different time zones and arrange the groups and meeting times accordingly. The class size ~40, so I think we can each take turns quickly to mark our locations on the map.

2. From Andrea Hyde

Where in the world: To start, everyone needs to use the gallery view (in Zoom). In the game I would start by saying “ Where in the world is” and then naming a person in the conference. Everyone in the room would point to where that person is in relation to themselves (up, down, left, right, diagonal). This can be really funny if there’s a lot of variety in where people are on the screen. The person being named may need to say hello and wave so everyone can find them in a new group or software that doesn’t show names. That person then continues by saying “Where in the world is...” and naming another person. The game goes on until everyone has been named and pointed to.

Variant:You could even extend the game by asking people to state a fact about themselves in a traditional ice breaker fashion. “I’m Andrea and I love dogs. Where in the world is...”

3. From Tyler Holden (Not eligible for prizes)

Introduce students to the game of Nim. Explain the rules but don't tell them the name of the game, and create breakout rooms of size 2. Let the students play for a bit, without worrying about the mathematics of the game. After 5-10 minutes, invite two students to play the game for the whole class. (You can share your screen and keep score, or use the chat). If you can see that a student has the winning strategy, stop after this game and explain. If not, let the champion defend their title, and continue to invite students to challenge. Students of all calibre enjoy this game, and can determine the winning strategy after playing long enough. Depending on the skill level of the students, you can explain the mathematics (induction on the two pile game, bitwise XOR in the 3+ pile game), or just do this as a fun activity.

Game Rules: You have two jars filled with exactly 20 pennies each. Each player takes a turn. On their turn, a player chooses a single jar, and withdraws as many pennies as they like (they must remove at least one). The player who finishes their move with both jars empty wins.

Variants: Change the number of piles. Allow the piles to have an unequal number of pennies. Change the rules, for example: You must remove either {1,3,4} pennies, but no other numbers are legal.

4. From Carmen Bruni

Give four pieces of information and students need to figure out what the mathematical object is. Every students needs to participate because the target cannot be computed without all four pieces of information.

Examples:

1. I’m a cubic polynomial My roots are 2 and 3 (and one of which is repeated!) The leading coefficient is 2. When evaluated at 0, we get the value -24.
2. I’m a prime number The remainder when I divide by 7 is 1 I’m a positive integer less than 100. The sum of my digits is 11.
3. I’m an angle in radians. I’m larger than 2\pi. I’m less than 9. The cosine of my value is -\sqrt{2}/2.
4. I am a side length. I am part of a triangle. Two side lengths are equal to 10. The contained angle is \pi/4.

You will need:

1. The ability to break students into groups. Each group should have the same number of people (in my examples below 4 is the number).
2. The ability to send private information. In this example, if we use the same question; we can send four emails (for example) each with one line corresponding to the group hint
3. The ability to control who is in what group. This might be harder depending on what software you’re using but another way to do this is to take your class list and then share some private link with the four group members.
You can choose how much to customize this - do you want every group to get their own problems?  Do you want them to discuss multiple problems?

5. From Alfonso Gracia-Saz in collaboration with Nicholas Remedios, based on an idea by Chris Tuffley.

I will give you a puzzle (in the style of puzzle hunts) and send you to breakout rooms to collaborate.  The puzzle must look interesting, the kind of puzzle that once you see it, you can't help but start solving it.  It is the type of puzzle that a single person may have trouble fully completing quickly, but any team of a few people will get through without trouble.  It should consist of a large number of small aha-moments, so that everyone can contribute.  You should not feel like you are participating in an ice breaker; rather, you are collaborating with strangers in a fun activity that you want to do.

What is the puzzle, you ask?  I can't show it to you now, as that would spoil the activity.  You will have to wait till August 24.

6. From Xinli Wang, originally University of Wisconsin

PDF document including several icebreakers.

7. From Andie Burazin

For this, we'll be using the polling interface in Zoom (or whatever platform we're using). Students start with 5 points, and are presented with three options:

• Option A -- Everyone receives +1 point.
• Option B -- Those who voted for B get +2 points, anyone who voted for A loses 1 point
• Option C -- Nobody gains or loses points this round. You also cannot lose points if B is chosen.
The option with a plurality of votes is the option that is taken. Students must keep track of their own points and be honest. This games scales well to any number of players.

To facilitate interaction, there are several options:

• Use breakout rooms to create groups, with each group casting a single vote. Let each group discuss their voting strategy.
• Open up the chat/mics and let the students discuss their strategies in the main room (microphones are class size dependent).

8. From TJ Yusun, Originally from Borscht with Anna

Activity: Correlation or causation?

Give a pair of axes labeled with two qualities and ask the class to locate themselves on the graph. You will end up with a scatterplot for the class that you can use for further discussions. Rinse and repeat. The sillier the better! (Think https://www.tylervigen.com/spurious-correlations but less morbid) (example image here)

Note you can also use categorical variables!

• Height vs. birth month
• (Average) Hours of sleep vs. hours gaming/watching TV/Netflix
• (do you say soda or pop or soft drink?) vs. (pineapples on pizza: yes or no?)
• Cups of coffee I drink in a day vs. number of courses I’m taking
• Etc. be creative!
• Then ask them to sound off in the chat & debate. The larger the class the better this works.

Notes:

• Ideally you would prepare the plots ahead of time on some slides so you can also indicate scales/label ticks. If not, you can use the whiteboard in Zoom and create the axes there (line tool / insert text).
• The arrows in Zoom (in the annotation bar) have names, but if the class is large you may ask students to use the “star” marker in Zoom instead which is smaller and unlabeled. Also, students may not be comfortable using their names on the first meeting. (And if they do use their names be cautious about putting them on the spot!)
• Source: https://borschtwithanna.blogspot.com/2020/08/remote-teaching-community-edition.html (this blog post has many other ideas)
9. From Math with bad drawings

A series of one-on-one math games for students to play. Some don't translate well to a remote environment though.

10. From Petra Menz . A big list of generic ice breakers.
11. From Asia Matthews, originally from MAA connect.

Zoom Paths
Everyone points in a direction.  Observe and draw the path that you see (everyone's screen is different!).
Question: Are there cycles?  What do the paths look like?  Are any paths the same on different screens?
Variation: consider the Zoom screen as a torus!
Accessibility: Max number in gallery view on a tablet is 9 and on a phone is 4