Connect Three
A Playful Way To Learn Algebra Concepts
Examples of three points on a straight line:
a) Points (-3,3), (3,3) and (9,3)
on horizontal line y = 3
with Slope = 0 and Y-intercept = 3
b) Points (9,-2), (9,3) and (9,9)
on vertical line x = 9
with Slope = undefined,
and X-intercept = 9
c) Points (-3,3), (5,7) and (9,9)
on sloped line y = 0.5x + 4.5
with Slope = 0.5, Y-intercept = 4.5
Topics: Linear Equations;
Point Slope Formula; X
and Y intercepts
Materials List
 Game board with
X-Y coordinates
 2 Dice of different
colors
 Games pieces (e.g.,
colored pawns,
colored tokens) 7 of
one color per player
 Optional: colored
push pins as game
pieces, foam board,
and two sided tape
adhered to bottom
of game board
 Optional: colored
squares die-cut
from Magnetic
Sheets as game
pieces and rubber
steel sheets
This activity can be used
to teach:
Common Core Math
Standards:
 Graphing (Grade 5,
Geometry, 1 & 2)
 Slope (Grade 8,
Expressions and
Equations, 5 & 6)
 Problem Solving and
Reasoning
(Mathematical
Practices Grades 5-8)
Playing this game students will learn about Cartesian coordinates, linear equations,
slope, and intercepts in a fun way.
Assembly (depending on game pieces used)
1. Optional: Laminate the game board to make it more durable.
2. If using colored push pins as game pieces: cut a piece of foam board of minimum
thickness of 1 cm (3/8”) to a size of 45 cm X 45 cm (18” X 18”). Apply 2-sided
tape to the bottom of the game board and adhere it to the foam board.
3. If using magnetic squares as game pieces: die-cut centimeter squares out of
colored Magnetic Sheets, and place Rubber Steel sheets under the game board.
To Play the Game (for 2 -4 players)
1. Each player needs a minimum of 7 game pieces of the same color.
2. Each player rolls one die to determine order of play: highest number goes first;
then players take turns in clockwise fashion.
3. All players agree which color die determines the x-coordinate; the other color die
determines the y-coordinate. Each player takes a turn to roll both dice to
determine the (x, y) coordinates to place a game piece on the board. Note: A
player has the option to bump another game piece off the board if he/she ends up
with the same (x, y) coordinates as a preceding player!
4. Optional variation: Players choose to use either positive or negative values for x
and y. For example, a roll of 4 and 6 would give the choice of (4, 6), (4, -6),
(-4, 6), or (-4, -6).
5. The first player rolls the dice for a 2nd time and determines the corresponding
(x, y) coordinates as above to place another game piece on the board. While the
next player is rolling the dice for the 2nd time, the first player determines the Rise
over Run ratio of the line going through the first two points (see The Math
Behind the Activity section below). Repeat for all the players.
6. The first player rolls the dice once more to come up with the (x, y) coordinates
for the 3rd point. To confirm whether this point is on the same straight line as the
1st two points, determine the Rise over Run ratio between the 2nd and 3rd points. If
this ratio is the same as the ratio determined in step 5, the student announces
“CONNECT THREE” and scores one point. Repeat for all players.
7. Continue play until all the game pieces have been placed on the game board.
Each time a new piece is placed, the player calculates the Rise over Run ratios
between the new point and the points already on the board (try all likely
combinations) to determine whether three points are connected.
8. The player with the most points wins. Multiple winners are possible!
Developed and written by Gus Liu (RAFT)
Copyright 2014, RAFT
The Math Behind the Activity
Playing this game helps the students to become familiar with the following:
- Points on the Cartesian coordinate system.
- The slope of a line through 2 points, (x1,y1) and (x2,y2):
Slope m = ratio of Rise over Run
= (y2 -y1) / (x2 -x1)
Example for points (-3,3) and (9,9):
Slope m = (y2 -y1) / (x2 -x1) = (9-3) / (9-(-3)) = 6 / 12 = 1/2
- The equation of a line through 2 points with known coordinates (x1,y1) and (x2, y2)
The corresponding linear equation is defined as (y- y1) = m (x- x1), with slope m = (y2 -y1) / (x2 -x1)
- The equation of a line in slope-intercept form, where the slope and the Y-intercept are known
Linear equation: y = mx + b, where m is the slope and b is the Y-intercept
Example: y = 0.5x + 4.5 , with Slope m = .5 and Y-intercept = 4.5
- The Y-intercept of a line: the Y-value where the line intersects the Y-axis (i.e. x=0)
Example: y = 0.5x + 4.5
To determine the Y-intercept, substitute the value of 0 for x, yielding the Y-intercept = 4.5
- The X-intercept of a line: the X-value where the line intersects the X-axis (i.e. y=0)
Example: y = 0.5x + 4.5
To determine the X-intercept, substitute the value of 0 for y, yielding the X-intercept = -9
Taking it Further


Instead of calculating the Rise over Run ratios to determine linearity between 3 points, derive the equation of
the line through 2 points and substitute the 3rd point into that equation. If the result is balanced, the 3rd point
is on the same line as the other 2 points.
Double up on the number of dice using 2 dice of each color and allow the students the following options to
determine the (x, y) coordinates of their points:
o add the numbers on the rolled dice of the same color.
o subtract the smaller number from the larger number on the rolled dice of the same color.
o subtract the larger number from the smaller number on the rolled dice of the same color.
Web Resources (Visit www.raft.net/raft-idea?isid=605 for more resources!)

Teacher designed math courses from the New Jersey Center for Teaching & Learning –
https://njctl.org/courses/math
Connect Three, page 2
Copyright 2014, RAFT