ACTIVITY 1:  POLYGON HIERARCHY

This activity serves to reinforce the introduction of basic polygon definitions, descriptions, and relationships among the various polygons.  Using the polygon ,  triangle , and quadrilateral  webpages, student partners create polygon hierarchy flowcharts for polygons, starting with the more general at the top, down to the more specific at the bottom.

ACTIVITY 2:  LINGUINE PLAY (Eschbach, 21)

Using a supply of linguine, each person in cooperative groups should complete the following:
1)  Break one piece of linguine into three pieces and form a triangle.  Students
    compare and discuss their triangles with the others in the group.
2)  Break a piece of linguine into three pieces such that a triangle cannot be made.
    Students discuss when a triangle works and when it doesn't.
3)  Provide an explanation for the Triangle Inequality Property.

ACTIVITY 3:  CONVEX AND CONCAVE POLYGONS

Referring to the  polygon webpage, students are to draw the following concave and convex polygons:  concave quadrilateral, convex heptagon, concave hexagon, concave pentagon, concave heptagon, and convex octagon.

ACTIVITY 4:  QUADRILATERAL SORT (Eschbach, 11)

Student groups are given a set of twelve various quadrilaterals.  Using the quadrilateral webpage as a reference, students do the following:
1)  Take turns selecting two quadrilaterals and identifying their selections by name.
2)  List 3 ways their two quaadrilaterals are the same and are different.
Next, all the quadrilaterals are put back into the center of the group.  One person divides them into two piles according to some reason.  The rest of the group tries to determine why some quadrilaterals went into pile 1 and the rest into pile 2.  This is called the reason for the sort.  Students record the reason in a table.  This is repeated until each person has had a turn to sort the quadrilaterals into two piles.
3)  Finally, students discuss which of the quadrilaterals can be tessellated referring to the tessellations webpage.

ACTIVITY 5:

In this activity students refer to the  tessellations webpage, and work to find the degree measures of the interior angles of regular polygons, making a chart of their findings. Students then apply this knowledge in the creation of tessellations.

ACTIVITY 6:  RIGHT ISOSCELES TRIANGLE FOLD (Eschbach, 10)

Students draw and cut out a right isosceles triangle, fold it in half, in half again, and in half a third time.  After unfolding the triangle, students consider and discuss the following questions:
1)  How many different shapes can you find?  Name them.
2)  How many different size triangles can you find?
            small  -
            medium -
            large -
3)  How many different triangles can you find in all?
4)  The original triangle is similar to how many of the smaller triangles?  Discuss what makes them similar,
5)  We could say we are measuring the area in triangle units instead of square units.  Find the area of each of the shapes you named in number one, in triangle units.

ACTIVITY 7:  DISCOVERING PI

Select or find five different circular objects.  One person in the group will measure the circumference of each object using a tape measure.  Another student will measure the diameter of the objects using a ruler.  Record the data.  The remaining group members will figure the ratio of the circumference to the diameter for each of the objects and record their findings.  The group will average the five ratios and see how close the average is to pi.  Students can refer to the pi and circumference webpages for reinforcement.

ACTIVITY 8:  CIRCUMFERENCE GUESS (Eschbach, 45)

Suggested supplies:  string or tape measure, 5 objects with circular bases (i.e., cup, toilet paper roll,), paper towel roll, tennis ball case

Have students number their papers from one to five.  Hold up five objects with circular bases.  Students should write YES or NO to the following question:
IS THE CIRCUMFERENCE OF THE CIRCULAR BASE GREATER THAN THE HEIGHT OF THE OBJECT?  Test each object using the string or tape measure to compare the circumference to the height.  Discuss the circumference formula in terms of the diameter.  It is easier to estimate three "diameters" than it is to mentally "unravel" the circumference.  Now hold up the paper towel roll divided into five sections A to E.  Students guess in which region the circumference will land.  Finally, hold up the tennis ball case.  Is the circumference of the circular base greater than the height of the container?  Write a discussion of the answer.

ACTIVITY 9:  EULER'S PRISMS AND PYRAMIDS

This activity gives students the opportunity to work with geometric solids.  Students will learn to recognize and identity various prisms and pyramids.  They work to discover the relationship between the number of faces, vertices, and edges of the three-dimensional figures.  Through inductive reasoning students identify the pattern and work to discover Euler's formula:  E = (V + F) - 2.

Using triangular, rectangular, pentagonal, and hexagonal prism, students count and record the number of faces, vertices, and edges on each,  They discuss the relationship they find among the number of faces, vertices, and edges.  Students then test their findings with pyramids to see if the same relationship exists.

ACTIVITY 10:   WASHINGTON D.C. GEOMETRY

Using a website map of Washington D.C. and a  landmarks
link, students complete the following:
1)  Discuss a minimum of ten geometry-related observations in detail using the correct vocabulary.
2)  Carefully examine the layout of the streets.  Are there any observations that can be made about the layout of the streets in relation to how they are named?
Examine the transportation network.  Describe any geometric patterns in the network.  Tell how these patterns contribute to the efficiency of the network.
3)  Using the list of landmarks from the website, discuss how you would schedule fifteen sightseeing stops over three days.  Explain your reasoning.