Special Parallelograms

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SWBAT define rectangles and rhombuses and apply knowledge of their distinguishing properties.

Big Idea

Dare to be extraordinary...In this lesson, students learn about the definitions and properties of special parallelograms

Concept Development

15 minutes

This lesson expands on a previous lesson, Definitions and Properties of Parallelograms. In this section of the lesson, I lead students through the Special Parallelograms Definition and Properties presentation.

As I go through the presentation, I keep the following learning targets in mind:

  1. Students will be able to explain the concept of inheritance as it relates to rectangles and rhombuses being members of the parallelogram class.
  2. Students will be able to recite the definitions  and distinguishing properties of rectangles and rhombuses.
  3. Students will be able to make relational statements based on their interpretations of the distinguishing properties of rectangles and rhombuses.

Teacher's Note: There are several slides in the presentation labeled Student Talk. I use these slides to check for student understanding and to give students opportunities to rehearse the actions identified in the learning targets. My students are arranged in A-B pairs and partner talk is a regular part of our classroom culture. Typically, I give a prompt, assign roles for A and B partners, set the time parameters and then let students talk. After students talk, I either provide a summary of the ideas that should have been discussed or I call on random non-volunteers to share what they have discussed with their partners. My goal is to increase student engagement with the mathematical ideas and to develop students' reasoning and communication skills.

Guided Practice

20 minutes

In this lesson, my goal is for students to internalize the properties covered in the opening section. With this goal in mind, I give students an opportunity to assess what they have retained from my opening presentation. As I hand out Definitions and Properties of Parallelograms Table, I ask my students to put their notes just out of sight. I say, "Your notes and resources will be there if you really need them...", but I challenge my students to use their notes only as a last resort. I say, "Try to recall facts or try to reason towards a definition based on what you know to be true."

Item #1 on the handout requires students to recall the definition and properties of parallelograms. While I expect students to know these, I do not take it for granted. I begin by giving students 30 seconds private thinking time to recall the definition of parallelogram. Then, I have each A-B student pair play rock, paper, scissors to determine who will recite the definition. After the recitations, I write my definition under the document camera for students to see.

Next I give the students 30 seconds of think time to recall the four properties of parallelograms. When my students appear ready, I'll call a random non-volunteer to nominate one of the properties. If, for example, the property is "opposite sides of a parallelogram are congruent", I will ask another non-volunteer to explain the property using the diagram. Before setting them on their way to complete the task, I model how to fill in the first row of the table using precise language and notation, based on what students have shared so far.

Having oriented students to the task, I plan to give them 10 minutes to complete the rest of the handout. As they work, I will walk around the room making sure that students are using precise language and notation. After the 10 minutes have elapsed, I will reveal the correct answers under the document camera (see provided key). I will also discuss any common misconceptions or errors I observed or heard while walking around the classroom.

Next, we will be doing some comparing and contrasting of different types of parallelograms. Comparing and contrasting is a good strategy for deepening understanding. I'll display Double Bubble Map_Rectangular vs Non-Rectangular using the document camera. As I do, I explain that that the central bubbles are for the common characteristics and the peripheral bubbles are for the characteristics that belong to only one of the classes. I then give students 5 minutes to complete the handout. When the 5 minutes have elapsed, I call on a series of non-volunteers to share one thing they put on the thinking map. As necessary, I clear up misconceptions and add any important characteristics that students do not mention.

After that, I give 5 minutes for students to complete the Double Bubble Map_Rhombus vs. Non-Rhombus. When the 5 minutes are up, I have students exchange papers with their A-B partners to see if they gain any new perspective. Then I put my version of the [completed map] under the document camera for students to see.

Independent Practice

25 minutes

Now I will ask my students to apply what they've learned by measuring and creating figures. Verify Definition and Properties of Rhombus and Rectangle by Measuring asks students to verify definitions and properties via measurement. In order to verify by measuring, students must know exactly what to measure; they won't succeed if they've merely memorized the words (MP7). I find that this activity often reveals learning gaps or misconceptions. If they do not arise, it helps to confirm that my students have internalized the concepts. 

Similarly, asking students to create figures to specifications requires students to apply concepts and pay attention to precision (MP6). With this in mind, I give students the Create Venn Members handout. I intend for the directions to be unambiguous and self-explanatory. I don't do much in the way of answering questions or providing clarification. I do walk around the room challenging students explanations of why a figure belongs in a particular region on the Venn diagram. When I do this, I'm assessing students' ability to construct a logical argument, and I'm modeling for them how to critique the reasoning of others (MP3).

As students complete the Venn Diagram task, I give them some Special Parallelograms Problem Solving work to complete as Independent Practice. As students are working on problems, I walk around asking questions that help students to make sense of the problems. I also focus their attention on how concepts from today's lesson can be applied. I don't plan to go over all of these problems. As necessary, I will model the problems that gave students the most trouble, either today or in a later lesson. I do plan to use Geometer's Sketchpad to show students a way of looking at item #6.  The demonstration would be similar to what you'll see in the video below. Check it out!