GEOMETRY: AN INTRODUCTION

Knight Foundation Summer Institute

Pamela Barnes, Roosevelt Middle School

Jennifer Fisher, Bryn Mawr College

Introduction:

This is a lesson to be used shortly after a geometry unit has been started. To begin, the teacher can review a past mathematics unit and tie it into the new topic. For example, reviewing positive and negative integers using a ditto sheet that relates this topic to geometry would work well. This is done by forming a maze where the students have to add or subtract numbers from a total depending on what shape appears next in the maze (see attached sheet). While this activity reviews integers, it also allows the students to begin recognizing and distinguishing basic shapes. The lesson combines Reading, Language Arts and Social Studies with Mathematics, more specifically geometry.

Pre-Skills: I

  1. Positive and negative integers
  2. Basic ideas of shapes in geometry

Objectives:

  1. To use writing in Mathematics
  2. To learn different shapes
  3. To be creative
  4. To practice observing and then recording observations
  5. To learn how to extract information from another source

Warm Up

Exercise #1 Maze of Numbers

Materials:

Procedure:

  1. Give out the ditto sheets and explain the instructions aloud to the students
  2. Let the students try to complete the task on their own
  3. Give the students help if needed
  4. Go over the sheet as a class, using the board or an overhead projector

 

Class Activities

Exercise #2 Geometry in the classroom

Materials:

Procedure:

  1. Tell the students to look around the room and select four objects
  2. Draw the objects on a piece of paper
  3. Write what shape each object is, under its picture
  4. Describe, either in sentences or by listing, other observations about the object such as color, texture, location, use, etc.
  5. Have the students share one of their objects with the class and read what they wrote about the object

Exercise #3 History in Geometry

Materials:

Procedure:

  1. Let each student pick one or two inventions of Leonardo da Vinci
  2. Illustrate the invention
  3. Have each student speak to another student about why they chose that invention and what information they have gathered about it
  4. Have the students write about the invention, encourage the students not to copy the information from the source, but rather write about what they had said to their classmate

Assessments:

To discover how much information the students have learned from these activities, they could be given a test where they have to identify shapes and know their names. This could be done in several different ways. The teacher could produce a sheet with only shapes and have the students name what shape each one is. The teacher could also make a sheet with the names of the shapes and the students have to draw them. There could also be any combination of these two methods to create a test.

Another way to test their knowledge would be to ask the students to pick an object from around the room and describe it on paper. They would have to know its shape, color, use and anything else that they had observed.

Yet another method would be to take the students to the library and have them each select a book about a different inventor. On their own, they would then repeat the History in Geometry lesson with their new inventor.

Extension Geometry Mobile

Materials:

Procedure

  1. Have the students name the different shapes that make up each object on the sheets of paper
  2. Have the students write the names of the shapes in them and then decorate the rest of the space
  3. Cut out the outline of the shapes (not every line, just the outside ones)
  4. Fold all of the black lines on the interior of the object inward
  5. Create the three dimensional shape by folding the paper so that the numbers match up
  6. Tape the open edges together
  7. Tape a piece of string to each object
  8. Tie the pieces of string to the stick/hanger/pole
  9. Space the shapes out on the stick~hanger/pole
  10. Hang the sticks from another piece of string from the ceiling

Philadelphia Mathematics Content Standards:

MATHEMATICS CONTENT STANDARD 3- GEOMETRY

More specifically, the standard requires that the students '`Understand space and dimensionality concepts; use them appropriately and accurately and communicate the results clearly." Benchmark one states that the students must be able to describe the historical developments of geometry in many cultures, disciplines and the effect on careers." The activity with Leonardo da Vinci is incorporated into this standard. Benchmark two states that they must "identify, describe, compare, classify and construct various two and three dimensional objects including squares, triangles, other polygons, circles, cubes, rectangular prisms, pyramids, spheres, cones and cylinders. And finally, benchmark four states that the students must know how to visualize and represent geometric figures with special attention to developing spatial sense."

 

Cross References:

This lesson uses Language Arts skills through the reading and writing of many of the activities. Social Studies is used with the research for the inventors. Art and creativity is needed for many of these activities.

 

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