Ohio Standards

Connection

Measurement Standard

Benchmark A

Select appropriate units for perimeter, area, weight, volume (capacity), time and temperature using:

objects of uniform size

U.S. customary units; e.g. mile, square inch, cubic inch, second, degree Fahrenheit, and other units as appropriate;

metric units; e.g. millimeter, kilometer, square centimeter, kilogram, cubic centimeter, degree

Celsius, and other units as appropriate.

Indicator 3

Identify and select appropriate units to measure; a. perimeter – string or links (inches or centimeters) b. area – tiles (square inches or square centimeters) c. volume – cubes (cubic inches or cubic centimeters)

Mathematical Processes

Benchmarks:

F. Recognize relationships among different topics within mathematics; e.g., the length of an object can be represented by a number.

Lesson Summary:

Students learn the units of measurement which describe the measures; perimeter, area and volume. Using physical materials, they measure attributes of a box and determine which measurement tools measure the attribute. Students practice finding measurements of perimeter, area and volume of classroom objects. In journals, students explain their understanding of each measure and the appropriate unit.

Estimated Duration: Two to three hours

Commentary:

The focus of this lesson is the conceptual understanding of perimeter, area, and volume. Young students often “treat length measure as a surrogate for area measure” (NRC, 2001, p. 283).

This means that students do not understand that measuring length is one-dimensional and has no space-filling capacity

(NRC, 2001). This lesson uses several activities to help students explore the differences between measuring length and measuring area, and also compares measuring area to measuring volume. To assist students’ development or the concepts, encourage them to think of “filling” with cubes,

“covering” with squares and “matching” the lines (Van de

Walle, 1998).

Pre-Assessment:

Write perimeter, area and volume on the board.

Have students use dry erase boards or paper to write their responses to the following questions.

1. Which of the measures would you use to find how much paper is needed to make a book cover?

2. Which measure would you use to the distance around a desk?

3. Which measure would you use to find out how much juice fills a container?

Allow students to write their answers, then discuss with a partner. Check the responses as students write and listen to discussions.

1

Ohio Standards

Connection

G. Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation.

Scoring Guidelines:

Assess students’ understanding of the three measures. Check student responses to the questions and record names of students who miss two or three. Make anecdotal notes of comments made during the discussion that contain misconceptions. Students who are not successful may need more practice recognizing situations using perimeter, area, and volume.

Post-Assessment:

Administer Perimeter, Area and Volume Post-Assessment,

Attachment A, to each student. The students read real-life situations choose the correct measurement unit and label.

Scoring Guidelines:

Using the Perimeter, Area and Volume Post-Assessment,

Attachment A, monitor which students have correctly identified the correct measurements. Complete the Post-Assessment Checklist,

Attachment B.

Instructional Procedures:

Part One

1. Review units used to measure length. Ask the class to make a list of units that are familiar to them (e.g. inches, centimeters, feet, miles,). Tell students that a measurement has a number and a unit. Select students to share and record on the board.

2. Show students a tissue box and explain it is going to be used as a home for ladybugs or other insects used in science class.

3. On an overhead, trace the bottom of a tissue box. Ask the students to imagine themselves as ladybugs getting ready to walk around the outside of the box. Ask how the distance around the box could be measured.

4. Determine the length around the outside of the tissue box. a. Wrap a yarn/string around the outside of the box and cut. b. Ask students to suggest a tool to measure the string. c. Match the string to a meter or yardstick to determine the measurement. d. Ask questions to clarify the measure and unit used.

What does the string represent?

Which unit if measure did we use to describe the length or perimeter?

Are there other units we could use?

2

5. Have students find the perimeter around classroom objects and materials. Distribute string and measurement tools. Reinforce the idea of matching the length of the string to the tool to find the measurement.

Part Two

6. Tell students that the bottom of the box is going to be covered with green paper.

Ask the students to describe how they would determine the amount of paper needed for the bottom of the box. Students may suggest that the length of the box should be measured and that is enough to determine the amount of paper. Follow this line of thinking to get kids to think about what is being measured. For example: the length of the box is 24 centimeters.

Show students a large sheet of construction paper with a length of 24 centimeters and a width which is obviously longer than the width of the box. Ask students if this is the amount needed to cover the box. (No, the sheet is too big.) Show students a sheet of construction paper 24 centimeters in length but only three to four centimeters in width. Ask them if this amount of paper will cover the bottom of the box. (No, the sheet is too small.)

7. Ask students what else is needed to know to determine how much paper is needed. Students may suggest measuring the width as well. Ask students if this would help determine the amount of paper. Ask students if the ruler is a good tool to measure the amount of paper.

(No, it only measures lengths or distances.) Use the string to measure the area of the bottom of the box.

8. Show students plastic square tiles or use Inch Squares, Attachment C. a. Ask students if the amount of paper needed to cover the box could be measured using squares. Allow students to discuss with a partner or in small groups. b. Select students to respond. Responses should include ideas that the squares can cover the area in the bottom of the box and the number of squares would give the measurement. c. Lay the squares on the overhead and count the number used. Record the number on the board.

9. Determine the unit of measurement. Ask questions such as:

Does the measurement “36 inches of paper” make sense? Why or why not? (No, 36 inches describes a length. It describes one-dimension of an object or distance, but it does not describe an area.)

