Quadrilateral Investigations using Geometer's Sketchpad

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Objective

SWBAT use Geometer's Sketchpad to investigate the properties of parallelograms.

Big Idea

Students work in groups to investigate properties of parallelograms and rectangles using dynamic geometry software.

Do Now

5 minutes

As students enter the room, I give them a small sheet of paper with quadrilaterals to cut out and to glue into their notebooks. On the sheet are a parallelogram, square, rectangle, and isosceles trapezoid. Students are instructed to identify which quadrilateral doesn’t belong with the rest and explain why they chose their answer (MP3).

After about 3 minutes, we go over the students’ responses. This question has multiple answers. Most students choose the trapezoid because there is only one pair of parallel sides. However, the parallelogram is the only quadrilaterals with diagonals that aren’t congruent.  When I call on a student for his or her answer, I ask the students to identify the quadrilateral by its type or its name using the vertices. This helps reinforce naming conventions learned in previous lessons (MP6).

While the students are working, I hand out laptops that my students will use for the next activity.

Reviewing Sketchpad Constructions

10 minutes

At the beginning of the mini-lesson, we review the names of the quadrilaterals from the Do Now. We then briefly review the definitions of the quadrilaterals. This leads into a discussion about parallel and perpendicular lines. We talk about ways of proving lines are parallel using their slopes, which will be needed for the activity.

I instruct students to open Geometer's SketchPad5 and I give them a couple of minutes to play around and re-familiarize themselves with the program. After two minutes, I ask the students to explain how to complete a few constructions using Sketchpad:

  • constructing parallel lines
  • perpendicular lines
  • midpoints

Then we review how to change from segments to lines and label items (MP5).   

Before we begin the activity, I ask if the students have any other questions about the program. Then, I hand out the worksheet and explain the next activity.

Activity

23 minutes

For this activity each group has at most four students with two computers. Two of the students in each group work on Investigation A and the other two students work together on Investigation B. Investigation A involves the properties of a parallelogram. Investigation B involves the properties of a rectangle. Although I have enough computers for my students to work independently, I find that by pairing them they share ideas more effectively and they help each other use the computer program more efficiently.

Students follow instructions and answer guiding questions on a worksheet. The questions lead the students to discover the properties of the quadrilateral they are investigating. As they work, I circulate and check their sketches. I see if the sketches pass the drag test. I drag the vertices and lines of the diagrams to see if they maintain the properties. Students often draw lines that look parallel instead of constructing lines that are parallel. The more often we use Geometer’s Sketchpad, the better students get at using the program. After 10 minutes, each partnership will share their sketches and discuss the properties with the other pair.

After 10 minutes, the students stop working. Students working on Investigation A share their sketches with the other students in their group, who take notes on the properties their group members have discovered. Then, after 5 minutes, the students switch roles. For the last five minutes, we share out as a whole class. I call on some students to describe the properties for each shape to ensure we have covered all of the properties. These properties will be used in later lessons to write proofs involving parallelograms and other quadrilaterals. 

Summary

5 minutes

At the end of the lesson I hand out today's Exit Ticket. Students are given a statement and asked to write an explanation of why it is true:

Ms. Laks says that a rectangle is always a parallelogram, but a parallelogram isn’t always a rectangle.

Based on the investigations from the lesson, students come up with answers, such as, “Rectangles have two sets of parallel lines and two sets of perpendicular lines, but parallelograms do not have to have two sets of perpendicular lines” or “Rectangles are parallelograms with congruent diagonals.” When the students finish, I collect their Exit Ticket.