NOTICE Lab - Video Club 2: Rat-a-tat Cat

Video Club 2: Rat-a-tat Cat

In this video, a group of three children play the card game Rat-a-tat Cat. One of the children explains the game to the other two. As she explains and the children start to play, they exhibit seeds of algebraic thinking.

Video Club Overview

Video Club Goals:

- Teachers will attend to and reason about the children’s seeds of algebraic thinking.
- Teachers will conjecture about why children might exhibit particular seeds (i.e., what life experiences could children have that supported the development of that seed?)
- Teachers will conjecture about how the seeds children exhibit could be connected to formal algebraic thinking and concepts.

Materials:

- Several copies of the Rat-a-tat Cat card game (for teachers to play in groups of 3-4)
- Video loaded on Anotemos and shared with all participants
- If watching in person, each participant should have a device on which they can view the video and headphones.

Get Ready (20 mins, could be done on a different day than the video club):

Split the teachers into groups, explain the Rat-a-Tat Cat rules and give teachers some time to play Rat-a-Tat Cat. As the teachers play, have them think about how the goal of the game, the game rules, and their strategies to achieve the goal could activate seeds of algebraic thinking.

Once teachers have played the game, have a discussion about the seeds that came up for teachers as they played the game.

Exploring the Math

Several seeds of algebraic thinking could be activated by the game:

Balance-When dealing cards, the dealer should deal one at a time until everyone has four cards. This reinforces the idea of balance, which is key in solving equations. It also relates to the distributive property. The dealer should perform the action of dealing an equal number of times to all the players. This concept is similar to, for example, ensuring that a constant or variable that is outside of a binomial is multiplied by both terms (e.g., 2(x+2)=2x+4).

In betweenness- The goal of the game is to minimize your score. In order to do so, there is a certain group/interval of cards (cards with cats) that players want because they have smaller point values. In other words, players will likely keep cards that are in between zero and four. There is another group/interval of cards (the rats) that players want to avoid because they have high point values. In other words, players will likely get rid of cards that are in between five and nine. The ideas of inequality and optimization are also relevant as players aim to get scores that are less than their opponents.

Replacement- Each player in the game has four “spots” where they can place a card. Some of these cards are replaceable, the player can replace them with cards from the deck or the discard pile. In this way, the cards act like a variable that can take on different values depending on what a player draws during the game.

Noticing structure- Some of the cards in the game can be swapped out and some of them cannot. You want to put your lowest cards where other people can’t get to them.

Note: This is not an exhaustive list of seeds! Encourage teachers to identify other potential seeds of algebra, even if they have not been cataloged.

Viewing and Discussing the Video

Have participants watch the approx. 6 minute video clip individually on the Anotemos platform. Participants should be encouraged to draw and comment on the video when they see interesting moments of student thinking, particularly those when seeds of algebra seem to be activated.

Discussion: In discussing the video, focus on the seeds of algebra that get activated as the children play the game. Talk about how those seeds might be connected to more formal algebraic thinking and concepts.

Description of Goal:

Teachers will attend to and reason about the children’s seeds of algebraic thinking.
Teachers will conjecture about why children might exhibit particular seeds (i.e., what life experiences could children have that supported the development of that seed?)
Teachers will conjecture about how the seeds children exhibit could be connected to formal algebraic thinking and concepts.

Table - Video Key Moments

VC2 table

Potential Discussion Questions:

The children spend a good amount of time talking about swapping cards. What might be algebraic about card swapping?
What sorts of strategies do the children talk about to win the game? How might these be algebraic?
What is significant about rats and cats? How might this idea help students with more formal algebraic thinking?

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