Cartesian Coordinates Suggested Games and Activities MathShop: Cartesian Coordinate Mat
Gr. 1 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Describe the relative locations of objects using positional language Specific Expectations Location and Movement Describe the relative locations of objects or people using positional language (e.g., over, under, above, below, in front of, behind, inside, outside, beside, between, along) Gr. 2 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Describe and represent the relative locations of objects, and represent objects on a map Specific Expectations Location and Movement Describe the relative locations (e.g., beside, two steps to two steps to the right of) and movements of objects on a map (e.g., The path shows that he walked around the desk, down the aisle, and over to the window. ) Gr. 3 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Identify and describe the locations and movements of shapes and objects Specific Expectations Location and Movement Describe movement from one location to another using a grid map (e.g., to get from the swings to the sandbox, move three squares to the right and two squares down Gr. 4 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Identify and describe the location of an object, using a grid map, and reflect two-dimensional shapes Specific Expectations Location and Movement Identify and describe the general location of an object using a grid system (e.g., The library is located at A3 on the map. )
Gr. 5 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes Specific Expectations Location and Movement Locate an object using the cardinal directions (i.e., north, south, east, west) and a coordinate system (e.g., If I walk 5 steps north and 3 steps east, I will arrive at the apple tree. ) Compare grid systems commonly used on maps (i.e., the use of numbers and letters to identify an area; the use of a coordinate system based on the cardinal directions to describe a specific location Gr. 6 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Describe location the first quadrant of a coordinate system, and rotate two-dimensional shapes Specific Expectations Location and Movement Explain how a coordinate system represents location, and plot points in the first quadrant of a Cartesian coordinate plane Create and analyse designs made by reflecting, translating, and/or rotating a shape, or shapes, by 90º or 180º (Sample problem: Identify rotations of 90 or 180 that map congruent shapes, in a given design, onto each other.).
Gr. 6 Suggested Activities These activities can be adapted for students in younger grades as appropriate. I Have... Who Has? Materials needed: Post it notes with letters (one for each letter of the alphabet). Activity cards with statements I have T, Who has (3,6) Note: H is on the coordinates (3,6) I have H, Who has (9,0) Note: E is on the coordinates (9,0) I have E, Who has (6,2) etc. An answer key should be created with the activity cards so that the teacher can follow along to ensure that the cards are being found correctly The letters should be placed on the grid to match the statements on the activity cards. Goal: to practise finding coordinates on a grid Procedure: Each student is given a card. You may hand two cards to some students so that all cards are used. One student begins by reading out their card. After the card is read, the student with the answer to the question reads their card aloud. Continue until all students have had a turn and the statements return to the first student. Optional : the letters on the grid can create words, quotes, or messages. Extension: Cards can be created beginning with the coordinates. For example: I have (4,0) Who has T? Note: T is on the coordinates (8,5). I have (8,5) Who has F? Note: F is on the coordinates (5,5). I have (5,5) Who has R? Continue Create one card for each student and a teacher answer key. Before playing, letters are placed on the grid to match the activity cards.
Battleship Materials needed: Checkers or game markers in two colours 4 squares to identify the battleship White board and marker to identify the ship s coordinates Goal: to sink the teacher/student s battleship using coordinates. Note: Begin in the first quadrant (top right) Procedure One person writes down the location of a battleship using 4 points that are connected horizontally, vertically or diagonally. Divide students into two teams. Each team uses one set of markers/checkers to keep track of coordinates. Students take turns trying to locate the battleship. If they successfully locate a part of the battleship, their turn continues. Their turn ends when they miss locating the ship s coordinates. Continue until the ship is found. Extension: The leader can hide more than one shop Cruiser- 4 points Patrol boat- 2 points Carrier- 3 points Tugboat - 2 points Use four quadrants. Two player game: Each player plots ships on a game grid. They will need on grid to plot their ships and another to keep track of their opponent s ships. Players take turns guessing the location of their opponent's ships until they sink all of the ships.
Four in a Row! Materials needed: Checkers/game markers in two colours Deck of cards with face cards removed Quadrant 1 on a cartesian grid Goal : to plot 4 coordinates in a row, vertically, horizontally, or diagonally Procedure: Divide students into two teams and alternate turns between players. The first student turns over two cards e.g., 5 and 2 and decides how to order them strategically. x y 5 2 (5,2) 2 5 (2,5) Once decided, they place a game piece on their coordinates. Players can knock off their opponent's game piece if they have the same coordinates. Continue until one team has plotted 4 coordinates vertically, horizontally, or diagonally.
