The Missing Piece

10/23/2019

One of my favorite stories about the nature of science is the sequence of events that made Mendeleev the "Father of the Periodic Table". Others before him had made lists of the known elements, and many even organized them into groups of similar properties. Mendeleev's stroke of genius came from his ability to recognize that his periodic table wasn't complete. He arranged his table of elements with gaps and use the patterns around them to predict the properties of these unknown elements

This TedEd video provides a really great summary of Mendeleev's pattern finding and predictive powers

The Challenge

If I gave you a standard deck of cards that was one card short, it would be pretty straight-forward for you to piece together what is on that missing card. Even if you had never seen a deck of cards before, there are some predictable patterns like suit, number, and symbol layout that would provide plenty of information to come to a conclusion.

In this task, students receive a set of cards with designs that are unfamiliar to them only to learn that one of them has been removed from the deck ahead of time. Students must work in groups to study the patterns on the cards that they have in order to determine what is on the missing card.

The Cards

These sets of cards are modeled off of an activity by American Educational Products. There are four key features on each card: top number, bottom number, number and shape of middle design, and number of side triangles.

I put together a couple of files so that I could print out sets of these cards in color or in black and white. There are 6 cards on each page so a full set of 24 cards requires 4 printed pages. Some examples of the cards are shown below

Before passing out the sets of cards I remove one from each set. I've found that this activity works best when I remove the same card from each deck. This way, groups can't just compare decks to locate the differences and it also makes it MUCH easier to check their answers at the end if you only have to remember one answer. I try to take out a card somewhere in the middle of the set. The card with a top number of 19 has been a good one that requires groups to focus on all of the design features.

The Process

I intentionally don't start the class off with any instructions besides "figure out what is on the missing card". From there I walk around and encourage their progress. I typically allow them 3 chances to check if they are correct but I don't give them any specific feedback about what they have right or wrong about their guess. I only tell them if they are correct or not ;)

As it getting closer to the end of class, it is often important to provide small hints to help students make progress towards a successful outcome. Some hints that help are:

"Try making groups and see if anything is missing..."
"How could your organize this into a table with patterns across rows and columns?"
"How does this number relate to the rows/columns before or after it?"

The Follow Up

Groups will naturally complete this task at different times. For groups that finish early, I provide them with the following wrap up:

On a piece of paper, record every pattern that exists in your organizational structure

Once all groups have successfully described the missing card, we come back together as a class and discuss the approach that the different groups took when going about this task. If we have time, I show the Mendeleev video posted above and we connect this back to the nature of science and the role that pattern finding has in advancing our understanding of the world around us.

Files

These files contain a version in color and a version optimized for black and white. The only difference is that one will have a rainbow spectrum while the other is gray scale so it can be printed out using a black and white copier. Personally, I have never used the color version since the black and white works just as well but doesn't cost as much to print :)