Triangles

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Objective

SWBAT classify triangles by their sides and angles.

Big Idea

Triangles can be identified as acute, right, or obtuse.

Opener

5 minutes

In today's lesson, the students identify triangles by their attributes. This aligns with 4.GA.2 because the students will classify two-dimensional figures based on the presence of angles of a specified size. 

 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 in the classroom with these types of angles. After they have thought for a minute I ask them to share their ideas with their 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.  Today, we learn to identify triangles by their lines and angles.

Whole Class Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion.  The Triangles powerpoint is already up on the Smart board.  I like for my students to be near so that I can have their full attention while I'm at the Smart board.  

This lesson is dealing with triangles.  We've learned about different angles and types of polygons.  Is a triangle a polygon?  One student said no.  I ask him to tell me why.  He could not tell me why he thought a triangle was not a polygon.  I call on a student to tell me why she said yes.  "It has sides."  Another student adds, "It is closed and has straight lines."  I agree with the students and let them know that because it is made up of line segments, and it is a closed two-dimensional shape, it is a polygon. I remind the students that they drew a triangle for one of their polygons on the activity the previous day.  

We're talking about a specific polygon today.  We have different types of triangles based upon the length of the sides and the measurement of their angles.  What are angles?    Student responses:  two rays make an angle, the lines meet and form corners, obtuse angles are greater than a right angle but less than a straight angle, right angles are always 90 degrees, and acute angles are less than a right angle. 

We review the Vocabulary on the Smart board.  I say the word, then the students repeat the word. We discuss each vocabulary word.  The students learn the meaning of equilateral, isosceles, scalene, right, obtuse, and acute triangles.   

Vocabulary:

Equilateral - all 3 sides are the same length

Isosceles - 2 sides are the same length

Scalene - All sides are different lengths

These vocabulary words are based upon the sides.  

Right triangle - One right angle

Obtuse triangle - one obtuse angle

Acute triangle - all 3 angles are acute

These vocabulary words are based upon the size of the angles.

I share with the students that they will be practicing drawing triangles with a partner.  We are using rulers for this lesson.  If you are drawing an equilateral triangle, you have to make sure that all of the sides are the same length.  So, use the ruler to draw each side the same length.  

Students will practice drawing triangles with a partner.

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 Triangle Group Activity Sheet, textbook, and a ruler.   The students must work together to draw models (MP4) of each type of triangle  using the textbook as a resource.  They must use the ruler to measure the length of the sides.  They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem.

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 (MP3).  From the Video on Triangles, 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 type of triangle is this?  How do you know?

2. What type of angles do you see?

3.  What are the measurements for each line segment?

As I walked around the classroom, I heard the students communicate with each other about the assignment.  From the video, you can hear the classroom chatter and constant discussion among the students.  Before Common Core, I thought that a quiet class working out of the book was the ideal class.  Now, I am amazed at some of the conversation going on in the classroom between the students.  

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.

Closure

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 (Student Work on Triangles.jpg), 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.  

 

Misconception(s):

Area(s) that need more practice:  Telling the difference between a scalene and isosceles triangle.  I will continue to provide the students the opportunity to work on and discuss triangles.