Triangle or Knot
Linda Horst & Tony Riehl
&
Will James Middle School
Billings, Montana
Triangle or Knot?
Teacher Notes
Supplies: 7 inch linguine (9 linguine for each student)
dice (three dice for each group)
permanent markers
scissors
snack size baggies (one for each student)
3-page worksheet
Before Day 1 have the students fill in the blanks on part one.
Day 1
You may want to demonstrate an easy way to mark their linguine at one-inch intervals. One method would be to have a sheet with lines at one-inch interval so that students can mark all nine straws at once (or 18 if they have a partner).
Then, have them roll the dice to do their 20 trials. When they are done rolling the dice then they can complete table 1. This may be done as homework.
Triangle or Knot?
1. Mark 9 linguine, 7 inches from one end.
7 inches
2. Break off the end so you have 7-inch linguine. Keep the 7 inch segments.
3. Mark the 9 linguine at 1-inch intervals with a permanent marker. (use the grid below to mark the 1-inch intervals)
4. Break a one-inch segment off three of the linguine. You will have three 1-inch pieces and three 6-inch pieces. (keep all 6 pieces).
5. Break a two-inch segment off three of the linguine. You will have three 2-inch pieces and three 5-inch pieces. (keep all 6 pieces).
6. Break a three-inch segment off three of the linguine. You will have three 3-inch pieces and three 4-inch pieces. (keep all 6 pieces).
7. Put all 18 segments in a Zip-Lock bag.
1 inch 1 inch 1 inch 1 inch 1 inch 1 inch 1 inch
Triangle or Knot?
Name: ______Period: ______
Define the following terms (place one letter on each space):
acute angle: An angle whose measure is between ______and 90°.
obtuse angle: An angle whose measure is between ______and 180°.
right angle: An angle whose measure is ______degrees.
by angle
acute triangle: A triangle with ______acute ______.
obtuse triangle: A triangle with ______obtuse ______.
right triangle: A triangle with ______angle.
by side
equilateral triangle: A triangle with ______congruent ______.
isosceles triangle: A triangle with at least ______congruent ______.
scalene triangle: A triangle with __ __ congruent ______.
Complete Table 2 (next page): Make an organized list of all the triangles that can be made with sides having lengths 1, 2, 3, 4, 5 and 6. (hint: first list all of the triangles that can be made with smallest side length 1, then smallest side length 2, etc.) You can use the same length more than once. There are 34 possible triangles. Complete the table.
Table 3: Complete Table 3 after you have completed Table 2.
Triangle Typeby sides / Frequency / Percent
Equilateral
Isosceles
Scalene
Total
Triangle Type
by angles
Acute / Frequency / Percent
Right
Obtuse
Total
Triangle or Knot?
Name: ______Period: ______
Part 1
Complete Table 1: Roll three dice and record the three numbers as sides, putting the numbers in increasing order. Complete twenty trials. Then complete the table. Use the sticks to try to form a triangle if necessary. If the three numbers do form a triangle find the two triangle types. In order to be a right triangle, the sides must be true in the Pythagorean theorem (a2 + b2 = c2).
Triangle type by side: equilateral, isosceles or scalene. Triangle type by angle: acute, obtuse or right.
Table 1
1. Make a conjecture about the lengths that will form a triangle and those that will not make form triangle.
2. Make at least two conjectures about the relationship between side lengths and the types of triangles they form.
Table 2
Smallest / Middle / Longest / 2 2 / 2 / Type / TypeTriangle / side (a) / side (b) / side (c) / a + b / c / by side / by angle
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Triangle or Knot?
Table 2 -- All possible triangles using 1, 2, 3, 4, 5, or 6.
Smallest / Middle / Longest / 2 2 / 2 / Type / Type
Triangle / side (a) / side (b) / side (c) / a + b / c / by angle / by side
1 / 1 / 1 / 1 / 2 / 1 / Acute / Equilateral
2 / 1 / 2 / 2 / 5 / 4 / Acute / Isosceles
3 / 1 / 3 / 3 / 10 / 9 / Acute / Isosceles
4 / 1 / 4 / 4 / 17 / 16 / Acute / Isosceles
5 / 1 / 5 / 5 / 26 / 25 / Acute / Isosceles
6 / 1 / 6 / 6 / 37 / 36 / Acute / Isosceles
7 / 2 / 2 / 2 / 8 / 4 / Acute / Equilateral
8 / 2 / 2 / 3 / 8 / 9 / Obtuse / Isosceles
9 / 2 / 3 / 3 / 13 / 9 / Acute / Isosceles
10 / 2 / 3 / 4 / 13 / 16 / Obtuse / Scalene
11 / 2 / 4 / 4 / 20 / 16 / Acute / Isosceles
12 / 2 / 4 / 5 / 20 / 25 / Obtuse / Scalene
13 / 2 / 5 / 5 / 29 / 25 / Acute / Isosceles
14 / 2 / 5 / 6 / 29 / 36 / Obtuse / Scalene
15 / 2 / 6 / 6 / 40 / 36 / Acute / Isosceles
16 / 3 / 3 / 3 / 18 / 9 / Acute / Equilateral
17 / 3 / 3 / 4 / 18 / 16 / Acute / Isosceles
18 / 3 / 3 / 5 / 18 / 25 / Obtuse / Isosceles
19 / 3 / 4 / 4 / 25 / 16 / Acute / Isosceles
20 / 3 / 4 / 5 / 25 / 25 / Right / Scalene
21 / 3 / 4 / 6 / 25 / 36 / Obtuse / Scalene
22 / 3 / 5 / 5 / 34 / 25 / Acute / Isosceles
23 / 3 / 5 / 6 / 34 / 36 / Obtuse / Scalene
24 / 3 / 6 / 6 / 45 / 36 / Acute / Isosceles
25 / 4 / 4 / 4 / 32 / 16 / Acute / Equilateral
26 / 4 / 4 / 5 / 32 / 25 / Acute / Isosceles
27 / 4 / 4 / 6 / 32 / 36 / Obtuse / Isosceles
28 / 4 / 5 / 5 / 41 / 25 / Acute / Isosceles
29 / 4 / 5 / 6 / 41 / 36 / Acute / Scalene
30 / 4 / 6 / 6 / 52 / 36 / Acute / Isosceles
31 / 5 / 5 / 5 / 50 / 25 / Acute / Equilateral
32 / 5 / 5 / 6 / 50 / 36 / Acute / Isosceles
33 / 5 / 6 / 6 / 61 / 36 / Acute / Isosceles
34 / 6 / 6 / 6 / 72 / 36 / Acute / Equilateral