MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
COUNTRY NAME
Belgium
Name of the game
Balancing figures
Which subject of
mathematics is related?
Geometry - Verticality
Aims of the game
Tools and equipments
(DT)
Finding the Center of Mass (Center of Gravity) of regular and
irregular shapes with a plumb bob
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Cardboard
Scissors
Pencil
Wooden skewers or sharp pencil
Plumb bob
Pin
Ruler
How many people played
with?
Please, tick appropriate
box:
(Age Range)
o
o
o
o
o
o
Pre-Primary Schools
Primary Schools
Secondary Schools
High Schools
Special Needs Schools
Other (please specify)
You can find the center of mass (or center of gravity in an object
experimentally by hanging it from several points and using a
plumb bob to mark the vertical line. The intersection of two or
more vertical lines from the plumb bob is the center of gravity
for the object.
1/ Finding
The center of gravity of a regular shaped geometric figure,
such as a rectangle , circle, square, triangle, parallelogram ….
is the same as it’s geometric center.
How to play?
A/ Finding the Center of mass of a rectangle
geometrically (geometric center)
1. Draw a rectangle on your piece of cardboard
(20cmx30cm)
2. Cut the rectangle
3. Using your ruler, draw a straight line from one corner
to the opposite corner. Now draw another line
between the other two opposite corners.
4. Press the point of your pencil (or the skewer) into the
point where the two lines intersect (cross) to make a
small indentation.
5. Now carefully try to balance the rectangle on your
pencil point where you just made the indentation.
6. You have found the geometric center of the rectangle
which is the point of intersection of the diagonals of the
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
rectangle.
B/ This can be checked by experimentation with the
plumb bob
1. Attach the rectangle with the pin on a wall or on the
board. Allow it to swing freely.
2. Suspend the plumb bob on the pin in front of the
rectangle .
3. When the rectangle stops swinging, draw a line on the
shape where the string of the plumb bob is hanging
4. Punch a hole in the shape in another point along the
edge (not too close from the first one).
5. Thanks to the plumb bob draw a line on the shape
once more.
6. Do this a third time.
7. If you have done this carefully, all three lines should
intersect at the same point you have found by the
geometrical method (the geometric center)
Going Further: Locate their Center of Mass of a circle
2/ Finding the Center of Mass (=Center of
Gravity) of irregular shapes
8. Draw on the cardboard any irregular shape ( or a bird
a butterfly....) about 30 cm long.
9. Cut out the shape
10. With a pin punch a hole in the shape anywhere near
an edge.
11. attach the shape with the pin on a wall or on the board.
Allow the shape to swing freely.
12. Suspend the plumb bob on the pin in front of the shape.
13. When the shape stops swinging, draw a line on the
shape where the string of the plumb bob is hanging
14. Punch a hole in the shape in another point along the
edge (not too close from the first one).
15. Thanks to the plumb bob draw a line on the shape
once more.
16. Do this a third time.
17. If you have done this carefully, all three lines should
intersect at the same point. If they don’t, check your
lines again
18. Press the point of a wooden skewers into the shape
where the lines intersect to make a small indentation.
19. Now try to balance this shape on your skewer (or you
pencil) at this point.
20. The shape will also be free to rotate about that point.
Photos / videos of the
Between 5-10
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
game
1/ Center of Mass of regular shaped geometric figure
Geometric center of a rectangle
The center of mass and the geometric center of a circle
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
2/ Center of Mass of irregular shapes
Material
The shape is held by the pin It can freely rotate around the pin; and the plumb line is dropped
from the pin .
The experiment is repeated with the pin inserted at different points of the object. The intersection
of the lines is the center of mass of the shap
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
Now try to balance this shape at this point on your skewer , you pencil or… your finger !