Here are three sample problems to discuss: Ask students how they might decide what types of problems to use it on, and how they would solve those problems. If applicable, remind students that this type of image might be provided as a reference on standardized tests. Why are we looking at two triangles? Are the triangles related? What are we going to do with these?) I was able to gain a better understanding of how well students understand the problems and to see which problems were giving them the hardest time.Īll of the foldables, activities, and homework can be found when you CLICK HERE.Ask students what they notice and what they wonder about the images. With this lesson, I joined in on the fun and switched papers with students too. Once they are finished checking work, they will repeat "Stand Up-Hands Up-Pair Up" and find a total of 11 different people to switch papers with. Students need to get back their ORIGINAL paper so they can check over the persons work.
They will sign their name in the box that they just completed. Students will switch papers with the person they pair up with and choose a problem on the other persons paper to complete. When they are finished, they stand up, raise their hand ,and look for somebody else who has their hand raised. Once they complete the problem, I have them sign their name at the bottom of the box. The first thing that I tell students to do, is to "Write their name at the top of the paper." Next, I tell students to choose only ONE out of the 12 problems to complete. On the third day, we practiced some more with a "Stands Up-Hands Up-Pair Up" activity.ĭirections: I hand out the Special Right Triangles: Hands Up-Pair Up to every student. They will now tell other students that in a 45-45-90 triangle, the "hypotenuse is always √2 times longer than the leg". I feel like the discovery and the "why" helped them the most. My special education students are ROCKIN' special right triangles. Overall, I feel like this lesson went GREAT. On the 30 60 90 paper, I told students that each side of the equilateral triangle is 2 inches and that they need to find the length of the altitude. Many students told me that the hypotenuse is always √2 times longer than the leg "because the Pythagorean Theorem says so." After students used the Pythagorean Theorem to find the length of the diagonal of the square, I asked them to tell me the relationship between the legs and the hypotenuse of a 45-45-90 triangle. I told students that each side of the square was 1 cm and they had to use the Pythagorean Theorem to find the length of the diagonal.
They had to use the Pythagorean Theorem to solve for the length of the diagonal (square) and the altitude (equilateral triangle). So, I had students discover the rules for 45-45-90 and 30-60-90 triangles by splitting a square in half and an equilateral triangle in half. Newell, why is the hypotenuse in a 45-45-90 triangle always √2 times longer than the legs? Why isn't it only 2 times the leg, since 45 is half of 90?" This question made me reflect on my teaching and it made me realize that I was not teaching the "why" in special right triangles. This is my third year teaching Geometry and every year, students have a hard time with special right triangles.
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