Lesson Title: Triangles and the Pythagorean Theorem

Hallie Bennett

EDMA S657

Lesson Plan

20 June 2013

Lesson Title: Triangles and the Pythagorean Theorem

*Note: For this lesson students can do work by hand or with a calculator depending on their ability level and accommodations on their IEPs.

State Standards:

M5.2.1 Identify and compare various triangles and quadrilaterals according to their sides and/or angles. (Review standard)
5] G-1 using the attributes and properties of angles and the number, length, and orientation of sidesto identify or compare triangles (scalene, isosceles, or equilateral) or quadrilaterals (parallelograms, trapezoids, rhombi) (M5.2.1)
[4] G-1 using the attributes and properties of angles to identify and compare triangles (acute, right, or obtuse) and regular polygons (M5.2.1)

M2.4.4 Use indirect methods, including the Pythagorean Theorem and right triangle trigonometry, to find missing dimensions.

[9] MEA-2 applying indirect methods, such as the Pythagorean Theorem to find missing dimensions in real-world applications (M2.4.4)

Cultural standard that teacher will meet: Culturally responsive educators use the local environment and community resources on a regular basis to link what they are teaching to the everyday lives of the students.

-Provide integrated learning activities organized around themes of local significance and across subject areas

Lesson Objectives:

Students will be able to correctly use the Pythagorean Theorem to determine the missing side lengths of a triangle.
Students will understand that the Pythagorean Theorem can only be used with right triangles.
Students will know how to take information from a word problem to use to find the missing side of a triangle.

Anticipatory Set:

Introduce standards and objectives for the day
Display the standards and objectives for visual learners
Verbally read the standards and objectives for auditory learners
Access prior knowledge about triangles and Pythagorean Theorem by handing out different size triangles for students to work with and by asking the following questions: (post on the board)
How many sides does a triangle have?
How many degrees do the angles of a triangle add up to?
Can you name some triangles or angles of a triangle?
Can you name the special triangles?
Do you know how to determine the missing angles or sides of a triangle?
What is the Pythagorean Theorem?

After you give students the triangles, and read and post the questions above, give students time to think about the questions and the triangles they have to help them recall information they may know about triangles. As students come up with information, have them record that information on the whiteboard for the “Graffiti Wall” (5-10 minutes)
After 5-10 minutes depending on how students are working, bring the class back together for a group discussion. Redirect students to the questions above, and have students raise their hands to answer the questions. If new information is presented during the discussion that was not recorded on the “graffiti wall” add it as it comes up. (Make sure to keep this wall for the end of the lesson as well)

“I do” (Model)

After the anticipatory set, remind students about the standards and objectives for the day. Remind students that today we will be using the Pythagorean Theorem to determine the missing sides of a triangle.
Display a right triangle on the SMARTBoard. Label the sides A, B, and C (C being the hypotenuse/longest leg of the triangle).
After displaying the triangle, also display the Pythagorean Theorem equation next to the triangle (a^2 + b^2 = c^2).
After recording both, explain to students that this equation is used to determine the missing sides of a right triangle. Also, explain to them that the variables in the equation refer to the matching variables recorded on the triangle. (After you have said this to the class, have some students relay the information back to you by calling on those who are raising their hands, or by using the helping sticks).
After students have repeated the information, present a right triangle with numbers recorded for sides A and B.
After you have displayed the triangle, with the labeled sides (shown below), demonstrate to students how to plug the information we know into the Pythagorean Theorem and record it on the board (3^2 + 4^2 = c^2)
Show students how to solve the problem to determine the missing side.
3^2= 9 (9 + 4^2 = c^2)
4^2 = 16 (9 + 16 = c^2)
9 + 16 = 25
c^2 = 25
√25 = 5
c= 5
After you have demonstrated to students how to solve the problem, and you have determined the answer, record it on the side that is labeled C.
After you have done this, ask students if they have any questions. Also, have students repeat the steps needed to determine C.

