<p>Students will investigate both standard and nonstandard length and width units, and they will compute and estimate the&nbsp;perimeter by using measurement concepts. Students are going to:&nbsp;<br>- acknowledge the importance of using standard measurement units for widths and lengths.&nbsp;<br>- measure items' widths and lengths to the closest half-inch.&nbsp;<br>- examine and arrange two and three objects according to their respective lengths.&nbsp;<br>- determine the length and width by using suitable or logical units.&nbsp;<br>- calculate the perimeter of rectangles on grid paper by counting the units around them.&nbsp;<br>- calculate the centimeter and inch perimeters of rectangles.&nbsp;<br>- use grid paper to draw rectangles that represent the given perimeters accurately.</p>

<p>- What does it mean to analyze or estimate a numerical quantity?&nbsp;<br>- How are the mathematical characteristics of things or procedures quantified, computed, and/or understood?&nbsp;<br>- How accurate must calculations and measurements be?</p>

<p>- Area: The measure, in square units, of the inside of a plane figure.&nbsp;<br>- Perimeter: The distance around a figure.&nbsp;<br>- Square Unit: The base unit for measuring the area of an object. A square with each side measuring one unit.</p>

<p>- Rectangle cutouts (M-3-1-2_Rectangles)<br>- Grid paper (M-3-1-2_Grid Paper)<br>- Fences activity (M-3-1-2_Fences)<br>- string<br>- linear measurement tools (rulers, tape measures, yardsticks, meter sticks, etc.)</p>

<p>- As the students collaborate to measure and arrange the rectangles' lengths, use the Random Reporter strategy.&nbsp;<br>- You can use inch or centimeter grid paper and Fences activity to assess students as they draw, measure specific rectangles, and calculate perimeters.</p>

<p>Scaffolding, Active Participation, Modeling, Explicit Guidelines<br>W: Provide students with an explanation of what perimeter means and let them know that you will be using various measuring tools to measure paths, objects, and circumferences.&nbsp;<br>H:&nbsp;Encourage your students to explore the various meanings of the words "foot" and "feet". Discuss other ways of measuring and explain the importance of standard units of measurement. Check out Rolf Myller's book, How Big is a Foot?&nbsp;<br>E: Allow students to practice measuring the length of squares and rectangles in the classroom using standard measuring tools and string. Once they have finished measuring, students can sort the items by length.<br>R: Solve a word puzzle to determine a space's perimeter and describe how scale models represent real measurements.&nbsp;<br>E: Evaluate students as they are working. Assign them extra items to measure, and have them collaborate with a partner to reconcile any discrepancies they discover. To demonstrate that the opposing sides are the same length and that the perimeter can be found by adding two lengths and two widths in any order, assign students the task of measuring only two sides of a rectangle.&nbsp;<br>T: Assign students the task of counting the steps they take to get from one place to another, noting any differences between students or for any one student over the course of the year. Instruct students to look for practical applications for measuring the perimeters of a room or another object.&nbsp;<br>O: The main goal of this lesson is to ensure that students understand the concepts of linear measurement and can use them to study perimeter. The lesson begins with a story that explains the importance of standard units of measurement. Follow-up activities allow students to practice both standard and nonstandard measurement techniques. Next, students investigate the perimeter using regular and irregular shapes. They explore the dimensions of rectangles by measuring their sides, adding them, and defining the resulting perimeter. Throughout the lesson, students demonstrate their understanding of these measurement and perimeter concepts using rulers, grid paper, and drawings.<br>Lesson extensions cater to students who require a higher level of challenge for the concepts covered in the lessons, those whose first language is not English, and those who learn best through tactile or kinesthetic approaches.</p>

