Interior/Exterior Angles

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Objective

SWBAT find missing angles interior and exterior angles using triangle and straight line relationships.

Big Idea

Students work in groups of 4 with a coach to help complete practice problems

Do Now

10 minutes

Students enter silently according to the daily entrance routine. In this assignment students will review proportions to find a missing angle, and area of a circle.  As we get ready to work with angle measures inside and outside of a shape, I make sure to warm up with similar geometric problems. Question #2 requires student identify which parts represent the area we need to calculate and which are not.  

For Question #1 I make sure to copy the triangles on a SMARTBoard document. On this document I am able to rotate and flip the triangles to show them that we DO have enough information to find the missing angle. When reviewing this problem, I also push students to use the equation to show the work. Many students are resisting showing the work this way, instead opting to show the addition and subtraction steps as separate vertical algorithms. I push students to show the work using algebra and a horizontal equation, so that they can continue to build on their understanding of algebra.

This algebraic form of showing work should also help students understand the steps take to answer the second question. Students’ equations should show the separate areas of the square and the circle being subtracted, and they will be asked to explain why the subtraction step is necessary.

 

Class Notes

15 minutes

After reviewing the answers to the Do Now, students are given Class Notes. Today we will review angle on the interior and exterior of a polygon when one side is extended. The picture at the top of the class notes is meant to be used to label interior vs. exterior angles.

For this particular lesson, it’s important to notice students who do not understand how to label angles. Sometimes, when labeling angles with arcs, those who are confused will ask, “why do you draw that there?” These students are either having a hard time understanding what is being measured and/or where the angles are actually located. For a lesson that distinguishes between interior and exterior angles, is it very important to catch these misunderstandings and clear them up as soon as possible. Using programs like Google’s free “GeoGebra” app or the more costly Geometer’s Sketchpad, students can see different examples of angles including those larger than 180 degrees.

 

Students must include the definitions for the following terms in their notes:

Linear pair: a pair of adjacent angles formed by two intersecting lines; their measure is 180 degrees

Adjacent angles: a pair of adjacent that share a common side and vertex

 

Students will also be identifying liner pairs in the example at the end of the notes. There is enough information to label all angles. Students will be working in groups of 4 to find the measures in a competition of speed and work shown. Students must find all the angles and show the work in a comprehensive way. If they do so, they receive a piece of chart paper to display the measurements of all the angles in this example.  We vote at the end of class on the winners; they receive a homework pass. 

Class Work

20 minutes

For the first couple of minutes of this section, most students will be working silently on the class work. They will be asked to prepare themselves to solve by reviewing each problem in the sheet, noticing the following:

  • What information are you given?
  • What information are you asked to find?

During those first few minutes, I will pull 5-6 students helpers/coaches. I will be instructing them to go outside of the class to work together to solve the problem I give them on an index card. One student must write down the work, neatly showing their steps to solve. They will be given 7 minutes to solve together.

This task, I explain to them, is meant to prepare them to help other students with solutions and vocabulary used when solving the class work problems. I urge them to work together asking and answering as many questions as possible to be ready for what other students may need help understanding.  

I will be working to show the rest of the class a few of the first examples in the classwork. Those who are able to show focus will be allowed to choose a coach to work with after that group of kids is done with their sample problem.

When the student coaches come back to class, I will check over their answers to ensure sound work, procedures and solutions. Then, I will separate them into our booths to coach any student who chooses to visit that coach. I will remind them to push their teammates to identify linear pairs, and encourage them to use the proper other key terms (adjacent, supplementary angles). Lastly, I will ask them too look out for students who may not remember that there are 360 degrees in a quadrilateral. There will be a 4 student limit per coach and some students may need to be persuaded to work with me instead.

While groups of students are working together, I will have individuals put up answers on the chalk board or a piece of chart paper. We will review these solution during the last 5 minutes of this section, giving students a final opportunity to ask questions.

 

Closing

10 minutes

After reviewing the answers to the class work and answering questions, students will complete an exit ticket. As the year comes to a close, we are struggling with some apathy and freeze moments. Students who are frozen in place, not completing work, under the excuse, “I don’t get it”. These students will be pulled into small groups, not in a punitive manner, but instead this will be framed as an opportunity:

  • I’m sorry you’re feeling frustrated/stuck. Why don’t you come sit over at this group so that we can complete the exit ticket together?
  • Would you rather work with a small group to solve?

I’m ok with students working together because I would prefer they are actively gaining more information about a problem rather than spending 10 minutes staring at a sheet of paper, giving me data I already know. It helps the student feel as though learning is more important than what an individual can or cannot do at any given moment. By pushing students to continue trying to understand we are also practicing MP1