Marble Masters
Rolling a Marble Confirms Coordinate Calculations are on Target!
Topics: Linear Equations;
Point Slope Formula; X
and Y
Materials List
 X-Y Coordinate
game board
 Foam board, thick
cardboard, or equal,
 Hanging file folder,
legal or letter sized
 Binder clips, small
and/or medium, 8
 Pushpin
 Transparency
 Marble
 Target “piece”
 Marker, or equal,
with a diameter of
~2 cm (3/4”)
 Small rubber band
 Paper and pencil
 Paper cutter/
scissors
 2 sided tape or glue
 Tape or stapler
 Permanent marker
This activity can be used
to teach:
Common Core Math:
 Graphing linear
functions (Grade 8,
Expressions and
Equations, 7; Grade 8,
Functions, 3; High
School, Interpreting
Functions, 5 & 7)
 Slope (Grade 8,
Expressions and
Equations, 5-6)
 Problem Solving and
Reasoning (Math
Practices Grades 7-9)
Target at
(x2,y2)
Pointed to
intercept
Pushpin at (x1,y1)
Example:
a) Launch point at (x1, y1) = (10,-10).
b) Target point at (x2, y2) = (-4,11)
c) General equation of the line through 2 points
(x1, y1) and (x2,y2) : y-y1 = m (x-x1)
with slope m = (y2-y1)/(x2-x1)
Derive the equation through 2 points (10,-10)
and (-4,11): y = -3/2 x + 5
d) Determine the intercept of the equation: Y=0
when X= (5*2)/3 = 3.3 (rounded).
e) Align transparency line from pushpin point to
3.3. Confirm slope calculation.
f) Assemble launch tube and holder. Place target
at (x2, y2). Launch marble toward target. A hit
confirms the calculations!
Students use a linear equation, slope, and X-Y intercept to aim a marble launch tube
so the marble will cross a specified set of Cartesian coordinates and hit the “target”!
Material Preparation
1. Optional: Laminating the game board will create a more durable playing surface.
2. Cut foam board, or equal, to make a square with 48 cm (19”) sides. If the pushpin
would poke all the way though the foam board then either cut additional squares
to glue together and/or cut pieces to attach as “feet” at the corners of the board.
3. Use 2-sided tape or glue to attach the game board to the foam board.
4. Cut across a hanging file folder starting about 4 cm (~1-1/2”) from the “hanging”
edge of the folder if using scissors. If using a paper cutter then cut the folder at a
point 20 cm (8”) away from the bottom. Either method will create 2 narrow strips.
5. Fold each strip along a line parallel to the metal hanger and as close as possible to
the enclosed metal strip. The goal is to create a nearly 90 degree fold in the strips.
6. To form a barrier to stop the rolling marble position the folded strips at the top
corner of the game board forming a right angle (see the top illustration).
7. Use big enough binder clips to attach the strips to the board, as shown above.
8. From the remainder of the hanging folder cut a lengthwise strip 2 cm (3/4”) wide
and then another strip 8 cm (~3”) wide. Cut the wider strip in half to make 2
sections 8 cm (~3”) by 15 cm (6”).
9. Use the pushpin to poke a hole in the center of one of the wider half sections.
10. At a point 1/4th of the way from one end the narrower strip - poke a centered hole.
11. Cut a 3 cm (or 1”) lengthwise strip from a transparency that has a preprinted line
down the center lengthwise or draw a line with a permanent marker. Use a
pushpin to poke a hole on the line and near one end of the transparency strip.
12. Use the remaining wide half section to roll around a marker, or other object with
about 2 cm (3/4”) diameter, to form a tube 15 cm (6”) long. Apply tape to the
seam in several places to keep the tube from unrolling. Push and/or pull the
marker out of the tube.
13. Position the “launch” tube with the seam at the top. Cut one end of the tube at a
slant and then notch the tip, as shown below.
Seam
End cut at a
slant
Side view
Developed and written by Gus Liu (RAFT) and Michael Pollock (RAFT)
Top view
Notch
Copyright 2014, RAFT
Playing the Game (for 2 players)
1. Player A picks a point (x1, y1), the launch point, in quadrant 4.
2. Player B picks a point in quadrant 2, the target, and tells the target’s coordinates (x2, y2) to player A.
3. Both players A and B determine the equation of the line going through the 2 points, the slope of the line, and
the intercept (see example at the top of page 1).
4. Insert the pushpin into the hole in the transparency strip and then into the point (x1, y1). Rotate the strip so that
the line on the transparency crosses, or is aimed towards the X or Y intercept calculated in step 3.
5. Both players confirm the slope of the line on the transparency matches the calculate slope.
6. Remove the pushpin from the transparency. Insert the pushpin into the hole in the narrow strip, the hole in the
wider strip, the hole in the transparency, and then the (x1, y1) point on the board. Slip a small binder clip over
the top of the pushpin. Position the narrow strip and launch tube as shown below.
7. Pull up the sides of the wider strip around the sides of the tube and add 2 binder clips as shown to tightly hold
the tube in place. Reposition the transparency as was done in step 4. Align the notch in the tube over the line
on the transparency by moving the narrow strip, which will rotate the tube.
8. Use a binder clip to secure the narrow strip to the edge of the board to prevent the tube from shifting.
Notched aligned over the
line on the transparency
Transparency
Wide strip folded over tube
Binder clips (bottom clip is attached over
the pushpin and inside the folded up
wider strip)
Narrow strip with longer end here to clip to the board
9. The board must be fairly level for the marble to roll in a straight line between the launch and target points.
Place a marble in the center of each quadrant and note if the marble tends to roll off. Raise the appropriate
corner(s) of the board, as needed, to create a more level surface.
10. Player B places a target piece (e.g., game token, wooden cube) at point (x2, y2) and player A inserts a marble
into the launch tube tube. If the calculations are correct, the marble will roll down the tube and hit the target!
11. Players A and B take turns positioning and launching the marble.
The Math Behind the Activity
Playing this game helps students to become familiar with the following:
- Points on the Cartesian coordinate system using the (x1,y1) form of notation.
- The slope of a line going through 2 points, (x1,y1) and (x2,y2):
Slope m = ratio of Rise over Run = (y2 -y1) / (x2 -x1)
- The linear equation of a line through 2 points with known coordinates (x1,y1) and (x2, y2) can be written in
one of three forms:
 In standard form: is ax + by = c, where a, b, and c are integers, and “a” and “b” are not both zero.
 In point-slope form: (y- y1) = m (x- x1), for a given point (x, y) on a non-vertical line with slope m
 In slope-intercept form : y = mx + b, where m is the slope and b is the y-intercept
Taking it Further



Player A picks 2 points in quadrant 4 to align the launching tube and tells the 2 sets of coordinates to player
B. After calculating the linear equation of the path of a marble rolling down the launching tube, player B
places a pawn on that path. “A hit or a miss?” That is the question!
Rather than aiming directly for the target, aim for a position on one of the bumpers to bounce the marble off
the bumper at the angle required for the marble to hit the target on the rebound.
Instead of utilizing quadrant 4 and 2, other combinations of diagonally positioned quadrants may be used as
the launching and target regions. Move the 2 bumper strips as needed.
Web Resources (Visit www.raft.net/raft-idea?isid=608 for more resources!)



Step by step lessons on graphing linear equations - http://www.purplemath.com/modules/graphlin.htm
6-8 grade examples of linear equations - http://mathforum.org/library/drmath/sets/mid_graphing_eq.html
Teacher designed math courses from the New Jersey Center for Teaching & Learning –
https://njctl.org/courses/math
Marble Masters, page 2
Copyright 2014, RAFT