Euclid s Muse In this activity, participants match geometry terms to definitions and definitions to words. MATERIALS Transparency: Euclid s Muse Directions Transparency/Page: Euclid s Muse Transparency/Page: Euclid s Biography Transparency/Page: Euclid s Sample Definitions Transparencies/Pages: Euclid s Muse: Words and Definitions Euclid s Muse Cards chart paper pens (different color for each group) tape VOCABULARY area perimeter triangle quadrilateral rectangle line point plane TIME: 40 minutes 1
TEACHING TIP: The name Euclid has been applied to the activity because of Euclid s connection with geometry. Euclid did not write all the activity definitions. TEACHING TIP: Before the workshop begins, place all the Euclid s Muse Cards in a bag and mix them thoroughly. Definitions with asterisks can be withheld in the interest of time for large groups. Go over any definitions removed from the cards as part of the Conclude section for the activity. INTRODUCE Welcome participants to the workshop. Explain that today they will review a number of concepts and terms related to plane geometry but that they will start with a game to test their memories. (Ask them not to open their pages until the game is over.) Tell them that they will work in groups to define the words and terms that you and they will use during the workshop. Have participants form 6 groups. DISCUSS AND DO Have one participant volunteer from each group come up front. Have each volunteer in turn draw a game card out of the bag. Repeat this process until all the cards are drawn. (Each person will have 6 cards.) 2
Euclid s Muse Directions First: Draw and label three columns on your chart paper as shown below. Name Picture Definition Tape your cards to the chart paper (3 per page) in the appropriate columns. Name the shape and write a definition if the card is a picture. Draw a picture and write a definition if the card is a name. Name the shape and draw a picture if the card is a definition. Transparency: Euclid s Muse Directions Directions Euclid s Muse First: Draw and label three columns on your chart paper. Tape your cards to the chart paper (3 per page) in the appropriate columns. Name the shape and write a definition if the card is a picture. Draw a picture and write a definition if the card is a name. Name the shape and draw a picture if the card is a definition. Second, as a group: Rotate to the next table and check the pictures and definitions. Put an asterisk, using your group pen, if you agree with a name, picture, and definition. Put an M if you disagree with any part and, using your group pen, write your modification or correction. Put a question mark if you have a question or would like to discuss the item. Repeat the rotation until you have reviewed all the charts. * We agree with the name, picture, and definition. M We disagree or want to add something. Our Modifications appear in our group color.? We would like to discuss or have questions about this item. Transparency: Euclid s Muse Have volunteers return to their groups. Distribute two sheets of chart paper and a pen to each group. Display Transparency: Euclid s Muse Directions. Walk through the directions with participants and model the example parallel lines as it would be done by participants if it were included in the list. Write the words parallel lines in the name column and draw a box around it to represent the card. Draw a picture of parallel lines in the picture column. Ask participants to help you write a definition in the definition column. (Parallel lines are lines that are always an equal distance apart. They never intersect.) Explain to participants that they will tape the cards they have drawn in the appropriate columns. Point out that in your example, you assumed that the card contained the name, but that their cards may be names, pictures, or definitions. Display Transparency: Euclid s Muse. Walk through the remaining directions. Explain to participants that they have 5 7 minutes to complete a shape, name, and definition for each card. Tell them that after they complete their charts, you will call time and ask the groups to rotate to a new set of charts. Explain that as a group, they will agree with, modify, or question each completed item, using their group pen. 3
Have the groups begin work. Allow 5 7 minutes to complete the initial work and 5 minutes for each rotation. CONCLUDE Euclid s Muse: Words and Definitions 1. acute triangle a triangle in which each of the three angles is less than 90º 2. altitude a line segment that shows the height of a figure; or, in a triangle, the line segment drawn from the vertex of an angle perpendicular to the opposite side 3. angle a geometric figure made of two rays or two line segments that share the same endpoint, called a vertex 4. circle the set of all points in a plane that are equidistant from a given point 5. circumference the distance around a circle 6. congruency having the same shape and size 7. degree a unit for measuring angles; 360 of these make a complete revolution around a point 8. diameter the line segment passing through the center of a circle and connecting two points on the circumference of a circle 9. hypotenuse the side of a right triangle that is opposite the right angle 10. isosceles triangle a triangle with two congruent sides 11. line a set of points that form a straight path in two directions that are opposite each other 12. obtuse triangle a triangle that has one angle greater than 90º 13. octagon a polygon with eight sides Euclid s Biography Transparencies: Euclid s Muse: Words and Definitions Euclid is thought to have been a Greek mathematician who taught in Alexandria around 300 B.C. It is possible that he was the founder of its most famous mathematical school. Some theories suggest that his name is applied to the work of a group of mathematicians that made up the school. Euclid is best known for the multivolume Elements, the most widely known mathematical books of classical times books still used in many geometry classes today. Post all the charts on the wall. Walk through any that are modified or for which participants indicated a question. Refer to Transparencies: Euclid s Muse: Words and Definitions to resolve any disputes. Leave the charts up for group reference. Display Transparency: Euclid s Biography. Explain to participants that there are several theories about who Euclid was and when he lived, but that his books, Elements, still form the basis of the formal study of plane and solid geometry. Display Transparency: Euclid s Sample Definitions. Discuss with participants the similarities and differences between these definitions and those that they have written.... he introduces quite a number of definitions... Indeed, Elements begins with definitions and postulates. Transparency: Euclid s Biography 4
Euclid s Sample Definitions A straight line is a line that lies evenly with the points on itself. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another. A diameter of a circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle. Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle is that which has two of its sides alone equal, and a scalene triangle is that which has its three sides unequal. Point out that many of the discrepancies between the two versions are probably the results of language differences, both between Greek and English and those that result from the way language evolves over time. End of Euclid s Muse McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF PLANE FIGURES/11 Transparency: Euclid s Sample Definitions 5