## An UnCOMFORTable Situation

### Barbara Johnson

#### 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.

#### Objectives

The student writes notes, comments, and observations that reflect comprehension of content and experiences from a variety of media.

The student uses concrete and graphic models to develop procedures for solving problems related to measurement including length, weight, time, temperature, perimeter, area, volume, and angles.

The student solves real-world problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles.

#### Materials

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

#### Preparations

1. Secure a copy of Marilyn Burn's Spaghetti and Meatballs For All.
2. Preview the book and fill out a Seating Chart (to use later as a key) based on the information presented
3. Gather math journals
4. Gather square tiles for overhead and student manipulatives
5. Make student copies and an overhead copy of the Seating Chart
6. Check computer connectivity to access the online student lessons, -Fence Me In- and -Adam Ant-.

#### 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.

#### Assessments

Formative Assessment
Description:
Students' math journals should contain three entries that address the following question, -If shapes have the same area, do they always have the same perimeter? Explain your answer.-
Note: The second entry should also contain students' solutions to Mrs. Comfort's problem, as well as any adjustments made to the solution during Session II Step 13.

Journal Entries:
1) Session I Step 1--students respond based on personal knowledge and examples
2) Session I Step 5--students respond based on personal knowledge and examples from the book, Spaghetti and Meatballs for All!
3) Session II Step 15--students respond based on personal knowledge, examples from the book, and concrete experiences

Criteria:
Students' journal entries should reflect an understanding that shapes with the same area can have different perimeters. Review their journals to assess that:
a) students use written language to explain the concepts of area and perimeter,
b) students justify responses based on their investigations of perimeter and area after reading the book and manipulating the square tiles,
c) students offer a solution to the problem presented to Mrs. Comfort based on examples from the book and concrete experiences (second entry, part b)

#### 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?-)