## Puzzling Perimeters

### Debra Mastro

#### Description

Students use estimation, fractions and decimals to determine the perimeter of objects in the classroom.

#### Objectives

The student adds, subtracts, multiplies, and divides whole numbers, decimals, and fractions, including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

The student uses estimation strategies to predict results and to check the reasonableness of results.

The student solves real-world and mathematical problems involving estimates of measurements including length, time, weight/mass, temperature, money, perimeter, area, and volume, in either customary or metric units.

#### Materials

-Rulers
-Worksheet
-Two different colored writing tools
-Items to be measured

#### Preparations

1. The teacher decides what items he or she wants the students to use in their estimates and measures.
2. The teacher makes the worksheet with the columns headed: estimate, measured perimeter, nearness/difference.

#### Procedures

1.The teacher begins dialogue with students by saying, -35 inches,- or something related. The students appear puzzled and the teacher repeats, -35 inches.- Then the teacher says, -I think that your math book has a perimeter of 35 inches.- The students react, then the teacher takes out a ruler and measures the sides of the book. The information is written on the board and the students are allowed to instruct her on how to determine perimeter.

2.The teacher informs the students that they are going to be moving around while doing their class work today.

3. The students are told that they are going to be using their estimation skills to try to determine the perimeter of given objects.

4. The students are given a worksheet with a list of the items on it. The worksheet has three columns beside each of the items. The first is for their estimate. The second is for their measurement. The third is for their nearness/difference column.

5. The teacher reviews with the students the process of estimation and of determining perimeter.

6. The teacher tells each student to take out two implements that write in different colors. These may be crayons, pens, etc.

7.Students are told to go to each item on the list and to use one color to record their estimations.

8. After all students have made their recordings, the teacher instructs the students to take out their rulers.

9. Students are told to go to the same items and measure the perimeter using the ruler. They are to record these findings in the other color.

10. Students return to their seats. Discussion begins on how accurate their estimations were.

11. Students are told that they are going to -do the math,- to see how accurate they were. This process may require the students to work with decimals or fractions, depending on the items you choose for your class to use.

12. These calculations are recorded in the third column. After all calculations are completed, the students will share orally the nearness of their estimates.

13. Students are given an additional assignment: to determine the perimeter of the classroom so that they may calculate for adding wallpaper border to the top of the wall. Students work in assigned groups to gather the measurements.

14. The measurements are used to determine the perimeter of the classroom and the length of wallpaper border needed to cover top of the walls.

#### Assessments

This is a formative assessment. This tool is useful in determining weaknesses in the areas of estimation, perimeter calculation, and subtraction of decimal and fractional numbers. The following questions are used in assessing the students:
Did the student record the estimates?
Did the student record the measurements?
Did the student arrive at the correct perimeter?
Did the student record the nearness of the estimate to the actual measurement?
Did the student share the nearness with the class?
Were the students able to accurately calculate the perimeter of the room so that they could plan for a wallpaper border?

#### Extensions

Students should have knowledge of estimation, perimeter, and subtraction of decimal and fractional numbers.