<p>Read How Big Is My Foot?&nbsp;aloud to students.&nbsp;Discuss with your students the various meanings of the terms "foot" and "feet." Describe other approaches to measurement and the need for standard units.<br><br><strong>"Today's lesson will cover measuring the lengths of paths, objects, distances, and even the space surrounding certain shapes. How do you measure objects and distances?"&nbsp;</strong>(Students will likely mention common measuring instruments like tape measures and rulers.)&nbsp;<strong>"What happens if these tools are not handy? Then, what could you do?“</strong>&nbsp;(Instruct students to come up with unconventional methods for estimating measurements; some examples include counting the length of paper clips, the height of hands, or the number of steps needed to cross a hallway.)<br><br><strong>"How can the distance around something be measured? Does anyone know the unique term we use to refer to that measurement?"</strong>&nbsp;(Although few students might be familiar with the term <i>perimeter</i>, you can define it and post it on the board for reference.) Discussing the various meanings of the terms "feet" and "foot" at this time is also beneficial, especially for students whose first language is not English.<br><br><strong>"We must first be able to measure length before we can measure the&nbsp;distance around an object or space. I'll be handing you some squares and rectangles to measure with a ruler. To determine the length of each shape and arrange them in order of shortest to longest, you will collaborate in groups. It will have the longest side."</strong>&nbsp;Now is the time to go over measuring techniques with the students, if needed.&nbsp;Give students the task of measuring and recording the length of three or more rectangles while working in small groups. You can either have students cut apart the provided rectangle cutouts (M-3-1-2_Rectangles) or you can use squares and rectangles cut from art paper. Next, have groups report their findings, rounding to the closest half-inch or centimeter, and list the measurements in order of shortest to longest.<br><br>Give each group a set of three or four standard classroom objects (such as a folder, sheet of paper, textbook, note card, etc.) that can be measured with a standard ruler to carry on with the group work. Once more, after measuring the objects' lengths to the nearest half-inch or centimeter, each group will arrange the objects in order of shortest to longest and then present their findings to the class.<br><br>As a final task, distribute a string that is approximately three feet long to each group. Then, ask the students to select three rectangles or objects from the previous class and measure the perimeter of each object using the provided string. After measuring, the students should cut the string to match each object's perimeter. Next, students should arrange the objects in order from the greatest to the least circumference by comparing the lengths of the strings when they are stretched out. During the post-activity discussion in the classroom, ask the students to sort the objects by length using the perimeters produced in the same order.<br><br>Tell the students that scale drawings are frequently used to estimate how much material will be needed to create a border around an area or an object. Display or project the M-3-1-2_Fences exercise, "Fences." As the students study the scale drawings, read them the following problem:<br><br><strong>"Mr. Abrams must construct two outdoor spaces for his horses. He plans to enclose each space with a wooden fence. To illustrate the locations for fencing, he draws a picture. The drawing's units all correspond to one yard."</strong>&nbsp;(Take a moment to ensure that the students comprehend the meaning of "unit" in this particular context. On the grid paper, one square represents a unit.)&nbsp;<strong>"How many yards of fencing does Mr. Abrams need to purchase?"</strong><br><br>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. In total, 64 yards of fencing are needed to surround both rectangles. Please let the students know that while the rectangles are not of the same shape, they have the same perimeters. However, we will discuss the area of these spaces in the next lesson.<br><br>During class discussions and small-group work, it's possible to use student responses to guide instruction and conduct informal assessments of class progress. To conduct a written evaluation, you can make use of the rectangle cutouts. Instead of cutting them apart, students will measure the rectangles' sides this time around. They should be instructed to identify each side of each rectangle before adding the measurements to determine and note its perimeter. Encourage students to collaborate and correct each other's work to settle on contrasting answers. The goal of the exercise is to teach students that perimeter is the distance around an object or the sum of its sides. The proper perimeters for the rectangles should be 16 inches, 11 inches, and 14 inches.<br><br><strong>"It is possible to find the perimeter of a rectangle by measuring only two of its sides. How can this be true?"</strong>&nbsp;Students who can politely respond to this question show that they have a solid understanding of how to calculate a rectangle's perimeter. In the initial stages of learning, students are not required to come up with a specific formula for determining the perimeter of a rectangle. Instead, they should focus on measuring rectangles until they realize that length and width measurements provide all the necessary information. In simpler terms, the line segments on either side of a rectangle are always equal. Students should also be aware that the perimeter of a rectangle can be calculated by adding the length and width twice, in any order. The algebraic formula for the perimeter of rectangles and squares is 2l + 2w = P. Gaining a deeper understanding of this formula involves examining the perimeters of various polygons and drawing the conclusion that the perimeter is always equal to the sum of the sides.<br><br><strong>Extension:</strong><br><br>You can modify the lesson to fit the needs of your students throughout the year by using the strategies and activities listed below.<br><br><strong>Routine: </strong>students should keep track of the number of steps they take to get to and from school, as well as to and from other locations within the school premises, like the cafeteria and playground. These measurements should be repeated throughout the year to observe variations in the results. For instance, a student may discover that it takes them fewer steps to reach a place if they experience a growth spurt that lasts for three months or longer. The importance of using standard units of measurement will be emphasized through a discussion of these changing results.<br><br><strong>Tactile activity: </strong>ask students to trace an object onto a piece of art paper and then stick dried beans around the drawn perimeter. Encourage students to choose both regular shapes (such as a mug or a ruler) and irregular shapes (such as a hand or a pair of scissors). Next, have each student exchange their bean tracings with a partner, both of whom should keep their eyes closed. The partners should then count the beans around the perimeter using their fingers and try to guess what object was traced.<br><br><strong>Kinesthetic exercise:</strong> students can calculate the number of steps it takes to walk along the base of each wall in the classroom to investigate its perimeter. This exercise helps students understand that counting the steps taken around a room is one method of estimating its perimeter, regardless of its shape. After the exercise, students can compare their responses, discuss the reasoning behind differing answers, and consider situations where standard measurements may be more useful. They can also explore the importance of knowing a room's perimeter. Encourage students to draw connections between what they learn in class and practical experiences, such as calculating the amount of trim needed to install wooden facings along the bottom of each wall.<br><br><strong>Expansion:</strong> Give each student a 24-inch length of nonstretching string and a sheet of 1-inch grid paper (M-3-1-2_Grid Paper). Students should trace each rectangle on the grid paper after experimenting with various methods to create rectangles with a 24-inch perimeter. You can substitute 24-cm strings and centimeter grid paper, but the smaller units are more likely to produce skewed results if the string gets frayed at the ends or slightly stretched.</p>