Description

Students explore the relationship between the area of square units and their perimeters in a hands-on activity. Observations are recorded, and students begin to recognize that shapes with the same area can sometimes have different perimeters.

Materials

-Math journals
-Burns, Marilyn, Spaghetti and Meatballs For All New York: Scholastic, 1997
-Small square tiles for each student or groups of students
-Overhead projector with overhead square tile manipulatives
-Student copies and overhead transparency of Seating Chart worksheet (see Associated File)
-Pencils
-Computer(s) with Internet access for reviewing perimeter (optional)

Procedures

Background: This lesson explores the relationship between the area of square units and their perimeters based on various arrangements. Students should have a clear understanding of both area and perimeter. If review of perimeter is needed, students may complete the online student lessons, -Fence Me In- and -Adam Ant,- available from the Beacon Learning Center.

(Session I)
1. Briefly review the concepts of area and perimeter. Have students respond to the following question in their math journals: -If shapes have the same area, do they always have the same perimeter? Explain your answer.- Encourage students to draw examples as needed to help explain their answers. Explain that the math activities they will participate in the next few days will help to answer this question.

2. Read the book Spaghetti and Meatballs For All by Marilyn Burns, but STOP at the next to last page. (The last sentence on this page reads, -She sat down in her chair and didn't budge.-)
NOTE: If the book is not available, pose a similar scenario for the students based on the information presented in this lesson. The investigation needed to answer the initial question can occur given the parameters outlined in the following procedures.

3.Discuss the problems Mr. and Mrs. Comfort face during their family reunion. Review the facts presented in the book:
a) Thirty-two people are coming to the reunion.
b) Mrs. Comfort has ordered 8 square tables for the guests.
c) As the guests arrive, tables are rearranged to accomodate seating.
d) With each new arrangement, Mrs. Comfort says, -But that won't work!- until she finally gives up!

4. Ask the students, -Why does Mrs. Comfort keep saying, 'But that won't work'? How does she know that their arrangements are wrong?- Allow students to discuss their observations from the book and explain their reasonings for Mrs. Comfort's skepticism.

5. a) Have the students re-read their math journal entries, and respond to the same question again. Encourage them to draw examples from the book to help explain and adjust their answers. b) Ask them to predict how the story will end. Review the present arrangement of tables (4 arrangements of 2 tables each) and ask them to write a solution or ending to the story in their journals.

(Session II)
6. Tell students that today they will use concrete materials to investigate and solve Mrs. Comfort's unCOMFORTABLE situation.

7. Review the problem faced by Mrs. Comfort and re-define the concepts of area and perimeter.

8. Pass out eight square tiles to each student, or pair of students.

9. While the teacher rereads the book, students arrange the tiles according to the table arrangements. With each arrangement, students record the guests seated, the table arrangement, the perimeter, and the area of the tables on the Seating Chart.

10. Students rearrange the tiles each time more company comes and records the data, while the teacher models and records the process on the overhead transparency.

11. Discuss what is happening to the perimeter of the tiles each time the seats are changed. Talk about the size of each arrangement and the number of people the new arrangement seats.

12. Show the different arrangements on the overhead after students have had time to explore and the teacher has had time to observe the manipulation of tiles.

13. Ask students how they think Mrs. Comfort's problem will be solved. Just when she is ready to give up, what do they think will happen next in the story? Allow students to adjust the solutions entered in their journals during Session I, before discussing ideas orally.

14. Read the last page of Spaghetti and Meatballs For All by Marilyn Burns. Discuss with students whether or not their predictions were correct.

15. After completing the Seating Chart and reading the solution, have students return to their math journals and re-answer the question from Session I: -If shapes have the same area, do they always have the same perimeter? Explain your answer.- Encourage students to draw examples from their observations today to support and adjust their ideas. Read and respond to journal entries according to the criteria detailed in the assessment.

Extensions

Extensions:
1) Use the tiles to investigate similar problems by changing the number of people that are seated or the amount of tables used.
2) Reverse the initial question and allow students to investigate and formulate an answer based on concrete experiences (i.e., -If shapes have the same perimeter do they always have the same area?-)

Attached Files

This is the Seating Chart students use to record the arrangements of tables, and the related perimeters and areas that occur with each new arrival.     File Extension: pdf