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Length and Perimeter

Lesson Plan

Length and Perimeter

Objectives

Students will explore standard and nonstandard units of length and width and will apply measurement concepts to estimate and calculate perimeter. Students will:

  • recognize the need for standard units of measuring lengths and widths.
  • measure lengths and widths of objects to the nearest half inch.
  • compare and order two and three objects by their lengths.
  • estimate length and width by selecting appropriate or reasonable units.
  • find the perimeter of rectangles on grid paper by counting the units around.
  • measure perimeters of rectangles by centimeters and inches.
  • draw rectangles on grid paper to represent given perimeters.

Essential Questions

  • What does it mean to estimate or analyze numerical quantities?
  • In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted?
  • How precise do measurements and calculations need to be?

Vocabulary

  • Area: The measure, in square units, of the inside of a plane figure.
  • Perimeter: The distance around a figure.
  • Square Unit: The base unit for measuring the area of an object. A square with each side measuring one unit.

Duration

 

90–150 minutes


Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

  • AAA Math, http://www.321know.com/geo.htm, see the learn, practice, play, and explore activities related to perimeter.
  • AAA Math, http://www.321know.com/mea.htm, see the learn, practice, play, and explore activities related to measurement.
  • How Big Is a Foot? by Rolf Myller. Yearling 1991. A book that teaches a king that measurement by his foot and by the foot of the young apprentice result in very different outcomes.
  • IXL Math Practice Site, http://www.ixl.com/math/grade/third/, free online practice questions for time, measurement, geometry, and other math concepts.
  • Alternative Books:
    • How Long or How Wide? A Measuring Guide by Brian P. Cleary. First Avenue Editions 2009. A humorous approach to measuring length and using measuring tools.
    • How Tall, How Short, How Far Away? by David Adler and Nancy Tobin. Holiday House, 1999. A book that introduces several measuring systems and presents the need for standard units of measure.
    • Keep Your Distance! by Gail Herman. Kane Press, 2001. In the context of sibling rivalry and sharing a room, sisters learn about measurements of distance and time.
    • Length (Measuring Up) by Peter Patilla. Belitha Press, 2000. An interesting discussion of measuring systems past and present with examples of unusual lengths.
    • Racing Around by Stuart J. Murphy. Steck-Vaughn, 2002. A story of racing around a perimeter.
    • Super Sand Castle Saturday by Stuart J. Murphy. Steck-Vaughn, 1999. A tale of using nonstandard units of measurement to compare sizes of sand castles.

 

 

Formative Assessment

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    • Use Random Reporter as a strategy while students work together to measure and order the lengths of rectangles.
    • You can also use the inch or centimeter grid paper and the Fences activity rectangles to formally assess students as they draw and measure specific rectangles and calculate perimeters.

Suggested Instructional Supports

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    Scaffolding, Active Engagement, Modeling, Explicit Instruction
    W:

    Introduce students to the term perimeter, and let them know you will be measuring the distance around objects as well as the lengths of objects and paths, using various measuring devices to do so.

     
    H:

    Read the book How Big is My Foot? by Rolf Myller. Discuss with students the multiple meanings of the words “foot”/“feet”. Discuss alternate methods of measuring and explain why standard units are necessary.

     
    E:

    Allow students some time to practice using a ruler to measure lengths of some squares and rectangles. Have students measure classroom objects with both standard measuring tools and with string, and then order the objects from shortest to longest.

     
    R:

    Work through a word problem to find the perimeter of a space, and explain how scale models are used to indicate actual measurements.

     
    E:

    Assess students throughout their work time. Provide additional items to measure and have them work with partners to resolve any differences they may find. Ask students to find the perimeter of a rectangle by measuring only two sides, illustrating that the opposite sides are the same length and that perimeter can be found by adding two lengths and two widths in any order.

     
    T:

    Have students count the number of steps they take to walk somewhere and note the variations from student to student, and for any one student throughout the year. Ask students to look for practical applications for measuring perimeters of a room or some other object.

     
    O:

    The focus of this lesson is to make sure students understand concepts of linear measurement and then apply that knowledge to studies in perimeter. The lesson begins with a story that sets the purpose or need for standard units of measurement. Follow-up activities allow students to practice standard and nonstandard measurement techniques. Then students use regular and irregular shapes to begin explorations of perimeter. Explorations with string are extended to formal measurements of the sides of rectangles, adding the sides, and defining the result as perimeter. Throughout the lesson students use rulers, grid paper, and drawings to demonstrate their understanding of these measurement and perimeter concepts.

    Extensions of the lessons focus on students who learn best through tactile or kinesthetic approaches, those whose first language is not English, and students who need a higher level of challenge for the lesson concepts.

     

     

Instructional Procedures

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    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.

Related Instructional Videos

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Final 04/12/13
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