Area of Kite Students are asked to find the area of a kite by composing it into rectangles or decomposing it into triangles.

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1 Status: Published This is a resource from CPALMS ( where all educators go for bright ideas! Resource ID#: Primary Type: Formative Assessment Area of Kite Students are asked to find the area of a kite by composing it into rectangles or decomposing it into triangles. Subject(s): Mathematics Grade Level(s): 6 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, area, kite, quadrilateral, triangle, rectangle, decompose, compose, polygon, real-world problem Instructional Component Type(s): Formative Assessment Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_AreaOfKite_Worksheet.docx MFAS_AreaOfKite_Worksheet.pdf FORMATIVE ASSESSMENT TASK Instructions for Implementing the Task This task can be implemented individually, with small groups, or with the whole class. 1. The teacher asks the student to complete the problem on the Area of Kite worksheet. 2. The teacher asks follow-up questions, as needed. TASK RUBRIC Getting Started The student does not have a correct strategy to determine the area of the kite. The student: Finds the area of only one triangular section of the kite. page 1 of 6

2 Tries to apply the formula for the area of a triangle to the area of the kite, writing: A= (16)(15). Calculates the perimeter of the whole kite or the perimeters of the decomposed triangles (correctly or incorrectly). Tries to apply the formula for the area of a triangle to the area of the kite but substitutes the lengths of the sides of the kite for base and height. Uses the wrong formula for the area of a triangle when attempting to calculate the area of each triangular section. Combines the values from the diagram with some other combination of operations. Does not provide enough work (or clarity in their work) to determine their solution strategy. Questions Eliciting Thinking What does the problem ask for? What do compose and decompose mean in this context? page 2 of 6

3 How will finding the perimeter help you? What were you trying to find by multiplying those numbers? What is the formula for the area of a triangle? Does that same formula also apply to the area of a kite? Can you explain the steps you have taken in your calculations? What are you trying to find? Ensure that the student is familiar with triangles and rectangles and the terms used to describe their dimensions such as base and height. Provide the student the opportunity to identify and label the base and height of a variety of triangles including obtuse triangles. Emphasize that the height must be perpendicular to the base. If needed, review area and perimeter. Reinforce that perimeter is a linear measurement determined by adding the lengths of all the sides while area is measured in square units and is a measure of the surface contained in the interior of a polygon. Have the student experimentally verify the relationship between the area formulas for rectangles and triangles, demonstrating how the area of a triangle is one-half the area of a rectangle with the same dimensions. Model for the student how to compose a rectangle using a triangle. Explain (or use a demonstration) to show that the area of a triangle is half the area of a rectangle with the same base and height. Guide the student to compose rectangles using the triangular sections of the kite. Ask the student to label relevant dimensions and calculate the sum of the areas of each section. Encourage the student to show all work neatly and completely and to label the answer with the appropriate unit. Provide manipulatives such as pattern blocks for the student to explore in order to gain hands-on experience with composition and decomposition of two-dimensional shapes. Partner the student with a classmate to practice composing and decomposing shapes into familiar figures such as rectangles and triangles and to develop strategies to calculate area. Provide additional opportunities for the student to compose and decompose polygons into rectangles and triangles in order to find area. Moving Forward The student makes conceptual errors in finding the area of the kite. The student demonstrates an understanding of composing the figure into rectangles or decomposing the figure into triangles to find the area, but is not able to correctly solve the problem. The student: Does not correctly list the dimensions of the decomposed triangles. Finds the areas of two (or more) individual triangles, but does not find their sum. Finds the area of half the kite. Uses the wrong values in the formula (e.g., does not identify the base and height of each triangle correctly). Writes the formula correctly, but omits a step when evaluating (e.g., does not divide by two or multiply by ). page 3 of 6

4 Questions Eliciting Thinking How did you decide which values to use when calculating the area of each triangle? Can you outline each triangle individually and show me its base and height? What type of angle must the base and the height of a triangle make? When you decomposed the shape into triangles, what were the dimensions of each new shape? What is the question asking you to determine? What do you need to do to find the total area of the figure? Why did you choose that formula? What does each variable represent? Can you show me where those values are in the figure? What is the correct procedure for evaluating this formula? Model for the student how to compose a rectangle using a triangle. Explain (or use a demonstration) to show that the area of a triangle is half the area of a rectangle with the same base and height. Guide the student to compose rectangles using the triangular sections of the kite. Ask the student to label relevant dimensions and calculate the sum of the areas of each section. Encourage the student to show all work neatly and completely and to label the answer with the appropriate unit. Provide additional opportunities for the student to compose and decompose polygons into rectangles and triangles in order to find area. This worksheet can be edited to change the lengths of each dimension for further practice. Almost There The student makes minor mathematical errors. The student makes a minor error in computation or labeling units. The student: Calculates incorrectly in one step of the problem but all other work is correct. Transposes a number from one step to the next. Uses the wrong units or no units at all. Indicates square units by putting the exponent of two on the numerical answer, rather than on the units (e.g., rather than 168 ). Writes a mathematically incorrect statement in some step of the work [e.g., writes multiple steps together into one long (incorrect) equation: 21 x 8 = 168 x = 84]. Questions Eliciting Thinking Can you check your work for errors? What units should be used in this problem? Why? How is different from 168? What does each mean? Does 21 x 8 = 84? Can you show your work in individual steps? Review multi-digit multiplication and division and order of operations as needed. Provide specific feedback concerning the error(s) made and ask the student to revise the work. Provide additional opportunities for the student to compose and decompose shapes and use formulas to find the areas of polygons. page 4 of 6

5 Consider implementing the MFAS task Area of Quadrilaterals (6.G.1.1) or Area of Triangles (6.G.1.1). Got It The student provides complete and correct responses to all components of the task. The student is able to compose the kite into rectangles or decompose the kite into triangles to find the area of the kite, 168 showing work clearly to support this answer. The student may have found this area by: Decomposing the shape into smaller triangles and finding their sum. Four small triangles. Two large triangles. Composing the kite into rectangles, finding and summing the areas of each rectangle, and scaling the sum appropriately to represent the area of the original kite. Questions Eliciting Thinking Can you think of a different way you could have found the area? When using the formula for the area of a triangle, what does each part mean? How would your problem have changed if you decomposed it into fewer (or more) triangles? How could you find the perimeter of the figure? Are there any missing dimensions you would need to find first? If so, how could you find those? Ask the student to find areas of polygons whose dimensions include rational numbers. Challenge the student to find a general strategy for finding the area of a kite in terms of the lengths of its diagonals (i.e., A = ). Consider implementing other MFAS tasks from the standard (6.G.1.1). ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: Area of Kite worksheet SOURCE AND ACCESS INFORMATION Contributed by: MFAS FCRSTEM Name of Author/Source: MFAS FCRSTEM District/Organization of Contributor(s): Okaloosa Is this Resource freely Available? Yes Access Privileges: Public License: CPALMS License - no distribution - non commercial page 5 of 6

6 Related Standards Name MAFS.6.G.1.1: Description Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. page 6 of 6