The set up:
Use this link to get a game board on desmos: Conic Capture Game Board 1
I found it useful to put it on Projector Mode. Press play for the four points that are animated.
Put your class into at least two teams and have them pick a color for their team (green, purple, orange, or black).
Teams take turns writing equations that will capture points on the screen. Capturing blue points is good, capturing red points is bad. Students capture an ordered pair or ordered pairs by having a conic section around it.
In the screen capture below, the black team captured one blue ordered pair at (4, 0) with a circle.
In this screen capture, the orange team captured 3 ordered pairs with an ellipse. Two of the ordered pairs were static and one was animated.
Teams take turns back and forth until there are no more blue points to capture. Game ends and the team with the most points wins.
Each blue static point captured is worth 1 point
Each blue animated point captured is worth 2 points
Each red point is worth -1 points.
If a team captures points with one type of conic section, the multiplier for the points is 1.
When a team has used two different types of conic sections in the game, the point multiplier is 2.
Three types of conics --> multiplier of 3
The black team used a circle to capture 1 static blue point. 1 point with a multiplier of 1 equals 1.
On their second turn, the black team captures 1 static blue point and 1 animated blue point with a parabola. Since this is the second type of conic section used in the game, the multiplier is two for this round. (1 + 2) * 2 = 6 total points for this round and total of 7 points for the game.
Formula to determine points earned in a round:
(Number of Conic Sections used in the game) * (1 * # of blue static points this round + 2 * # of blue animated points this round - 1 * number of red points this round)
Intersecting another team's conic section will lead to a deduction in 1 point per intersection.
The screen capture below shows a loss of 2 points, because they intersect twice.
Have the teams write down their equations, then the teacher or a designated student will type the equation into desmos, remember to change the equation color for each team.
Some students may find it hard to see the graph from their seats, printing a copy of the game board for each student will help with this.
In order to capture an animated point, it must stay within the conic section the entire time.