Area of Triangles Students are asked to find the area of two different triangles.

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1 This is a resource from CPALMS ( where all educators go for bright ideas! Resource ID#: Primary Type: Formative Assessment Area of Triangles Students are asked to find the area of two different triangles. Subject(s): Mathematics Grade Level(s): 6 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, area, triangle Instructional Component Type(s): Formative Assessment Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_AreaOfTriangles_Worksheet.docx 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 problems on the Area of Triangles 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 triangle. The student: Calculates the perimeter of the figure (correctly or incorrectly). page 1 of 5

2 Multiplies all the values given in the diagram. Does not have a consistent strategy for finding area. Estimates the area by counting the squares on the grid. Randomly assigns lengths to each side of the triangle on the grid before calculating area. Does not provide enough work (or clarity in their work) to determine the solution strategy. What does the problem ask for? How does finding the perimeter help you? What were you trying to find by multiplying those numbers? Can you explain the steps you have taken in your calculations? What are you trying to find? How did you determine the number of square units when counting partial squares? Is there a way you could determine the area exactly? Why did you assign those numbers to each side of the triangle? Where do you find the base and height in a triangle? 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 for each of the two given triangles. Ask the student to label relevant dimensions and calculate the area of the composed rectangles. Guide the student in determining that the areas of the rectangles must be divided by two to represent the areas of the triangles. 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 to gain hands-on experience with composition and decomposition of two-dimensional shapes. Partner the student with a classmate to practice composing rectangles from triangles and developing a strategy to calculate area. Provide additional opportunities for the student to compose rectangles from triangles in order to find area. Moving Forward The student makes conceptual errors in finding the area of the triangle. The student demonstrates an understanding of composing into a rectangle or using the formula for the area of a triangle, but is not able to solve the problem. The student: page 2 of 5

3 Does not count the length of the base and height on the grid correctly. Uses the wrong values in the formula (e.g., does not identify the base and height of the figure correctly). Writes the formula correctly, but omits a step when evaluating (does not divide by two or multiply by ). How did you decide which values to use when calculating the area of each triangle? Can you outline each triangle and show me its base and height? In what kind of angle do the base and the height of a triangle meet? When you composed the shape into a rectangle, what are its dimensions? How does the shape of the triangle compare to the shape of the rectangle? Why did you choose that formula? What does each variable represent? Can you show me each dimension on the diagram? What is the correct procedure for evaluating this formula? Model for the student how to compose a rectangle from a triangle. Explain that the area of a triangle is half the area of a rectangle with the same base and height. Guide the student to develop a general formula for finding the area of a triangle. Provide a variety of triangles (e.g., right, acute, and obtuse) and ask the student to find the area of each triangle by either composing rectangles from the triangles or using the area of a triangle formula. Encourage the student to show all work neatly and completely and to label the answer with the appropriate unit. 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. page 3 of 5

4 Writes rather than Writes a mathematically incorrect statement in some step of the work [e.g., writes multiple steps together into one long (incorrect) equation: 39 x 52 = = 1014]. Can you check your work for errors? What units should be used in this problem? Why? How is different from1014? What does each mean? Does 39 x 52 = 1014? 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 his or her work. Provide additional opportunities for the student to compose and decompose shapes and use formulas to find the areas of polygons. Consider implementing the MFAS task Area of Quadrilaterals (6.G.1.1) or Area of Kite (6.G.1.1). Got It The student provides complete and correct responses to all components of the task. The student is able to correctly find the area of each triangle: 1,014 for the first triangle and 27.5 (or 27 ) for the second triangle, showing work clearly to support those answers. The student may have found this area by: Composing the shape into a rectangle, and dividing the product by two. Using the formula for the area of a triangle. 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 could you show the formula for the area of a triangle is equivalent to the area of a rectangle divided by two? page 4 of 5

5 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. Consider implementing other MFAS tasks from the standard (6.G.1.1). ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: Area of Triangles 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 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 5 of 5