Graphics Sourced from Google Images
This fun game teaches students to get very good at plotting (x,y) points, as well as reading points on the Cartesian Plane, and it is lots of fun.
The game was developed here at Passy’s World by Passy and Jack, and has been trialed in classrooms with great results. (Thanks to Jack for coming up with most of the ideas on this one!).
There is a PPT Presentation for this Game which will be very useful for instructing the students on how to play the game.
Overview of Game
Students plot 20 points of their choice on a Cartesian X-Y Grid, which ranges from -6 to 6.
A special Positive / Negative Virtual Dice is rolled, to generate a “Bingo Coordinate”.
If a student finds they have that coordinate marked down, they circle it in red pen on their grid.
(Repeat drawing Bingo Coordinates by rolling the special dice)
Once a student has FIVE Coordinates circled anywhere on their Grid, they call out BINGO, and get their grid checked and win a prize.
Image Copyright 2013 by Passy’s World of Mathematics
Equipment Required for Bingo Coordinates
Grid Paper / Graph Paper (one per student)
PPT Presentation (See end of this lesson for Details)
Laptop PC and Data Projector (for Virtual Dice and PPT)
Lollipops or individually wrapped candy / lollies for Prizes.
Instructional PowerPoint
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Setting Up the Grid Paper
Students Rule up an X-Y Axis on their Grid Paper that forms a 6×6 Grid like the one shown below.
We need a 6×6 Grid because we will be rolling Dice to generate the Bingo Coordinates.
Image Copyright 2013 by Passy’s World of Mathematics
If you need some printable Grid Paper, then try the following links:
Four to a Page Cartesian Grids
Picking Points – Pre-Game Discussion
Students will need to plot 20 different random points of their choice onto their Grid.
We will be rolling dice to generate the Bingo Game Coordinates, and they will have to hope they get lucky, and some of the Dice Coordinates match their coordinates.
(We have found that 20 points makes for a game that goes for about 20 minutes and shopuld have at least 6 winners).
(You can also award some tasty treats for good answers during this pre-game discussion).
BEFORE THEY PICK THEIR POINTS – GO THROUGH THE FOLLOWING:
See if the students can figure out how many different points there are on the Grid.
ANSWER: The Grid is 12 x 12 = 144 possible points.
But what if we allowed Fraction and Decimal Coordinates ?
ANSWER: Infinite
For our game we are only using whole number integer coordinates – you can plot fractions or decimals if you like, but they will never come up on the dice!
There are certain whole number points on the Grid which should not be used – What are they ?
ANSWER: X-Axis points like (1,0) (-3,0) etc and Y-Axis Points like (0,2) (0,-5) etc as well as the Origin – because these coordinates have a zero in them, and zero can never come up on a Dice!
So how many usable points are there on our Grid for the Game ?
ANSWER: 144 – 6 – 6 -6 – 6 -1 (for the origin) = 144 – 25 = 119
So what are the chances of one of your coordinates being called as a Bingo Coordinate ?
ANSWER: 20 / 119 which is roughly 1/6 .
Note that the Game was not deliberately designed to make the chances 1/6 on the Grid, be the same as the Dice Chance; and if we played with only 10 coordinates, the chance for each one coming up would be 1/12.
What are the chances of a Bingo Coordinate coming up; AND then on the very next dice roll, the exact same coordinate coming up again ?
ANSWER: 1/6 x 1/6 = 1/36
Note from classroom trials, the game usually ends with no repeat Bingo coordinates happening during the whole 20 minute game.
Now get the students to mark on their grid their 20 chosen coordinates.
Their finished competition entry should look something like this:
Image Copyright 2013 by Passy’s World of Mathematics
Note the anime girl in the above image is upset because she just noticed that her friend plotted lots of her entry’s points on the X and Y Axis!
Positive and Negative Virtual Dice
The virtual dice which are needed to play the game can be found at the link shown below.
Two rolls need to be done for each coordinate, the first roll is the X-coordinate, and the second roll is the Y-coordinate.
The teacher, or a reliable student, needs to note down each coordinate which is rolled during the game, and also plot the Dice Rolled Coordinates on a Grid, for later answer checking.
Click the following link to access the virtual dice
Positive and Negative Virtual Dice App
Note that an alternative would be to use a Coin with a real Dice (Head = Positive, Tails = Negative)
Playing The Game
Project the Virtual Dice App onto a Screen at the front of class.
Roll the Virtual Dice once for the X-Coordinate, and one again for the Y-Coordinate,
Call out the resulting (x,y) Coordinate
(Teacher or an appointed student needs to note down the coordinate, and also plot it on the answer grid)
If a student has that coordinate they circle it in red pen
Keep rolling the dice until a student has 5 coordinates and calls out Bingo
Check the Student’s entry and award a prize
Keep playing for about 20 minutes until about 10 prizes have been awarded.
Positive Coordinates Game
Our Bingo Game can easily be adapted for beginners doing only Positive Coordinates.
Make a 12 x 12 Y-X Grid, which has (0,0) in the bottom left hand corner, and (12,12) in the top right hand corner.
Then use Two Dice to generate the coordinates.
There is a virtual Dice for this at the following link:
Click here for Virtual Double Dice App
Note that the game will be a little biased towards Coordinates containing 7’s, because 7 is the highest probability result for rolling two dice.
(Eg. 2 and 5, 6 and 1, 3 and 4, 4 and 3, 5 and 2, 6 and 1 = 6/36 = 1/6; whereas 12 is only from 6 and 6 which is a 1/36 chance).
See if this becomes apparent at all, as the game progresses.
Play the rest of the game as normal – Roll the two dice and add the result to get the X Coordinate, then roll them again to get the Y-Coordinate.
Note that Coordinates containing Zero or One will never come up in the Bingo Coordinates, because the lowest possible result from two dice is 1+1 = 2
Related Items
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The Cartesian Plane
Plotting Graphs from Horizontal Values Tables
Plotting a Linear Graph using a Rule Equation
Plotting Graphs from T-Tables of Values
Finding Linear Rules
Distance Between Two Points
Mountain Gradients
Real World Straight Line Graphs I
Real World Straight Line Graphs II
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