Countdown! Materials needed: Quadrant 1 on grid Assorted letters on the grid. These letters are used to create words. Numbered cards: 10,9,8,7,6,5,4,3,2,1, Oh no! (optional) Extension : you can use all 4 quadrants Goal: to figure out the hidden word before countdown. Use spaces to represent the number of letters in the word below the grid. For example, the word Paris would need 5 spaces. Procedure: Place assorted letters on ordered pairs in quadrant 1. Choose a word. You may want to give a clue e.g., math words, sports, animals, cities Students have 10 chances to guess the word. Students choose a letter for the hidden word by using the ordered pair for its location for example: I want the letter a and it is located at (4,9). If the correct coordinates are given the letter is removed if it is in the target word. If not, another student chooses a new set of coordinates for another letter. Each time a letter is selected correctly, it is placed on the blank word spaces below. Countdown from 10 to 0 each time a letter is not in the word. It is a race to see if the word can be figured out before countdown! Shopping Cart Materials needed: Pictures of food from a grocery store. They should be approximately the size of a small post-it note. Spinner divided into 5 sections (free turn, happy face, happy face, happy face, sad face) If students spin a sad face it means that they forgot their money at home and all of their groceries must be put back on the grid. Quadrant 1 on the grid. This can be increased to include 2 or all 4 quadrants, as appropriate. Timer
Goal: to gather the largest number of items in a given time. Procedure: Place assorted grocery items on the grid. Set the timer for 10 minutes. Divide students into two teams. Team 1 begins. In order to select an item, the student must say the coordinates. If they want the red apple, they must say (4, 8). If they give the incorrect coordinates (8, 4), their turn is over. Once they have the item, they spin the spinner. A happy face means keep the item and place it in a pile with their teams groceries. Free turn allows the student to choose another item. If the student spins the sad face ALL items from their pile must be placed back on the grid. Alternate turns. When the time is up, teams count their groceries and the team with the most groceries wins. Move It! Materials needed: One spinner with four sections (right foot, left foot, right hand, left hand) One set of coordinates on index cards e.g.,( 2, 4), (-4,5), (-6,-4) Two judges/experts to ensure that coordinates are plotted correctly Goal: to plot ordered pairs on a grid using body parts. Students work in teams of 4, earning one point for each body part successfully placed on the grid. Procedure: Divide students into teams of 4. The first person on the team spins the spinner to determine which body part will be placed on a point e.g., right foot. An index card is turned over telling the student where to place their right foot e.g., (-4, 3). Alternate turns until each student has 4 turns. If a student is not able to hold their position they move off the grid. If they are unable to reach a coordinate they forfeit their turn (but stay on the grid). If they spin left foot for a second time, they can choose to move their foot or stay in the same place.
If a student does not locate the correct coordinates on the grid, they forfeit their turn (but stay on the grid) After 4 turns, the team scores one point for each body part on the grid to a maximum of 16 points. Repeat for the next team. Get Rich! Materials needed: One set of coordinates on index cards e.g.,( 2, 4), (-4,5), (-6,-4). Create cards for the quadrants you want to use. Assorted play money Game markers in two colours or shapes Timer Goal: To locate coordinates on the Cartesian grid and describe how to move to a new location find some money. Procedure: Place 5 or 6 pieces of money on the grid. Set a timer for 15 minutes. Divide students into two teams. Students take turns turning over two cards and deciding which one is x and which one is y. A marker is placed on the coordinates. The student can then make two moves to capture some money. For example: if they begin at (3,2) they can say I will move up 3 squares and right 4 squares to get the loonie. If this is correct, they remove the money. A new piece of money can be placed on the grid each time one is removed. Play until the time is up. The team with the most money wins! Optional: Do not replace money on the grid and play until all of the money is gone. Continue until all the money is removed. Note: This grid can be used to create and analyse designs made by reflecting, translating and/or rotating shapes using clear plastic sheets.
Task Cards Create task cards using clear acetate sheets to practise Translations, Rotations, and Reflections in the First Quadrant of the Cartesian Coordinates Grid. Draw a shape on the acetate. You may want to begin by practising one type of transformation first e.g., translations. You could create a legend to be used with a die or spinner to review curriculum taught. Roll a 1 = translate up 5 units Roll a 2 = translate 4 right, up 2 Roll a 3 = rotate the figure clockwise 90 degrees etc. Gr. 7 Curriculum Expectations Geometry and Spatial Sense Overall Expectations Describe location the four quadrants of a coordinate system, dilatate two-dimensional shapes, and apply transformations to create and analyze designs Specific Expectations Location and Movement Plot points using all four quadrants of the Cartesian Coordinate plane Gr. 7 Suggested Activities Use all four quadrants for the activities above, as appropriate. Unite Materials needed: Giant Cartesian Coordinates grid Deck of cards Game markers in two colours Chart with legend to explain the value of the cards Black cards = positive number Red cards = negative number Clubs = quadrant 1 Spades = quadrant 2 Diamonds = quadrant 3 Hearts = quadrant 4 Goal: to plot points on the Cartesian Coordinates Grid by uniting two team members together.
Procedure: Divide the students into two teams. Team members take turns choosing a card from the deck. If it is a 10 of spades the student moves to quadrant 2 and waits for a partner from their team to join them. If a student chooses a 6 of hearts they move to their quadrant When two team members are in the same quadrant, they form an ordered pair. They place a game marker on their ordered pair after they name it and move off the grid. The first team to create 5 ordered pairs wins. Cartesian Toss Game played during our Jump2math program Grades: 6-8 Players: 3-10 One of the number cubes has negative and positive numbers for the x-axis. (horizontal) The other has negative and positive numbers for the y-axis (vertical) Both number cubes contain numbers up to 10 only. Procedure: Form a circle with the players around the cartesian mat. Have the players pass the number cube to each other in one direction using alternate methods: 1. Their feet only 2. Two fingers only 3. Elbows only 4. Slow motion When you call out Plot!, both players left with the number cubes drop them on the mat and plot both coordinates with one suction cup or marker Check to see if correct and repeat.
Quadrant Hop Game played during our Jump2math program Grades 5-8 Procedure: Give students a point like ( 5, 2 ), and have them jump on the correct quadrant. Remember the first number is on the vertical x -axis and the second number is always on the horizontal y-axis. (y) Points with answers (4, 3) -----------> Q1 (-3,4) -----------> Q2 (-6, -7) ---------> Q3 (4, -5) ----------> Q4 (4, 5) -----------> Q1 (-10, -4) --------> Q4 (-6, -7) ---------> Q3 (8,-7)------------> Q4 (4, -5) ----------> Q4 (-9, 3) ----------> Q2 (-8,-8) ----------> Q3