Activity 2.4: Assessment and Extension Ideas
This activity provides teachers with a variety of tools to assess student understanding and ideas to extend the learning for advanced students or to connect the topic to other concepts. These suggestions can be adapted for use in class, as homework, or in larger projects.Formative AssessmentUse these strategies during or immediately after the lesson to gauge student understanding in real-time.
- Exit Ticket
- Task: Use the applet to create a specific triangle on the projector (e.g., an Obtuse Scalene triangle). Ask students to write down its full classification on a slip of paper and explain why it fits that classification (e.g., "It has one angle over 90° and all its sides are different lengths.").
- Purpose: A quick and effective way to see if individual students can apply both classification systems correctly.
- Show Me on Your Whiteboard
- Task: Call out a triangle classification, like "Right Isosceles" or "Acute Scalene." Give students 30-60 seconds to try and create it using their applet. Then, have them write down the side lengths and angle measures they achieved on a personal whiteboard and hold it up for everyone to see.
- Purpose: Allows you to quickly scan the room and see who is grasping the concepts and who might be struggling.
- Classification Quiz
- Task: Provide a worksheet with 5-6 pre-drawn triangles, complete with side and angle measurements. Students must write the full, correct classification for each (e.g., "Acute Isosceles"). Include one or two "impossible" triangles (like a triangle with two obtuse angles) and ask students to explain why it cannot exist.
- Purpose: A traditional method to assess if students have mastered the definitions and their application.
- "Triangle Hunt" Mini-Project
- Task: Ask students to find and photograph 3-5 examples of triangles in their real-world environment (e.g., a yield sign, a roof gable, a bridge support). For each photo, they must estimate the type of triangle and justify their classification.
- Purpose: Encourages students to see geometry in the world around them and apply their knowledge in a practical context.
- Discovering the Triangle Inequality Theorem
- Challenge: "Using the applet, try to build a triangle with side lengths of 3, 4, and 8. What happens?"
- Exploration: Students will discover that the two shorter sides don't connect. This leads to an investigation of the theorem: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Angle Sum Theorem Investigation
- Challenge: "Create five very different triangles—make them scalene, isosceles, right, obtuse, etc. For each one, write down the three angle measures and add them together. What do you notice?"
- Exploration: Students will discover that the sum of the angles in every triangle is always 180°. The applet provides compelling visual proof.
- Relationship Between Sides and Opposite Angles
- Challenge: "In any scalene triangle you create, find the longest side. Now, look at the angle directly across from it. Then, find the shortest side and the angle opposite it. What is the relationship you see?"
- Exploration: This guides students to discover that the largest angle is always opposite the longest side, and the smallest angle is always opposite the shortest side.