Brian SarkozyMAT 529

Brief Overview

Purpose Students should understand and apply twenty essential geometric

terms Students should use application, analysis, synthesis and evaluation

processes Students should make connections to the real world

Focus Geometric shapes and spatial understanding activity Communication among students for analysis and evaluation of each

other

Audience 7th grade honors pre-algebra students from three middle schools Parents, students, teachers and community members on “Expo Night”

Standards

NCTM Standards Analyze characteristics and properties of two-dimensional geometric

shapes and develop mathematical arguments about geometric relationships Understand relationships among angles, side lengths, perimeters, areas, and volumes

of similar objects

Use visualization, spatial reasoning, and geometric modeling to solve problems Draw geometric objects with specified properties, such as side lengths or angle

measures Use visual tools such as networks to represent and solve problems Recognize and apply geometric ideas and relationships in areas outside the

mathematics classroom, such as art, science, and everyday life

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others Recognize and apply mathematics in contexts outside of mathematics

Standards

Connecticut Standards Classify and describe polygons and solids using defining characteristics

(MA8:6b, c) Draw geometric objects with specified properties, including angle

measure (MA8:6b) Examine the congruence, similarity, and line and rotational symmetry

of objects (MA8:6d) Investigate the relationship among the angles, side lengths, perimeter

and areas and volumes of similar objects (MA8:6d)

Key Points of Activity

First Requirement Study stained-glass designs from ancient history to present day Use online resources, library materials, and videotapes on artists Discover geometric configurations in cards and stationary, buildings,

artwork, furniture and wallpaper

Second Requirement Write a definition, find an example, draw an illustration, and determine

an application for each of the essential geometric terms The students were required to incorporate twenty terms, which were

given to them Various methods and formats were used when students created their

glossary of terms

Key Points of Activity

Examples of Stained-Glass

Key Points of Activity

Third Requirement Each student created their own original stained-glass-window designs

that incorporated the twenty geometric figures They drew blackline patterns on computer paper and made two copies This was their template, which they put under the glass of an 8inx10in

picture frame, painting the glass based on their pattern

Fourth Requirement Each student assessed another student’s work. Each student used the

given symbols to analyze, mark, and label the twenty required figures of one of their classmates blackline design, then wrote an evaluation of how the design met the requirements

The teacher evaluated each student’s work, as well as their assessments of each other

Key Points of Activity

Implementing Activity in the Classroom With prior knowledge of geometric shapes and similarities and

differences with them, students would be able to fully participate in the activity

To make it less time consuming, the first requirement does not have to be used

Over two days or three days, the students should be able to complete the other three requirements of the project

Instead of using paint and glass from picture frames in order to save on cost, students can use construction paper and markers or colored pencils

Additional information could be found for each object For each shape used within the twenty objects, students could be required to

find lengths of sides, perimeters and areas Each student could use their own numbers, making each project even more

unique

Other shapes can also be used, such as parallelograms and rhombuses

Is This Activity Useful?

Would the students gain the requirements of the given standards while participating in this activity?

Would this activity be something high school students would be motivated to want to do? Would they find it interesting enough to stay engaged?

What are some other ways this activity could be changed in order to make it more meaningful or more engaging for high school aged students?

Bibliography

Morris, Barbara H. The Beauty of Geometry. Mathematics Teaching in the Middle School, Vol. 9, No. 7, March 2004.