Quadrilaterals

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Objective

SWBAT identify quadrilaterals by the length of their sides and angles.

Big Idea

Quadrilaterals are four-sided polygons that have distinctive attributes.

Opener

5 minutes

In today's lesson, the students identify quadrilaterals 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 important terms we have learned that will help with this lesson.  This allows me to make sure the students have learned what they need for this lesson.  I ask the students to describe a line segment and right, obtuse and acute angles, sharing first with their neighbors.  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. Student responses:  line segments stop in both directions, acute angles are smaller than a right angle, right angles are 90 degrees, obtuse angles are larger than right angles.  Today, we learn to identify quadrilaterals by their lines and angles.

Whole Class Discussion

10 minutes

Our lesson for today is dealing with Quadrilaterals.  When we started working on polygons the other day, quadrilaterals was one of the shapes you had to draw.  We talked about the word "quad."  What does quad mean?  The students respond 4.  So a quadrilateral has 4 sides.  I let the students know that there are several types of quadrilaterals, such as a rectangle and a square.  What we're going to do today is identify some quadrilaterals by their characteristics or attributes.  

I'm going to give you an activity sheet.  It has the definitions for each type of quadrilateral in this lesson.  You're going to identify shapes that I have put in a bag based upon the definitions on the activity sheet. We have some new words in this lesson.  

Vocabulary:

Our first word is rhombus.  Let me hear you say the word.  A rhombus is a quadrilateral that has opposite sides that are parallel and all of its sides are the same length. It is a quadrilateral, so it has 4 sides.  The definition says that it has opposite sides that are parallel.  We talked about parallel lines at the beginning when we first started talking about geometry.  What are parallel lines?  I call on a student to respond.  She responds, "Lines that never intersect."  This means that they never meet.  Let's go back to the definition.  It says opposite sides are parallel.  You're going to have to extend the lines to see if they are parallel when you work on the activity.  

—A trapezoid is a quadrilateral with only one pair of parallel sides.  If you find a shape in your bag that only has one side that is parallel, then it is a trapezoid.  That means that the other two sides are going to meet some how.  In a minute, I'm going to show you how to figure out if sides will meet.  
A parallelogram has 2 pairs of parallel sides. On your shape, if you extend the lines and they do not meet on either side, then you have two pairs of parallel lines.  That shape is a parallelogram.  If it only has one pair of parallel lines, then you can not call that shape a parallelogram.
Some of the shapes in the bag will have more than one name.  You will have to determine, by the definitions, the name of the shapes. 

—A rectangle has 4 right angles. 

A square  has 4 right angles and all sides are the same length.  That is something you learned a long time ago.  

After discussing the vocabulary, I show the students how to determine if a shape has parallel lines. On the Smart board, I show a quadrilateral.  I let the students know that when I want to determine if a shape has parallel lines, I would take my pencil and extend the line.  

The shape in the power point is a rectangle.  I show the students how to extend the lines to determine that the rectangle is a parallelogram.  I also let the students know that a rectangle can be called a quadrilateral.  

I'm going to give you an activity sheet, ruler, and shapes.  Why do you think I am giving you a ruler?  One student responds, "If it is a square, you need to measure it to see if it is the same."  When you draw the shapes, I need to see you extend the lines to see if they are going to meet.  Using the definitions on the activity sheet, name the shape in as many ways as you can.

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 Quadrilaterals Group Activity Sheet, a bag of quadrilaterals, and a ruler.  (If you do not have the wooden geometric shapes, then you can cut out quadrilaterals for the students to use.) The students must work together to draw models of each type of triangle (MP4).  They must use the ruler to measure the length of the sides (students working).  Together, they determine the attributes of each quadrilateral.  From the attributes, the pair must identify the shape by as many names as possible.  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, 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 angles are there in this quadrilateral?

2.  Are there parallel sides?  How many?

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, 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):

I corrected several students on how they extended their lines to determine if the sides were parallel. In the sample of student work, you can see how the students extended the lines incorrectly on the trapezoid.  For some reason, several students thought that they were just to draw vertical lines on both sides of the shape.  I had the students go back and trace the sides of the trapezoid in the directions that the lines were going.  From that, they saw that the opposite sides of a pair of lines did meet.  We will continue to practice this skill of determining if lines are parallel.