DIDL HO 3C Lesson Plan: Measuring Perimeter Grade 5 Context: This lesson is being taught to a group of fifth graders as part of a unit on geometry. They began by exploring and categorizing shapes in the classroom and looking at weavings to describe shapes and patterns. There are 26 students in the classroom. Almost half of the students were served in bilingual education programs through grade 3. Two students attend resource classes for language arts and reading but come into math about 15 minutes after the lesson has started. Three students are identified as gifted and talented, with one achieving at a level that far exceeds his peers. One student is extremely distractible and intermittently takes medication for ADD/ADHD--at times his mother reports that she can’t afford to have the prescription filled. The class is generally talkative and gets along well socially, although there have begun to be several cliques that some of the students struggle to be included in. TEKS: 111.17(b) Knowledge and skills: (4) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to: (B) estimate to solve problems where exact answers are not required. (11) Measurement. The student applies measurement concepts. The student is expected to: (A) measure to solve problems involving length (including perimeter), weight, capacity, time, temperature, and area; and (B) describe numerical relationships between units of measure within the same measurement system such as an inch is one-twelfth of a foot. (14) Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (A) identify the mathematics in everyday situations; (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (C) select or develop an appropriate problem-solving strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and (D) use tools such as real objects, manipulatives, and technology to solve problems (16) Underlying processes and mathematical tools. The student uses logical reasoning to make sense of his or her world. The student is expected to: (A) make generalizations from patterns or sets of examples and nonexamples; and (B) justify why an answer is reasonable and explain the solution process. Adapted from Jones, Ash, Golley & Schwarzhoff in Irvine & Armento (2001) DIDL HO 3C Objectives: •Students will learn or review the concept of perimeter of geometric shapes. •Using copies of Navajo rug patterns, students will estimate the perimeter of geometric shapes. •Given a choice of manipulatives, students will compare the effectiveness of different units of measure for finding perimeter and provide a rationale when selecting the most appropriate unit for a given task. •Students will find the perimeter of geometric shapes taken from Navajo rug patterns, using a 10 x 10 grid or centimeter paper, with 80% accuracy. Materials: 10 x 10 grid paper, centimeter grid paper, coloring pencils or crayons, rulers, examples of Navajo rug patterns drawn on plain paper and grid paper, math journals, string, M&Ms, pattern blocks, centimeter cubes Advanced Organizer: The teacher asks students to get out their homework from the previous evening. They were asked to find a pattern at home or in the neighborhood and draw a picture or write a description of the pattern. The teacher selects several patterns and hangs them on the board. The teacher asks which pattern has the longest boundary. Why? The teacher then explains that sometimes it is important to find a figure’s boundary. Students are asked what they would need to know if they wanted to put a wallpaper border around a room. The teacher then shows the students examples of Navajo rug patterns and asks them to notice that many of the rugs have borders. The weavers need to estimate how much wool they will need for the boundary or border before they begin to weave. The teacher then asks the students for the mathematical term for the boundary of a figure. The teacher writes all the answers on the chalkboard. If no one volunteers the word perimeter, the teacher writes it on the chalkboard and asks the students to write it in their math journals. Input and Modeling: The teacher shows fabric swatches or pictures of Navajo rugs or blankets. Students are asked to describe the patterns and to speculate about what the patterns might represent. The teacher distributes patterns 1 and 2 on plain paper and explains that they were taken from Navajo patterns. The teacher asks students how they would determine the distance around each shape and which distance would be longer. Which shape has the larger perimeter? Students are allowed to work individually or in pairs to discuss how they might answer these questions. The class then discusses the responses. The teacher asks students how they could check their estimates. The teacher asks students to work in small groups. Each group should select one type of manipulative and use it to measure the perimeter of the two patterns. When they are finished the teacher asks which units of measurement are best to use for the perimeter? Why? Why do different groups get different answers? The discussion should focus on the fact that Adapted from Jones, Ash, Golley & Schwarzhoff in Irvine & Armento (2001) DIDL HO 3C measurement is dependent on the size of the unit of measure. If you were to measure the perimeter of the room, which units of measurement would you use? The discussion should focus on the need for larger units to measure the perimeter of the room. The teacher then asks the groups to create three other shapes that have the same perimeter as one of the patterns. The teacher distributes patterns 1 and 2 on grid paper. The students are asked to describe the grid paper in mathematical terms. What shapes are on the grid? What do you know about squares? Can you think of a way to find the perimeter of the patterns using the grid paper? The class discusses how to use one side of the square as one unit of measurement. The teacher then distributes a third pattern that contains diagonal lines. The teacher challenges the students to compare this pattern to the other two patterns they measured. Is the perimeter larger or smaller than Pattern1? Pattern 2? How can you tell? The teacher then asks the students to (1) estimate the perimeter or Pattern 3 and (2) calculate the perimeter of pattern 3. Students will have to devise a method of finding the length of diagonal lines. Afterwards, the class should discuss which methods worked, particularly for diagonal distances. Closing: The teacher asks the class the meaning of the word perimeter. How do you think you might find the perimeter of larger spaces, like the top of your desk or your bedroom floor? Assessment: Distribute a paper showing five patterns drawn on a 10 x 10 grid. The homework assignment is to calculate the perimeter of each. Adapted from Jones, Ash, Golley & Schwarzhoff in Irvine & Armento (2001)

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