Mathematically-Themed Icebreakers 1: Review Dominoes

Many times, we use the same old icebreakers at the beginning of a class: go around the room, introduce yourself, your major, a hobby or something interesting about yourself. What if instead, we could get our students working together and engaging in mathematical problem-solving from the get-go? Today’s post is the first in a four-part series where we'll present several ideas and strategies to accomplish this, most of which are appropriate for any level of mathematics course.

Review Dominos

We have found that this activity works great in many situations-- Our favorites uses:

• An icebreaker on the first day of class, while also reviewing material from a previous class.

• Low stakes group work to practice basic computation relating to newly learned material on an average class day

• A group warm-up, reviewing material from a previous day that is crucial to know before beginning class.

• A small-group project before an exam review.

This activity requires a small amount of preparation up front, but at the end of this post we provide a Latex template that you may use to create your dominoes.  The main idea: You will create dominoes where pairs are made by equating two mathematical expressions.  You can design it so that when the dominoes are all matched up they create a line, circle, or some other fun shape.  This is best explained by example, so we’ve created a small version of a game, and its solution, shown below. The cards are on the left, and the 'solution' is on the right.

This game can be used at all levels!  At the calculus level, you can create antiderivative dominoes with an indefinite integral on one side, antiderivative on the other.  At the elementary level, you use dominoes to practice fractions and decimals, or fractions and their reduced form.  In algebra, you can create factoring dominoes, with an expanded equation on one side and a factored equation on the other, or dominoes for exponentials and logarithms.  The possibilities are endless! Here are a few examples:

To create the dominoes:

1. First, decide on a desired 'shape' for dominoes to make when they're matched up together correctly, and sketch it on a piece of paper.  We have successfully experimented with forming a full loop, several small loops, or a combination of loops and trains.  (See the "Fraction Dominoes" example above for an example of a 'train'!)
2. Next, count the number of dominoes, and come up the appropriate number of equivalent statements or equations. 
3. Finally, use the latex file provided, or your own template, to create the dominoes.  If your shape is something other than a line, you may want to write the equations on your sketch before creating the dominoes to ensure that everything will work out correctly.

Benefit of using dominoes:

• It is easy to track each group’s progress by looking at the number of dominoes that they have matched up.

• Since you created the dominoes in such a way that a specific shape should be formed, it is very easy to tell if students have achieved (or are working towards) the correct solution!  If they do not have the desired shape, then you can let them know that they need to go back and check their work, without having to read through all of their solutions. 

• Students can work in many different ways.  The following are the most common strategies:

• The group may split their set of dominoes into subsets, and try to match their own with those of another student.

• They may lay all of the dominoes on the table in front of them, and simultaneously work to find pairs.

• One person may deal out cards, one by one, while all students in the group look for pairs with the most recently dealt card.

• In many cases, students can work “in both directions” to find pairs.  For example, if you have dominoes where functions are matched with their inverses, you may work with either domino in a pair to find an inverse and find a match.  When this is possible, the first strategy listed above is great for keeping all group members engaged, doing computations, and working together.

That’s it for this week’s icebreaker!  Check back in two weeks for another!