Classification of Quadrilaterals

Goal & Introduction

I began today's lesson by reminding students of our goal: I can classify 2D shapes by their properties. I explained: So far, you have learned that polygons are 2D shapes have straight sides and are closed figures. You have also learned that all 3-sided polygons are called... (Students: Triangles!) And that quadrilaterals are polygons with how many sides? (Students: 4!) And that pentagons are polygons with how many sides? (Students: 5!) And that hexagons are polygons with how many sides? (Students: 6!) Today, we are going to take a closer look at quadrilaterals!  

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. 

Getting Started

Prior to today's lesson, I printed this document: Quadrilateral Posters and created a poster for each type of quadrilateral. I wanted students to discover that some quadrilaterals, such as squares, can also be classified as a parallelogram, rectangle, and rhombus! Students would also be provided with further practice examining the properties of 2D shapes for classification purposes. 

I explained: Today, you will be investigating types of quadrilaterals on each of these posters. We will be rotating posters from one group to another. I will give each group a specific color marker, so if you get a red marker, you are the red group. Before recording your own thinking on each poster, take the time to make sure that comment hasn't already been made. Also, make sure you agree with all other comments and if you don't agree, explain why!

I wrote a List of suggestions on the board and continued: Here are some suggestions! You can make conjectures, ask questions, make comments, or record observations. For example, you might write: All kites have...

Constructing Viable Arguments

Just like yesterday's lesson, I purposefully created an open-ended investigation based on the question, What makes each type of quadrilateral special? This way, students would naturally engage in Math Practice 3: Construct viable arguments and critique the reasoning of others. They were determined to find the answer to this question on their own by investigating shape properties! 

Monitoring Student Understanding

While students were working, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Again... Math Practice 3). 

1. What have you noticed so far? 
2. Have are the properties of a rhombus?
3. Do you agree with other group's comments? Why or why not?
4. What argument can you make based upon the evidence gathered?
5. How is a rectangle different from a trapezoid?
6. How can you make this argument more precise?

Conferences

Here are several conferences that took place during this time: 

Making Connections with Isosceles Triangles: Here, I encourage a group to think apply their prior knowledge of isosceles triangles to help them understand isosceles trapezoids. 

Applying Learning from a Previous Poster: This is a short clip, but it captures students applying what they have learned from a previous poster!  

Adding on to Other's Comments: One of the hardest parts of this activity was when students had to read other's comments and decide whether or not they agreed. 

Looking for Parallel Sides: Here, I show students how to label sets of parallel sides. It's always tough for students to distinguish between 4 parallel sides and 2 sets of parallel sides. 

Making Revisions: Even though our focus is on math, I try to encourage complete sentences, correct spelling, and the use of more precise language. 

Squares vs Rectangles: These students examined the relationships between squares and rectangles.

Testing Other's Conjectures: I loved encouraging this group to test and modify other's conjectures!  

Student Work

Here's what the posters looked like after this activity! 

• Quadrilateral Posters
• Kites Poster
• Trapezoid Poster
• Isosceles Trapezoid Poster
• Parallelogram Poster
• Rectangle Poster
• Square Poster
• Rhombus Poster

Displaying Posters on Board

As we finished the exploration activity, I invited students to the front carpet and asked them to place all their quadrilateral posters on the front board using magnets. 

I also asked students to bring their math journals to take notes. I knew this would increase student engagement! 

Teacher Demonstration Poster

To help students organize their observations and categorize quadrilaterals by their properties, I printed this document, Teacher Demonstration Quadrilaterals, and created this poster, Teacher Quadrilateral Poster. Next, I colored around the edge of each group of quadrilaterals, Quadrilaterals Categorized by Color, to aid student understanding. 

Here's what the poster will look like at the end of this demonstration: Completed Poster.

Quadrilaterals

I asked: Based on your investigation today, what can you tell me about quadrilaterals? As the students commented, I labeled the poster: 

• Have 4 sides
• Polygons: 1. 2D shape, 2. Closed figure, 3. Straight sides only

Referring to each of the chart headings, I explained: What you need to know about quadrilaterals, is that some have 0 sets of parallel lines, 1 set of parallel lines, and 2 sets of parallel lines. I then held up each shape, one at a time and asked students which category it belonged in. Here's the result: Categorizing Shapes by Sets of Parallel Lines.

Labeling Kites

I wanted to begin by discussing and labeling the easier categorizes first, kites and trapezoids, before moving on to the most complex category, parallelograms. 

I asked: What are some properties of kites? Altogether, we labeled the kites with the following properties: 

• A kite always has one lines of symmetry.
• 2 sets of congruent sides that are adjacent (side by side). 

Trapezoids

We then discussed and labeled the properties of trapezoids:

• 1 set of parallel lines

And then isosceles trapezoids:

• 1 set of parallel lines
• Has one set of congruent sides
• Has one line of symmetery

Parallelograms

Next, we discussed and labeled parallelograms: 

• 2 sets of parallel lines
• 2 sets of of congruent sides 
• Therefore... all rectangles, squares, and rhombuses are parallelograms.

Rectangles, Squares, & Rhombuses

Finally, we differentiated between special types of parallelograms:

Rectangle

• Special kind of parallelogram
• Four 90 degree angles

Rhombus

• Special kind of parallelogram
• Has all congruent sides
• Can have two acute angles and two obtuse angles
• Also can have four right angles.... which is a square!

Square

• Special kind of rectangle
• Special kind of rhombus
• Four 90 degree angles
• All congruent sides

Final Graphic Organizer

To help students gain a deeper understanding of the categorization of quadrilaterals, l also drew a Graphic Organizer. Students also drew this graphic organizer in their notes.

1. First, I drew a large circle and explained, "All shapes inside this circle are quadrilaterals... or 4-sided polygons."

2. We have three groups inside the quadrilateral circle. One group has 0 sets of parallel sides. We call these kites.

3. Another group of quadrialaterals has one set of parallel sides. This group is called the trapezoids.  

4. Next, we have a group of quadrilaterals that has two sets of parallel sides. These are all called parallelograms. 

5. When a parallelogram has four right angles and at least two sets of congruent sides, we call these rectangles. 

6. When a parallelogram has four congruent sides, we call it a rhombus. 

7. Then, there's a square. A square is a special kind of rectangle because it has four right angles, but it also has four congruent sides.

8. A square is also a rhombus because any quadrilateral with four congruent sides is a rhombus. 

Practice Page

To provide further practice and to formatively assess student knowledge, I printed a shape classification practice page from Math-Aids.com. I reminded students: All shapes on your practice page could be identified as polygons. They could also be identified as quadrilaterals, however, I'm looking for you to identify the most specific classification possible. 

Conferences

Here are a couple examples of student conferences during this time. Here, I support a student with Identifying a Rhombus. 

Another student, Exact Classifications, made connections between the Quadrilateral poster and the figures on the page.