STRAW TRIANGLES
Relation to Curriculum Outcomes:
Mathematics 20-2
Number and Logic
Mathematics 30-2
Probability
Mathematics 30-3
Probability
Mathematics 30-1
Perms/Combs/Binom.
SLO 1
SLO 1
SLO 1
SLO 3
This activity touches upon the SLOs listed above and can be used as an
introductory activity. It also addresses the triangle inequality theorem.
MATERIALS: Bag containing 5 straws having lengths 1, 2, 3, 4, and 5
units.
PROCEDURE:
1. Working in pairs, one student is to draw three straws at random from the
bag and arrange them on the table in a triangle, if possible. The second
student is to record the lengths of the three straws and whether a triangle was
possible. The straws are then put back in the bag and the procedure is
repeated. Students should take turns drawing and recording until twenty
observations have been recorded.
2. Using the data collected in step 1, calculate the probability of drawing
three straws at random that will form a triangle.
3. Working together, make an organized list of all the possible combinations
of straw lengths that can be drawn from the bag 3 at a time.
4. Using the list, try to make triangles out of each combination and note
which ones do.
5. Using the information from step 4, calculate the probability of three
randomly drawn straws forming a triangle. Is this the same or different from
your result in step 2?
6. Using the information from step 3, suggest a rule to be able to predict
when three straws of differing lengths will form a triangle. Use your rule to
predict whether each of the following sets of three straws will form a
triangle.
3,6,10
4,7,8
3,4,11
12,15, 23
STRAW TRIANGLES EXTENSION
Relation to Curriculum Outcomes:
Mathematics 20-1
Relations and Functions
SLO 7
The assumption is that the original straw triangles activity will have been
used as an introduction to develop the triangle inequality theorem. This
activity is intended as an individual followup examining the conditions
necessary to form a triangle using three random lengths from a theoretical
perspective and the probability of them forming a triangle.
MATERIALS: Graph paper
PROCEDURE:
1. Draw a horizontal line on a piece of paper and label the endpoints 0 and 1.
Mark two random points on the line labelling one X and the other Y.
2. Using the diagram from step 1, write expressions to represent the three
lengths that would result if the line were cut at X and Y.
3. Using the triangle inequality theorem, write all the possible inequalities
using these three lengths and solve each inequality. What are the restrictions
on X and Y?
4. Graph your results from step 3 on the same set of axes and calculate the
area of the resulting figure.
5. Repeat steps 1 through 3 starting with a diagram in which the positions of
X and Y are reversed.
6. Graph your results from step 5 on the same set of axes used in step 4.
Calculate the area of the resulting figure.
7. How is the area of the two figures from steps 4 and 6 related to the unit
square? How is this related to the probability of three random lengths
forming a triangle?