Here's what you'll need:
1. Painter's tape
2. At least two colors of construction Paper
3. Markers
4. A list of angles and sides for non-right triangles and right triangles
5. Handouts with diagrams of triangles for your students (see 2nd link)
How to make your list of angles and sides (step 4):
Your angles should be a mixture of numbers that add up with 90 degrees to make 180 degrees.
EX: 45 and 45, 60 and 30, 70 and 20
Each angle should go on different pieces of construction paper, but all on the same paper so all of the angles are red, for example, and sides are all blue.
Your sides should stay proportionate to your angles (thinking of special right triangles here), but can also be random.
EX: If you are introducing right triangles completely, you might want to use sides that do and don't add up to be greater than the longest side. So a triangle with the sides 3, 7, and 10 would not make up a right triangle, because 3+7 is not greater than 10. Just make sure that you include a 4 or 8 so your students can find three sides that would make up a right triangle.
Your list should mainly revolve around what you're introducing. If you're showing them that the sum of the two smallest sides must be greater than the longer side in order to make a right triangle, then you should focus more on my last point. If you're showing the relationship between angles and their sides, the first point is more relevant.
In the end, your list should be a list of numbers like:
Angles: 45, 45, 70, 20, 50, 60...
Sides: 3, 4, 5, 12, 13, 25...
**If you're using this to introduce SOH-CAH-TOA, you should include a theta symbol in your angles, and a variable in your sides.
Set up:
1. Cut both colors of your construction papers in half, and keep them separated so one color is for your angles and the other is for your sides
2. Label one color with all of your numbers from your list of angles, and label the other with your list of sides
3. Arrange your room so that the desks are surround a large open area in the middle (if you have the room, try making two or three open areas. Just make sure you have enough side and angle cards for each group)
4. In that large open area, use the tape to make a large right-triangle on the ground
Instructions:
You could either have your class work on this as a group, or in two or three small groups.
TO SHOW THE RELATIONSHIP BETWEEN THE SIDES OF A RIGHT TRIANGLE:
To start, have three students volunteer to be a part of the activity. Give each student a "side" card and let them choose where to stand on the triangle.
**Pay attention: if the student with the longest side doesn't stand on the longest side, make a point to stop and ask the class if this looks okay. This encourages critical thinking, and keeps your triangle accurate.
Once they've chosen an appropriate side, have the audience label their handouts with the corresponding sides from the life-sized triangle.
Now start a discussion with your triangle legs: do they make a triangle together?
If they're not sure, bring the rest of the group in. If they do, then why? If not, have your triangle legs look through your other side cards and find cards that do work together. Maybe one of the small legs needs to be bigger, or maybe the bigger leg needs to be bigger.
As they're going through this process, encourage the rest of the group to make note of this on their handouts, and label their original triangle as "Not a right triangle." When the legs find the correct grouping, have everyone else label a new triangle with new numbers and a "Right Triangle."
Continue this as needed, switching out volunteers as you go. Remember to introduce and encourage mathematical language like hypotenuse, sum, etc.
TO INTRODUCE SOH-CAH-TOA:
This process is fairly similar to that from the last one, but a step up in terms of what we're learning.
Again, ask for three volunteers. Either let them choose between a side, angle, variable, or theta, or assign one to each. MAKE SURE that you have someone who is either a theta or a variable, though, or else there will be nothing to solve for. You should let them choose where to go on the triangle, though.
**Pro-tip: If two students choose two sides, this would be a great opportunity to review Pythagoras' theorem.
When they've chosen their sides, have everyone else copy the corresponding sides and angles onto their handout.
EX: Let's say Leslie chooses a variable and stands on the hypotenuse, Jacob chooses an angle labeled 54 degrees, and Hailey chooses a side labeled 6 feet.
**When your class is labeling their handouts, it may be necessary to point out that Leslie is on the hypotenuse, and Jacob is the angle opposite to Hailey.
Now ask your triangle volunteers how they're going to find the variable, or Leslie in this case. If they know, have them walk everyone through it. If they're unsure, invite the rest of the group to help them out until we give the variable and "identity" as I like to say.
Again, be sure to use and encourage mathematical language like hypotenuse, oppose side, sine, cosine, angle, etc.
There are many more ways to adapt this lesson to other topics involving right triangles, so I invite you all to send your suggestions and let us know how it went!
SMPs:
1 - Make sense of problems and persevere in solving them
3 - Construct viable arguments and critique the reasoning of others
6 - Attend to precision
8 - Look for and express regularity in repeated reasoning