Measuring Angles

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SWBAT draw and measure angles.

Big Idea

Angles can be drawn and measured using a protractor.


5 minutes

In today's lesson, the students measure angles in two-dimensional shapes. This aligns with 4.GA.1 because the students will draw angles, and 4.MD.C6 because students measure angles using a protractor.

 To get started, we review the definitions for acute, right, obtuse, and straight angles.  This allows me to make sure the students understand the differences before we begin the lesson.  I ask the students to name things that have angles and to describe the angles.  "Think about it for a minute."  I like to make sure that my students actually think about the question before they answer.   "Share your ideas with your neighbor."  By doing this it allows students to share their way of thinking, as well as it may help some students who do not know how to come up with the answer.  I take a few student responses.  Some student responses:  a book has right angles, door has right angles, and a clock can have any type of angle depending on the time. I tell the students, "Today, we learn to measure angles in two-dimensional shapes."

Whole Class Discussion

15 minutes

Our lesson for today is measuring angles.  "How many rays will it take to form an angle?" I call on one student who has been having difficulty in math this year.  It was disappointing that he could not answer the question because we had just discussed this minutes earlier when we reviewed the vocabulary.  I call on another student to help him out.  She responded, "Two."  I let her know that she is correct.  I tell the students that in order to form an angle, those two rays must have something in common.  "What must they have in common?"  I let the students think about it for a few minutes.  This proved to be a little difficult for the students to understand.  Therefore, I drew a grid on the board to show the students.  From my model, the students saw that they must have the same end point.  

We are going to learn to measure angles.  In order to measure angles, we must use a protractor.  Angles are measured in what's called degrees. (I demonstrate how to write a degree symbol on the board.)    Let's review for a minute.  What are the types of angles we discussed yesterday?  The students name the angles:  acute, right, obtuse, and straight.  One student said a line segment.  I had to remind the students that a line segment is part of a line, it is not an angle.  

"What do we know about a right angle?"  The students says that it can make a square corner.  I let the students know that all right angles are 90 degree angles.  When we went over the definitions for the angles, if you notice, they referred back to the right angle.  An acute angle is smaller than a right angle.  An obtuse angle is greater than a right angle.  So if you know the right angle is 90 degrees, then you should be able to identify other angles by their degrees.    For example, an 85 degree angle is an acute angle because it is less than a right angle.  "Can you name other measurements for an acute angle?"  I went around the room calling on students to give me a measurement for an acute angle.  Some numbers the students called out are:  35, 16, 15, 26, 45, 20, 30, 50, 70, and 89.  Next, I explained to the students that a straight angle is always 180 degrees. Therefore, an obtuse angle is greater than a right angle but less than a straight angle.    I asked students to give me numbers that would represent an obtuse angle.  Some of the students' responses:  135, 100, 130, 140, 107, 170, 150, 179, and 91.

I demonstrate measuring the angle with a protractor on my Smart Board.  I show the students how to line the circle in the center of the protractor on the vertex.  For example, the angle I drew on the board was angle ABC.  I let the students know that "B" is the vertex.  It is the point that each ray has in common.  "When you measure angles,  there are two numbers that the angle will cross.  If it is an acute angle, use the smaller number.  If it is an obtuse angle, use the larger number."

I give the students practice on the skill by letting them work in groups.

Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others.

For this activity, I put the students in pairs.  I give each group a Group Activity Sheet on Measuring Angles, Dot Paper, and a protractor (MP5).   The students must work together to measure angles.  They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem.  The dot paper is an important part of the lesson because it will allow the students to draw the angles precisely as possible.

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  From the video, you can hear the students discuss the problem and agree upon the answer to the problem.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill.  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1. What is measurement of the angle?

2. What type of angle is this?  How do you know?

3. Explain the difference between a right angle and an obtuse angle.

My Observation(s):

Because this is a new skill, the students needed guidance on using the protractor.  In some groups, there was at least one person who could place the protractor on the angle correctly in order to measure it.  However, there were a couple of groups that I worked with directly on lining up the protractor on the angle.  As I walked around the room to question the students, I guided some of the students to the correct measurement by asking, "What type of angle is this?"  After the students identified the correct angle, then my next question was, "If it is not a right angle, then is it greater than a right angle or less than a right angle?"  This type of questioning helped lead the students to the correct number to use on the protractor.

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing.


15 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.  

Overall, the students did as well as I expected them to do.  With this being the first time for them to use a protractor, I was pleased with the outcome.  From the sample of student work, you can see that this pair of students identified the angles correctly.  The dot paper helped the students draw the lines of the angles almost perfectly.   Of course, we will continue to work with using protractors in small group or centers.