Summary
This activity shows a different way to find the area of a circle using the circumference.
Materials
Additional Resources
Books
Sir Cumference and the Isle of Immeter by Cindy Neuschwander; ISBN 1-57091-681-0
Background for Teachers
This activity shows a different way to find the area of a circle,
A = 1/2 Circumference x radius. Students will decompose a circle
into a number of wedges and rearrange the wedges into a shape that
approximates a parallelogram (or rectangle) to develop the formula for
the area of a circle. Students should have an understanding of a circles
radius and circumference before starting this activity.
Instructional Procedures
Invitation to Learn
In their math journals, have students create a K-W-L chart on
area and perimeter. For the "K" section, have them write down
all they know about the perimeter of figures (squares, rectangles,
parallelograms, triangles, circles) and what they know about the area of
figures (same figures as previously mentioned). For the "W" section of
their chart, have them write what they want to know about perimeter and area of figures. Have them leave the "L" section blank. After the
activity they will write what they learned about perimeter and area.
Have a class discussion on what they put on the "K" and "W" sections
of their K-W-L charts.
Instructional Procedures
- Begin reading, Sir Cumference and the Isle of Immeter.
- After the first page, stop. On the overhead, put up tiles like the
square Sir Cumference made. Explain what the book means by
inners and edges.
- Read the next page, on the overhead put the shape that Lady Di
made. Talk about the inners and edges.
- Give a few more examples of squares and rectangles so students
understand how to find inners and edges.
- Read page 5, and explain what Per said about finding the inners
and edges with squares and rectangles.
- Read until the bottom of page 8, and then put tiles on the
overhead representing the first doorway. Explain how Radius
found the inners so quickly (multiplied the length by the
width).
- After reading page 10, ask students what they think the clue
means. "Count half as many inside as out. This unlocks the
towers without a doubt."
- Read until the bottom of page 16.
- Hand out the copies of the circles divided into eighths to groups
of students. Have them cut the wedges and form it into a
rectangle. Discuss how it is a "lumpy, bumpy rectangle".
- Hand out the copies of the circles divided into sixteenths. Have
the groups cut the wedges apart and form it into a rectangle.
Have the groups try and figure out what the long side of the
rectangle represents (one half of the Circumference) and what
the short side of the rectangle represents (the radius). Discuss
their ideas as a class.
- Read page 17 and discuss how Per multiplied 1/2 the
Circumference by the radius (or length x width), to figure out
the area of a circle.
- Read page 18 and 19, and then make sure students understand
what Per is doing.
- Show the Circles Overhead of the three circles, and have the
groups figure out the area by multiplying 1/2 Circumference by
radius.
- Read until the end of the book. Review the area and perimeter
(inners and edges) of a figure and discuss any questions the
students have about the book.
- Explain to students that we normally don't use the formula 1/2
Circumference x radius to get the area of a circle. Show them
the steps of how A = (1/2 C) x r can be changed to the standard
formula of
A = pi x r².
- In their math journals, have students write what they learned
about the perimeter and area of figures in their "L" section of
their K-W-L chart. Have a class discussion on what they added
to their chart.
- Have students complete the worksheet, Area and Perimeter.
Extensions
- Have students create their own picture book explaining a
mathematical concept.
- Have students create a quiz on perimeter and area that they can
trade with a classmate.
Family Connections
- With your family, measure three circular objects in your
home. Show your family how to find the area of the circles by
multiplying 1/2 the Circumference by the radius.
- Read Sir Cumference and the Isle of Immeter with your family.
Answer any questions they may have about perimeter,
circumference, radius or area.
- Play a game of inners and edges with your family.
Assessment Plan
- Informal assessment includes class discussion, Circles Overhead,
and the K-W-L chart in their math journals.
- Area and Perimeter
Bibliography
Von Drasek, L. (2006). Teaching with Children's Books: The "Wow" Factor. ERIC Source
(ERIC # EJ729683). Retrieved March 14, 2007, from http://www.eric.ed.gov
Teaching math through children's books motivates children to
learn math in exciting new ways; encourages students to think and
reason mathematically and builds students' appreciation for math and
literature.
Ward, R. (2005). Using Children's Literature to Inspire K-8 Preservice Teachers' Future
Mathematics Pedagogy. ERIC Source (ERIC # EJ738003). Retrieved March 14, 2007,
from http://www.eric.ed.gov
A growing body of research in the fields of mathematics education
and literacy supports the inclusion of children's literature with the
teaching and learning of mathematics. The author presents a variety of
activities and ideas that are sound strategies for effectively integrating
children's literature with the teaching of mathematics.
Created: 07/06/2007
Updated: 02/01/2018
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