What is another way to describe the measurement? Students may suggest something to do with squares or ask if a square is appropriate. Inform students that squares are units of measurement and can be used to describe and determine the measurement of an area.

10. Have students use the squares to find the area of classroom items and furniture such as, desk tops, book covers or sheet of paper.

11. Distribute grid paper and display a grid on the overhead. Draw regular and irregular shapes on the grid. Have students determine the area of each shape. Have students find the perimeter. Model for students how to find area and perimeter on the grid. Provide several examples as time permits.

12. Have students write about perimeter and area in a journal. Tell them to include examples of perimeter and area. Collect the journal entries and read to informally assess student progress.

13. Assign Ladybug Measurement, Attachment E, for homework.

3

Part Three

13. Have students share examples of perimeter and area from their journal entries and the yards they designed for homework.

14. Explain to students that living things need adequate space to live. Ask students to think about the space in the box and how the space can be measures. Allow students to discuss with partners or in small groups. Select students to share ideas from discussion.

15. Ask students for ideas about measuring space in the box. Tell students to think of the space as the amount of air, water or other objects the box can hold if we filled it to the top. For example, if the box is filled with dirt, how would you measure the amount of dirt in the box?

16. Model using the string and squares to measure the space in the box. Students should conclude that string and squares are not adequate.

17. Introduce cubes. Ask students how the cubes could be used to measure the amount of space in the box. Responses should include placing cubes in the box and counting the number needed to fill the box. Model placing cubes in the box and determine the number needed to fill the box.

18. Ask students what unit would be used to describe the measurement of space. Students may suggest or ask about a cube unit. Inform students that there is a cube unit that measures space.

19. Introduce the term volume is students do not have prior knowledge of the term. Relate volume to space. Volume is the amount of space something takes up. If a box is filled with cubes, the volume can be determined.

20. Allow students to find the volume, in cubes, of classroom items such as, a crayon box, supply box, or small containers.

21. Have students describe volume and the unit used to measure volume in a journal.

Differentiated Instructional Support:

Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s).

Give students pre-made drawings of ladybug yards with fences. Have students use the units on Ladybug Manipulatives, Attachment F to cover the yard and determine the area and perimeter.

Give students fixed perimeters and have them find as many different areas as possible with that given perimeter. Give a constant area for shapes and have students make the shapes with different perimeters.

Provide a small chart which matches the measure and the measurement unit as a reference.

Extensions:

Have the students use cubes to build towers with a given volume. Have the students describe the volume of the tower and explain how volume is measured.

Give a perimeter measurement and have students design a shape with that perimeter.

Have students create stories in which the main character uses perimeter, area, and volume.

Home Connection:

Have students discuss ways their families use perimeter, area, and volume in their homes.

4

Materials and Resources:

The inclusion of a specific resource in any lesson formulated by the Ohio Department of

Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site’s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students.

For the teacher: tissue box, string, yard or meter stick

For the student: cubes, square tiles, colored pencils, ladybug manipulatives

Vocabulary:

area

cubic unit

perimeter

square unit

unit

volume

Technology Connection:

Students use drawing software to create objects with different perimeters or areas.

Research Connections:

Cawletti, Gordon. Handbook of Research on Improving Student Achievement. Arlington, VA:

Educational Research Service, 1999.

National Research Council. Adding It Up: Helping Children Learn Mathematics. J. Kilpatrick, J.

Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education,

Division of Behavioral and Social Sciences and Education. Washington, D.C.: National

Attachments:

Attachment A, Perimeter, Area, Volume Post-Assessment

Attachment B, Post-Assessment Checklist

Attachment C, Inch Squares

Attachment D, Inch Cube Pattern

5

## Perimeter, Area, and Volume Post-Assessment

Name: ______________________________ Date: ___________________

Directions: Read each situation. Choose the correct measure.

1. Dan wanted to know how many carpet squares it would take to cover the floor. perimeter area volume

2. Jeri measured how much water that her glass would hold. perimeter area volume

3. Betty wanted to measure the distance around her school. perimeter area volume

Directions: Read each situation. Record which measurement unit you would use.

4. Amy counted how many 1 centimeter stickers it would take to cover her notebook. centimeter square centimeter

5. Jennifer measured how much distance around her desk. cubic centimeter cubic inch inch square inch

6. Kim had to fill a square container with cheese cubes.

centimeter square centimeter

7. Three students measured how much paper it would take to cover the television screen completely. Here are their answers.

Nancy said that it would take 100 square inches.

Kip said that it would take 100 inches.

Brian said that it would take 100 cubic inches.

Which student is correct? _______________________

Explain why the other two students’ answers are incorrect.

6

Student Names

Understands

Perimeter

Understands

Area

Understands

Volume

Correctly

Uses

Labels

Applies

Concepts

7

8

## Inch cube Pattern

Directions: Copy the cube patterns on paper. Have students fold up into a cube and glue the shaded areas.

9

## Attachment E

Name: _________________________________________ Date: ______________________

Your job today is to design a yard with a fence for a ladybug! Use a colored pencil to draw the fence for the yard. Make sure the lady bug has enough area to live. Be creative!

Record you perimeter here: _________________________

Record the area of your fence. ______________________

10