Cartesian Connections for Grade 6 – Elementary Ed. Resource Sharing

Mathematical Learning Object: Cartesian Connections

Sydney Bolton & Hannah Sharples

Explanation of Game

Our Math Learning Object is a game based on the game Connect4 and the Cartesian plane. In Connect4, the object of the game is to connect 4 tokens in a line before the other player by dropping them into the grid. In this game, the goal is to create a straight line, consisting of at least 4 data points on a Cartesian plane before your partner. Students will take turns rolling 2 dice. They must then record and plot the two numbers shown on the dice onto the game board (a blank Cartesian plane). Students can plot the numbers in any order — (dice1, dice2) format or (dice2, dice1) — but once the point has been plotted on the game board, it cannot be changed. This allows students to think critically about their choices and strategize their data points to make a straight line. Students also have the option (depending on grade level) to make either or both of the numbers negative in order to achieve a straight line, however, they must decide before plotting the point. As previously mentioned, in order for a student to complete their line and win the game, the line must have at least 4 data points. They must plot every dice roll on the game board, even if it is not included in their final line, in order to increase the amount of practice the students have with plotting data points.

This game is best for grades 6 and up. The younger grades (6 and 7) will likely play the first version of the game, with only the positive quadrant of the Cartesian plane. As the students become more comfortable with the Cartesian plane, it can be expanded to include all four quadrants.

Curricular Objectives

There are a number of curricular components that are addressed in this activity. Pulling from the grade 6 curriculum specifically:

Big Idea: Linear relations can be identified and represented using expressions with variables and line graphs and can be used to form generalizations.
Curricular Competency: Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Curricular Content: line graphs, including: plotting points on a Cartesian plane using whole-number ordered pairs, transformations (translations, rotations, and reflection) on a single 2D shape, drawing, and describing image.

This activity also fits nicely into the curriculum for older grades as well, when they start to learn about equations of a line. Students will continue to learn and become familiar with the Cartesian plane and this activity can be adapted as they become more competent.

Adaptations

There are several adaptations that can be made to Cartesian Coordinates to ensure the game is appropriate for the learners playing. To expand the possible domain and range of coordinates on the graph, dice with more than 6 sides can be used. If students wish to play the game at home but do not have access to various sided dice, Google has a virtual dice roller tool that can be used if access to the internet is possible (https://www.google.com/search?q=dice+roller). The desired shape the coordinates form may be flexible. For example, instead of a straight line with four connecting points, students may be asked to create a specific shape with their coordinates (such as a triangle, rectangle, hexagon, etc.) in order to win the game. To make this task more achievable, students are to be encouraged to use transformations (such as rotations, translations, and reflections of their current coordinates) to move them and create a specific shape. This would create an added element of challenge and critical thought for students who had mastered concepts associated with cartesian planes at a more basic levels. When making transformations, students would be required to write out the equation and explain their thinking. To decrease the challenge of the game, a cartesian plane with only the positive quadrant rather than all 4 may be used, and different coloured dice may be used to determine the X-coordinate and the Y-coordinates. Lastly, to increase student collaboration, communication, and problem-solving in the game, students may also be asked to create a more complex shape and work together to transform the coordinates. Students could also be encouraged to think up ways to adjust the game and explain their rationale to the teacher and their peers.

Assessment

Cartesian Coordinates is a game designed to be used as a formative assessment tool. This can be achieved by the teacher or peers cross-checking the completed game sheet and ensuring the points on the line are correctly plotted. This encourages students to think critically about their own work as well as their peers. The teacher could also check in with different partners and observe them problem solving and communicating together as they play, specifically looking out for how students are communicating when they disagree with a coordinate placement or when they are explaining a transformation, or when they are working together to create a shape. Teachers may also choose to play the game with students to gain an understanding of the student’s grasp on the material and how they can communicate their thinking. When observing or playing the game with a student, it would give the opportunity for teachers to ask prompting questions about why students have chosen to place a coordinate where they did.

Cartesian Connections:

Record each roll of the dice as you plotted it on the game sheet.

X= __4____ Y= __3____

X= _______ Y= _______

Cartesian Connections:

Record each set of coordinates as you plotted it on the Cartesian plane.

___(-3, 2)______

______________

_____________

Leave a Reply Cancel reply