After you have completed the first example, go through another example with students following the same procedure as before. (c= 13)

After you have completed the 2nd example, explain to students that we are going to take our learning one step further by incorporating word problems into our lesson. Following the steps above, show students how to complete a Pythagorean Theorem problem when having to take the information from a word problem. Let students know that they get the information they need from the word problem, and that they should try and picture the scenario in their head. Let them know it may be helpful to label the picture, like below.
It’s bird-hunting season in Stebbins. Two hunters went out in hopes of finding bird that they could bring home for their family to eat. One hunter came across a bird that was 9 feet up in the air. He was 12 feet away from it on the ground. At what angle does the hunter have to aim his gun, in order to successfully hit the bird? (Place Based Problem) (c= 10)

After you have completed the 3rd example, again have students retell what steps you took to solve for C. If students seem to have a grasp of how to solve for C then move onto guided practice. If students still seem to be struggling, continue to do the “I do Model” until students have a better understanding of the concept.

“We do” (Guided Practice)

After the “I do” section, move onto the guided practice. Explain to students that we will continue to work on using the equation, a^2 + b^2 = c^2 to determine the missing side of the triangle. However, this time we will work together, teacher and students, to solve the problems.
Display a triangle on the board with values plugged in for sides A and B. Also display the Pythagorean Theorem.
After displaying the triangle and equation, ask students what the first step in solving for c is. (The students should say plug in the information given into the equation- 9^2 + 12^2 = c^2) (Make sure to record student responses as they give them)
After this step-guide/ask students what step is next (square the two values-81 + 144 = c^2)
Again ask for the next step- (add the two square values together and have it equal to c^2) (225 = c^2)
Next step: Take the square root of both sides to determine the value of C. (15).

After students have completed the first problem with the help of the teacher, follow the same procedure as above and complete a second problem together.

(c = 17)

Now, follow the same steps as above for the word problem. Remind students that they get the information they need from the word problem, and that they should try and picture the scenario in their head. Let them know it may be helpful to label the picture, like below.
A ladder is leaning against the side of a building and is positioned so that the base of the ladder is 21 feet from the base of the building. The height of the building is 28 feet. What is the length of the ladder leaning against the side of the building? (Answer: 35 feet)

Ground (B)

After you have completed the 3rd example, have students restate what steps you took to solve for C. If students are able to recall the steps, and have demonstrated a good understanding of the steps throughout the guided practice and I do section, then move on to the independent work. If many students are struggling, continue to work on guided practice or go back to the I do model. If only a few students are struggling, work with those students individually to help them understand the concept, when other students move on to independent practice.

“You do” (Independent Work)

After the guided practice section, students will work independently on the following problems that use the Pythagorean Theorem.
(c= 10)

(c= 25)

In the village of Stebbins, a new store is being built. To comply with the law and to assist those community members that have a hard time with stairs, a ramp will be built. The ramp will have a length of 9 inches from the ground up to the entrance of the store (Side A). The length of the bottom of the ramp will be 12 inches (Side B). Can you determine the number of inches for the side of the triangle that will serve as the ramp (Side C)? (Place Based Problem) (C=15)

After students have finished the problems on their own, they will raise their hand to have their problems checked. If their answers are correct, they may go around and help other students. If there are problems that need to be fixed, have the students go back and fix those parts. After they have finished they can have them checked. (After the students get their problems rechecked-have them explain, where they may have made their mistake-this will help prevent them from making it again)
After all students finished, go over the problems as a class.

Closure

After students have completed the independent practice and you have gone over them as a class, wrap up the lesson with a review of the objectives and standards to ensure that they have been met. In the review, students should recall the steps needed to find the missing side of a right triangle using the Pythagorean Theorem. After the review, students should add any additional information they learned about triangles or the Pythagorean Theorem to their “Graffiti Wall” that they started at the beginning of the lesson. After the review, explain to students that tomorrow we will continue working with the Pythagorean Theorem and how it relates to our own lives. Before students leave, they should complete an exit slip stating or showing at least two things they learned today during the lesson.

Summative/Formative Assessments

Formative assessments will occur throughout the lesson through observations made by the teacher. This assessment will also take place when students are brainstorming the prior knowledge questions, when adding information to the graffiti wall, and during guided practice as students answer questions and participate in solving problems for C. Students will receive participation points for participating in class and for finishing their independent practice and exit slip.

Farther into the unit, students will complete a Glogster or other technology piece, depending on needs and ability level as a summative assessment to assess what the students have learned about triangles, Pythagorean Theorem, and how it all connects to real life.