1 class period that runs 45 minutes.
Students will represent the shape of the pond using fractions of simple geometric shapes. Students will identify the role of the numerator and denominator.
Construction Paper; Scissors; Sample Geometric cutout shapes; a map, drawing, or airplane photo of the pond. If you do not have access to a pond, print the virtual pond image. Several templates or patterns of circle
Background For Teachers:
It is assumed that students have been introduced to and can create the following geometric shapes: circles, squares, rectangles, parallelograms, trapzoids, rhombi, and triangles.
Intended Learning Outcomes:
Students will create congruent fractions of simple geometric shapes. Students will identify the kinds of information conveyed by a numerator or a denominator.
Paper Chain dolls are created when a paper is carefully folded into quarters and a doll is cutout of all four parts at one time with the hands extending to the folded edge. When unfolded, a paper person chain can be seen. Demonstrate this technique to your class. 1. Discuss how the congruent fractional parts created by the careful folding created paper humans of the same size and shape. Congruent parts are also helpful when measuring the surface area of a pond. Explain to the class that the challenge today will be to represent the shape of the pond as closely as possible using simple geometric shapes or fractions (1/2, 1/3, 1/4, 1/8) thereof. 2. Group the students so that each group has a pair of scissors and sample geometric shapes (they may have created these in an earlier lesson). Give each group a handout showing the pond and using the overhead transparency, demonstrate how to approximate the shape of the pond using a combination of shapes or congruent fractional shapes. 3. Let several groups present the combination of shapes and congruent fractional shapes used to 'best' represent the shape of the pond. Be prepared to accept several solutions to representing the shape of the pond. 4. After the presentations are complete, ask the students to create a circle from the construction paper using a template or pattern. Show them how to fold the circle in half (through the center) and create a half circle. 5. Explain that mathematicians use the symbol 1/2 to represent half. The top number tells how many sample shapes are involved, while the The bottom number tells into how many equal pieces the object is to be cut. The bottom number is called the denominator. The top number tells how many congruent pieces must be combined to create a half circle. The top number is called the numerator. 6. Have the students cut out another circle and then fold it into congruent quarters. Explain that the symbol for a quarter circle is 1/4 circle. The circle is cut into four pieces and only one is combined to create a quarter circle. 7. The fraction 3/4 indicates that we must cut the object (circle) into four pieces and combine 3 of the pieces to create a 3/4 circle. What is created by 2/4 of a circle? How does it compare to 1/2 of a circle?
This might be an opportune time to help students discover that whenever the numerator and the denominator are the same number, the entire shape is recreated. In other words, 2/2 of a circle is the same as 3/3 of a circle is the same as 4/4 of a circle.
Created Date :
Mar 19 1999 13:38 PM