Breaking the Stick

G 1 4
T: You were able to make triangles with the segments in A and in C but not with those in B, in
D, and in E. Why?
S: The two short pieces together must be longer than the longest piece.
T: Let’s measure to check what you are saying.
S: The three lengths in A are 5 cm, 8 cm, and 7 cm. 5 + 7 is more than 8, so we can make a
triangle.
S: The three lengths in B are 3 cm, 5 cm, and 12 cm. 3 + 5 is less than 12, so we cannot make
a triangle.
T: In C, what are the three lengths?
S: 9 cm, 2 cm, and 9 cm.
T: So we have to compare 9 + 2 to 9 since we must use a 9 cm segment as a longest piece.
S: 9 + 2 is more than 9, so we can make a triangle. It will be a narrow triangle.
In a similar manner, discuss D and E.
Begin a table on the board similar to that on Blackline G14(b). Provide students with a copy. Draw a
20-cm line segment on the board, marking one end 0 and the other 20. Then place breaking points at
5 cm and 14 cm.
T: If we break the 20-cm stick
at 5 cm and at 14 cm, what
would the lengths of the three
pieces be?
S: 5 cm, 9 cm, and 6 cm.
T: Could we make a triangle?
S: Yes, 5 + 6 > 9.
Record the information in the table. Instruct students to use the five 20-cm line segments on
Blackline G14(a) to enter data in the table. Continue the table with other choices for the breaking
points, occasionally letting students choose them. Be sure to include an example in which one of the
three lengths is 10 cm and, hence, the sum of the lengths of the other two segments is exactly 10 cm,
giving a failure.
G-62 IG-VI