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Drawing Triangles AAA Resource ID#: 68423 Primary Type: Formative Assessment This document was generated on CPALMS - www.cpalms.org Students are asked to draw a triangle with given angle measures, and explain if these conditions determine a unique triangle. Subject(s): Mathematics Grade Level(s): 7 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, triangle, angles, sides Instructional Component Type(s): Formative Assessment Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_DrawingTrianglesAAA_Worksheet.docx MFAS_DrawingTrianglesAAA_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 problems on the Drawing Triangles AAA worksheet. 2. The teacher asks follow-up questions, as needed. TASK RUBRIC Getting Started Misconception/Error The student is unable to draw a triangle with the given conditions. Examples of Student Work at this Level The student draws a triangle with incorrect angle measures. The student draws a figure that is not a triangle (e.g., an open figure with three sides). Questions Eliciting Thinking What are the features of a triangle? What strategies would you use to draw a triangle given the measures of the angles? Where is a good place to beg How would using a protractor help you draw a triangle with the given measurements? Instructional Implications Define a triangle as a polygon with three sides. Make clear that an open figure with three sides is not a triangle ( Provide the student with a manipulative such as or software such as Geogebra (www.geogebra.org) to Guide the student to draw a triangle with given conditions. Assist the student in using a protractor to draw and m Next, ask the student to draw a working line and measure a length that is double the length of one side of the tria intersect in the third vertex of the triangle. Have the student measure the lengths of these sides and compare them as an opportunity to conclude: Three angle measures do not determine a unique triangle. Two angle measures determine the measure of the third angle of the triangle. Two angle measures and their included side length will determine a unique triangle. Relate these conclusions to the relevant aspects of the exercise. Allow the student to further experiment to confir Moving Forward Misconception/Error The student is unable to correctly determine if the given conditions form a unique triangle. Examples of Student Work at this Level The student is able to draw a triangle with angle measures 110°, 30°, and 40° but says it is not possible to draw m The student justifies this decision by explaining: If you tried to draw a different triangle with the same angles, you’d get the same triangle but it would jus There is only one way that you can make the angles the right measure. No matter how you arrange the angles, they will always be the same distance from each side. Questions Eliciting Thinking How long are the sides of your triangle? Did they have to be these lengths? What if you doubled the length of each side of the triangle? Would the angle measures change? How can you fin Instructional Implications Ask the student to draw a working line and measure a length that is double the length of one side of the triangle in the third vertex of the triangle. Have the student measure the lengths of these sides and compare them to the le opportunity to conclude: Three angle measures do not determine a unique triangle. Two angle measures determine the measure of the third angle of the triangle. Two angle measures and their included side length will determine a unique triangle. Relate these conclusions to the relevant aspects of the exercise. Allow the student to further experiment to confir Almost There Misconception/Error The student does not adequately explain why the given conditions do not determine a unique triangle. Examples of Student Work at this Level The student is able to draw a triangle with angle measures 110°, 30°, and 40° and says it is possible to draw mor The student explains: You can extend the sides and not change the angles. You can have the lengths different but the angles the same. You could have the same angle measures but different lengths of the sides. For example, if you shortened They would still have the same angle measures just different sides. Questions Eliciting Thinking Can you change the side to any length or do they have to be proportional to the original lengths? How do you kn Show me (draw) an example of another triangle with different lengths but the same three angle measures. What What vocabulary words describe this situation? Do you know what proportional means? Instructional Implications Explain to the student that three angle measures do not determine a unique triangle. Provide opportunities for the drawings, the lengths of sides change by a scale factor (e.g., proportionally) but the relationship between the side explanation using mathematical terminology. Got It Misconception/Error The student provides complete and correct responses to all components of the task. Examples of Student Work at this Level The student is able to draw a triangle with angle measures 110°, 30°, and 40° and says it is possible to draw mor Questions Eliciting Thinking What do you mean by increase or decrease all the lengths? Are you referring to addition and subtraction or mult Instructional Implications Address any issues with the use of notation or the placement of symbols in the drawing. Pair the student with a Moving Forward partner to share strategies for drawing triangles. Consider implementing the MFAS tasks Drawing Triangles SAS, Drawing Triangles ASA, Drawing Triangles S ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: o o o o Drawing Triangles AAA worksheet Ruler Protractor Technology such as Geogebra (optional) 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 License: CPALMS License - no distribution - non commercial Related Standards Name MAFS.7.G.1.2: Description Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.