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This lesson provided by:
Author:Jenny Hornby
System: Huntsville City
School: New Century Technology High School
Lesson Plan ID: 23995



This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

Content Standard(s):
MA2015(8) 23. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8]
MA2015(9-12) Algebra20. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [A-REI6]
MA2015(9-12) Algebra24. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. [A-REI12]
MA2015(9-12) Geometry1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1]
MA2015(9-12) Geometry9. Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [G-CO9]
MA2015(9-12) Geometry11. Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [G-CO11]
MA2015(9-12) Geometry30. Use coordinates to prove simple geometric theorems algebraically. [G-GPE4]
MA2015(9-12) Geometry31. Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
MA2015(9-12) Geometry33. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [G-GPE7]
MA2015(9-12) Geometry34. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)
Local/National Standards:

NCTM Standards Apply appropriate techniques, tools, and formulas to determine measurements. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Primary Learning Objective(s):

Students apply formulas to classify quadrilaterals. Students will calculate distance between two points, midpoint of a line segment, slopes of lines, write equations of lines, solve linear systems, systems of linear inequalities, classify quadrilaterals and verify solutions to linear systems. AHSGE IV – 2 Find the distance, midpoint, or slope of line segments when given two points. d. Determining slope of a line given a line on the coordinate plane with two points on a line on the coordinate plane without any coordinates labeled V – 1 Graph or identify graphs of linear equations. II –3 Solve systems of two linear equations. The following may be required: a. Solving for the values of both x and y b. The options may be four graphs with lines plotted and the intersection point labeled with its ordered pair. IV – 1 Find the perimeter, circumference, area, or volume of geometric figures.

Additional Learning Objective(s):

When used at the end of Algebra 1 this project not only reviews half of the course of study objectives for algebra and many AHSGE objectives it allows students to discover the properties of quadrilaterals and become familiar with some of the vocabulary of geometry. Although comfort with math is not a learning objective it does enhance learning. Algebra students feel more comforable with geometry. This lesson may be used in geometry to explore properties of quadrilaterals and parallelograms using algebra. It prepares students for coordinate geometry topics covered later and in other courses.

Approximate Duration of the Lesson: Greater than 120 Minutes
Materials and Equipment:

Pencil, paper, grid paper, and poster sized grid paper.

Technology Resources Needed:

Printable grid paper, reproducible. Classification of Quadrilaterals and animation.


This lesson reviews algebra topics. Provide students with hand outs that have formulas. The reference page of the AHSGE provides students with all necessary background information. Completion of the project allows students to apply the formulas.

1.)I. Download student sheets and teacher sheets.

2.) Plot the points Q,U, A, and D on grid paper. Label the points with the correct letter and ordered pair. These points are called the vertices of the quadrilateral.

3.)With a straight edge draw line segments between each pair of points.

4.)Find the length of each segment using the distance formula. Simplify all radicals and approximate your answer to the nearest hundredth

5.)Find the midpoint of and using the midpoint formula. Label the midpoints M, N, O, and P respectively. Write the ordered pair next to the midpoint of each segment.

6.)Find the equation of the lines containing Q, U, A, and D. Write your answer in slope intercept form and in standard form. Show that each vertices is the intersection of two line segments by solving the linear systems.

7.)Find the slopes of the sides of QUAD. Verify that the slopes of the lines between the vertices of the quadrilateral by comparing it to the equation of the line segments.

8.)Determine if any two pair of lines are parallel or are perpendicular. Explain how you arrive at your answer.

9.)Draw diagonals from opposite vertices. Label the point that the diagonals intersect Z. Write the ordered pair for this point. Determine the midpoint of and each diagonals. Find the length of the diagonals using the distance formula.

10.)Classify QUAD as accurately as possible using the definitions of the quadrilaterals. You may use the link provided.
(quadrilateral lesson)

11.)Estimate the area of QUAD. Determine the area as accurately as possible. Explain your method and any formulas that you used.

12.) Review student work and provide feedback on Part I. Group students with the same quadrilateral. Allow students to complete I for homework so all groups will begin part II on the same day.After students complete Part I group them with students who have the same quadrilateral. Students should agree on solutions and work cooperatively. Begin Part II.

13.)Draw line segments connecting the midpoints (M, N, O, and P) of the quadrilateral QUAD. Using the coordinates of the midpoint.

14.)Find the lengths of the line segment sconnecting M, N, O, and P.

15.)Find the slopes of each of these line segments.

16.)Determine which of these line segments if any are congruent, parallel or perpendicular.

17.)Draw diagonals connecting the opposite vertices.

18.)Find the midpoint of the diagonals. Label it C. Which of the segments have the same length? Explain the process you used to determine your answer.

19.)Are the diagonals the same length, perpendicular or parallel?

20.)Classify the quadrilateral MNOP as many ways as possible. Justify your answer. you use the animation provided at the link provided.
(Quadrilateral Animation)

21.)Which pairs of triangles are congruent? Write a proof for at least one pair of triangles. This step is intended for Geometry classes only.

22.)Find the midpoints of the sides on MNOP. Label them H, J, K, and L. Make an hypothesis about this quadrilateral and quadrilaterals in general

23.)Prepare individual report. Submit individual reports paper clipped to group members. Download guidelines document.

24.)Present posters. Have students write down properties all QUAD(quadrilaterals) have in common. Have students write down all properties of MNOP(parallelograms) in common. List the properties of the the diagonals of the different quadrilaterals (QUAD).
(quadrilateral lesson)
Students should complete online lesson and take true/false assessment.

25.)Complete group evaluation. Students should research Quadrilaterals on the Internet. Students select a quadrilateral and research its properties.

Attachments:**Some files will display in a new window. Others will prompt you to download. Grading guidefor alex.rtf
quadproject 08 student for alex.rtf
project self-critiques j.rtf
Investigating Quadrilateralsalex.rtf
quadproject 08 teacherpagesforalex.rtf
Assessment Strategies:

Informally assess students as they work individually on Part I. Offer feedback if disagreements can not be resolved. As students complete Part II, provide feedback and encourage students to make conclusions. Assess student work for completeness. Student work should be accurate. This project takes considerable time to complete and many opportunities arise to determine strengths and weaknesses on an individual basis. Your assignment of specific quadrilaterals can be designed to provide peer tutors. When assigning QUAD, assign strong and weaker students same quadrilateral. Most of student work will be correct by the time their individual reports are turned in. The posters should reflect the properties of the different quadrilaterals.


This lesson can be extended to include formal proofs in geometry or have students justify the properties of parallelograms using coordinate proofs.


Select simpler quadrilaterals for weaker students. Students find it easier to work with rectangles. If this lesson is used at the end of Algebra 1 or Algebra 1B, all the activities are review activities and are tied to linear algebra. The time required for this project could be as much as two weeks for weaker students or as little as two days for Honors Geometry. This lesson provides opportunities to apply algebra to geometry and is excellent preparation for coordinate geometry. Pair students to provide peer tutoring opportunities.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

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The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
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