Breaking the Stick

G 1 5
Let students suggest and discuss devices (spinners, darts, and so on) that might be used for choosing
the breaking points.
T: Name some possible breaking points and let’s see if they are successes or failures.
S: 5 cm and 13 cm.
Locate the breaking points. Mark them with s and label them.
T: If we break the stick at 5 cm and at 13 cm, would the resulting pieces form a triangle?
S: Yes; the three pieces would be 5 cm, 8 cm, and 7 cm long—each is less than 10 cm long.
Continue the activity until five or six pairs of breaking points have been suggested and discussed. In
the next illustration, success (you can form a triangle) is shown in blue and failure (you cannot form
a triangle) is shown in red.
Refer to the first pair of breaking points (5 cm and 13 cm) listed on the board.
T: Let’s record this pair of breaking points with a blue dot at a point on the grid. Where
should we put the dot?
There are two points that would be natural to
use: (5, 13) and (13, 5). Mark each with a blue
dot and connect the two dots with a segment.
Continue by graphing the other examples of
breaking points listed on the board. Use blue
or red dots according to whether the points
give a success or a failure.
G-66
IG-VI