Read How Big is My Foot? aloud to students. Discuss with students the multiple meanings of the words “foot” and “feet.” Discuss alternate methods of measuring and explain why standard units are necessary.
“In today’s lesson, we are going to measure the lengths of objects, paths, distances, and even the distance around some shapes. What are some of the ways you measure objects and distances?” (Students are likely to name standard measurement tools such as rulers and tape measures.) “What if these tools are not handy? What could you do then?” (Encourage students to brainstorm nonstandard ways to estimate measurements, such as the number of paper clips long, the number of hands high, or the number of steps it takes to walk down a hallway.)
“How do you measure the distance around something? Does anyone know what special name we use for that measurement?” (Few students may know the word perimeter, but you can introduce the term and write it on the board for later use.) This is also a good time to discuss the multiple meanings of feet and foot, particularly for students whose primary language is not English.
“Before we can measure the distance around an object or a space, we must be able to measure length. I am going to give you some rectangles and squares to measure with a ruler. You will work together in groups to find the length of each shape and put the shapes in order from shortest to longest lengths. The longest side will be the length.” At this time, if necessary, review with students how to use a ruler to measure. Have students work together in small groups to measure and record the length of at least three rectangles. You may use rectangles and squares cut from art paper or have students cut apart the provided rectangle cutouts (M-3-1-2_Rectangles.docx). Then have groups share the results of each measurement to the nearest half inch or centimeter and describe the order from shortest to longest.
Continue the group work by giving each group a collection of three or four common classroom objects (i.e., folder, sheet of paper, textbook, note card, etc.) that can be measured with a standard ruler. Again, each group will record the length of objects to the nearest half inch or centimeter, place them in order from shortest to longest, and share the results with the class.
Finally, provide each group a string that is about 3 feet long. Have students select three of the previous classroom objects or rectangles, use the string to measure the perimeter of each object, and cut the string to match each perimeter. Then have students compare the outstretched lengths of the strings to put the objects in order of their perimeters, from least to greatest. During the classroom discussion after the activity, ask students whether putting the objects in order of their lengths resulted in the same order as using the perimeters.
Explain to students that scale drawings are often used to plan the amount of materials needed to make a border around a space or an object. Show or project the Fences activity (M-3-1-2_Fences.docx). Read the following problem to students as they look at the scale drawings.
“Mr. Abrams needs to build two outdoor areas for his horses. He wants to put a wooden fence around each area. He makes a drawing to show the places to fence. Each unit in the drawing represents 1 yard.” (Pause here to make sure students understand the meaning of “unit” in this context. A unit is one square on the grid paper.) “How many yards of fencing does Mr. Abrams need to buy?”
The first rectangle is 8 units long and 8 units wide, with a perimeter of 32 yards. The second rectangle is 11 units long and 5 units wide, with a perimeter of 32 yards. The combined amount of fencing needed is 64 yards. Point out to students that the perimeters of the fenced spaces are the same although the rectangles do not have the same shape. Postpone the discussion of areas of these spaces until the next lesson.
Monitoring student responses during discussions and small-group work can be used to informally assess class progress and to guide instruction. For one form of written assessment, use the rectangle cutouts. This time students will measure each side of the rectangles without cutting them apart. Tell students to label each side and then add the measurements to find and record the perimeter of each rectangle. Encourage students to work together to check one another’s work and to resolve differing answers. Although the correct perimeters should be 16 inches, 11 inches, and 14 inches, the focus of the activity is to help students understand that perimeter is the distance around an object, or the sum of the sides.
“It is possible to find the perimeter of a rectangle by measuring only two of its sides. How can this be true?” Students who can reasonably answer this question demonstrate a proficient understanding of finding the perimeter of a rectangle. Students do not need to devise a specific formula at this point, but they should measure rectangles until they begin to discover how measuring length and width provides all the necessary information. In other words, opposite line segments of a rectangle are equal. The algebraic formula for the perimeter of rectangles and squares is 2l + 2w = P, but students should minimally understand that the perimeter of a rectangle can be found by adding length + length + width + width in any order. Advanced levels of understanding include various ways to describe the formula and exploring perimeters of other polygons to conclude that perimeter is always the sum of the sides.
Extension:
Use the activities and strategies listed below to tailor the lesson to meet the needs of your students during the year.
- Routine: Ask students to count the number of steps they take to get from one place to another inside the school, around the school, around common areas such as a playground or cafeteria, or to get to and from school. Checking these measurements throughout the year is likely to have different results. For example, any student who has a significant growth spurt over three or more months may find that s/he takes fewer steps to get somewhere. A discussion of these changing results will further support the need for standard units of measurement.
- Tactile Application: Have students trace an object on art paper and then glue dried beans around the perimeter they drew. Encourage students to choose regular shapes
(e.g., the bottom of a mug, a ruler, or a rectangular whiteboard eraser) and irregular shapes (e.g., a hand, foot, shoe, sock, or pair of scissors). Then have students close their eyes and trade bean tracings with a partner. Each member of the pair should keep his/her eyes closed, use touch to count the number of beans around the perimeter, and try to guess the object that was traced.
- Kinesthetic Application: Students can explore the perimeter of the classroom by counting the number of steps it takes to walk along the base of each wall. Whether the room is a regular rectangular shape or an irregular shape, students will recognize that counting the steps taken around a room is one way to estimate its perimeter. Follow up the kinesthetic activity by asking students to compare answers, discuss reasons for different answers, consider when standard measurements might be more helpful, and explore why knowing the perimeter of a room might be necessary. Encourage students to make connections to real-world applications such as measuring the amount of trim it would take to put wooden facings along the bottom of each wall.
- Expansion: Give students a length of nonstretching string that is exactly 24 inches long and a sheet of 1-inch grid paper (M-3-1-2_Grid Paper.docx). Have students explore different ways to make rectangles that have a perimeter of 24 inches and trace each rectangle on the grid paper. Centimeter grid paper may be used instead, along with 24-cm strings, but the smaller units are more likely to have skewed results if the string has frayed ends or becomes slightly stretched.