Lesson 1: Constructing Quadrilaterals 1
(ideal for a 60-70 minute class period)
Intermath Task
Given two parallel lines, draw two more lines that intersect the two parallel lines,
forming various four-sided figures. Place the mouse over the picture below for an
illustration:
Discuss the properties of the different quadrilaterals formed (e.g., relationships
between sides, among angles (acute, obtuse, right, measures, etc.), with diagonals,
etc.) . Find as many properties of the quadrilaterals as possible that hold whenever
the intersecting lines are moved. What happens when the black lines are no longer
parallel?
Essential Questions (rationale):
 What are polygons?
 What are four-sided polygons?
 What are parallel lines? What do they look like?
 What properties are shared among the various quadrilaterals? Compare/Contrast
Intermath Alignment:
This task allows my students the opportunity to explore the properties of quadrilaterals
through constructions. Rather than relying solely on a textbook or a worksheet, I’m using
Intermath to provide them a lesson that incorporates Geometer’s Sketchpad
investigations. Students will brainstorm and make predictions on their own paper prior to
using technology. Students will use the features of GSP to accurately construct parallel
lines and equal lengths to illustrate the quadrilaterals.
Objectives:
Students will make predictions using graph paper and straight edges. Students will
construct various quadrilaterals and note their properties. After individual time, students
will join small groups to share their constructions. Finally, students will work with a
partner on Geometer’s Sketchpad to accurate construct their quadrilaterals (and look for
others that they may not have thought of).
Students have already worked with the term polygon, but it will be reinforced through
this lesson. It is imperative that students understand that polygons are simple, closed
figures whose lines do not cross. This information is valuable in their four-sided
constructions.
Assessment:
Informal – teacher will monitor and observe student progress; teacher will assist groups
as needed
Formal – students will print out their final products in GSP and write the shared
properties on the pictures
Reflection:
Students will be given a color (red, blue, green, yellow, or orange) upon entering the
room. This color is for the small group assignments. Students will be working with an
assigned partner on the GSP component. I will try to assign students with similar
abilities. Those that tend to do well on their own will be able to continue working.
Those that tend to struggle or need assistance will have me available. I want to avoid a
dominant person doing all the work.
Task Appropriateness:
I’ve adjusted the original Intermath assignment to meet the requirements of the sixth
grade curriculum. Our focus in sixth grade is the basic construction and properties of
quadrilaterals.
Task/Objective Alignment:
GPS
(note: with the new GPS, the standards are first addressed in fourth grade, but reinforced
in sixth grade as a preface to the sixth grade standards)
Multiple Representation: For additional practice and remediation, students will be
provided with colored thread and graph paper. Students are to use the graph paper and
thread to construct and label the quadrilaterals (after they have completed the GSP
component). Students are to use the colors to show how side lengths vary and/or to
show parallel sides. I added this portion to assist with the more kinesthetic learner who
needs to touch and feel it. The colored string was also added for visual learners.
PROCEDURES:
1. Distribute colored cards to students as they enter the classroom. (1 minute)
2. Review polygons as a whole class on the board. Discuss the properties of
polygons. (5 minutes)
3. Distribute graph paper to students. Allow time to construct quadrilaterals on the
graph paper. (8-10 minutes)
4. Have students join together in the colored groups. Students should share their
constructions and their descriptions. (8-10 minutes)
5. Call out (pre-assigned) partners and assign them to a computer station. Students
should know how to access Geometer’s Sketchpad from the desktop. Students
will work on GSP to construct their quadrilaterals. Students can print out their
final constructions. Teacher will monitor and assist as needed. (30-35 minutes)
6. Time permitting, students will go to the supply table to gather graph paper,
colored thread, and scissors for the remediation activity.
*This can be continued on the following day. (time remaining)