These pages are dedicated to the teachers in I-MATH. In this course, the teachers each create a project for their students. The following is a project completed by one of our I-MATH teachers.

Geometry

Descriptive Course Data:

Teacher: Melissa Speetjens

Course: General Math &endash; 6th grade

Duration: 3 weeks

Unit: Geometry Introduction &endash; 6th grade

Introduction:

This study introduces students to the connection of art and mathematics by means of tessellation.

Unit Description:

Focusing on basic geometry, this unit presents a general review of prior knowledge. With this knowledge base, students learn the connection of art through a study of M.C. Escher and geometry through the recognition and creation of computer as well as hand-generated tessellation.

Rationale:

Middle School philosophy depends on integration of core curriculum. By weaving the connection of M.C. Esher's art, the historical perspective of WWII Europe in Social Studies, and tessellation in math, students experience this integration. The universal concept of diversity was the driving factor in the curriculum study. Actualization of real-life application of tessellation is crucial for student success as the realization that math needs to have a practical application is met.

Goals:

The teaching goals for this unit are:

1) Understand the concept of tessellation

2) Mathematical study of the art of M.C. Escher

3) Recognize and appreciate tessellation in various forms

4) Develop student ability to create an original tessellation

5) Develop "making a model" problem-solving skills further

6) Use technology to create tessellation

7) Provide experiences in cooperative learning

Objectives:

At the end of this unit, students will be able to

1) Explain the basic geometric concepts to include line symmetry, rotational symmetry, and point of rotation

2) Demonstrate skill in the recognition and reproduction of tanagrams

3) Demonstrate skill in transformation, translation, rotation, and reflection

4) Use technology to research tessellation

5) Use technology to produce tessellation

6) Recognize and appreciate tessellation in real-life experiences

7) Demonstrate skill in tessellation by creating a hand-drawn tessellation

8) Demonstrate cooperative group learning by forming a tessellation for classroom display in small group

9) Demonstrate understanding by journalizing

Materials needed for this Unit:

1) Textbook and Teacher's Edition Middle School: 1 Math Advantage (Harcourt Brace, 1999)

2) Access to computer lab for internet research

3) Access to Mighty Math Cosmic Geometry &endash; Tessellation Station (Harcourt Brace 1999 Technology Link)

4) Access to I-MATH files and chapters

5) Access to videos: The Life and Works of M.C. Escher, Tessellations: How to Create Them by Jim McNeil

6) Supplemental lab sheets for computer lab

7) Tangram puzzle (teacher generated on construction paper &endash; die cut available)

8) Teacher generated reference packet/book &endash; includes internet sites, quotes from M.C. Escher, tessellation guide

9) Pencils and notebook/notebook paper

10) Graph paper

11) Scissors

12) Rulers

13) Colored pencils or ink

14) Construction paper/glue

15) Tag board

16) Tessellation tiles if available

Assessment of student learning:

Preassessment: a preassessment project will be used to determine students' current knowledge of geometry. This includes a written skills test as well as manipulation of moving figures and lines of symmetry.

Formative: daily participation, daily review quiz for concept reinforcement, homework, completion of lab sheets, cooperative teams for in-class problem solving, pair share, and journal to include definitions, problem solving, and reflection.

Summative: teacher assessment of math journal, scores on test, lab completion, and cooperative qualities during small group. Culminating project includes sample of real life tessellation, computer generated tessellation, and hand-drawn tessellation. The class at the beginning of the project develops rubric for project. Teacher, peers, and student will evaluate this project. Students will average their own grades and set goals throughout the quarter.

Math Content Standards Connection:

Measurement:

1. Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools and formulas for measuring

Geometry and Spatial Sense:

1. Analyze properties of objects and relationships among properties.

2. Use transformations and symmetry to analyze mathematical situations.

3. Use visualization and spatial reasoning to solve problems both within and outside of mathematics.

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