[b]Activity 2.1: Lesson Plan - A Guided Discovery[/b][b]Description:[/b] This 45-minute lesson plan guides educators through using the Interactive Triangle Classifier applet to foster a student-led, discovery-based learning experience. The goal is for students to construct their own understanding of triangle classifications through hands-on exploration.[b]Lesson Details[/b][list][*][b]Topic:[/b] Classifying Triangles by Sides and Angles[/*][*][b]Grade Level:[/b] 6th - 8th Grade[/*][*][b]Time Allotment:[/b] 45 minutes[/*][*][b]Learning Objectives:[/b] By the end of this lesson, students will be able to:[list][*][b]Identify[/b] and [b]define[/b] triangle classifications by sides (equilateral, isosceles, scalene).[/*][*][b]Identify[/b] and [b]define[/b] triangle classifications by angles (acute, right, obtuse).[/*][*][b]Classify[/b] a triangle using both its side and angle attributes (e.g., "Right Isosceles").[/*][*][b]Justify[/b] why certain combinations of classifications (e.g., "Obtuse Equilateral") are impossible.[/*][/list][/*][*][b]Materials:[/b][list][*]GeoGebra Interactive Triangle Classifier applet[/*][*]Devices for students (tablets, Chromebooks, or computers)[/*][*]Projector or interactive whiteboard for demonstration[/*][*]Optional: A simple worksheet with the questions from Activities 1.2, 1.3, and 1.4.[/*][/list][/*][/list][b]Lesson Procedure[/b][b]1. Introduction & Hook (5 minutes)[/b][list][*]Start by asking the class: "What makes one triangle different from another?" Project the applet on the board and show a few very different-looking triangles (e.g., a long skinny one, a perfect-looking one).[/*][*]Introduce the day's goal: "Today, we're going to be detectives and discover the secret 'names' or 'classifications' that all triangles have. This tool will help us do it."[/*][*]Briefly demonstrate how to drag the vertices (A, B, C) and point out where to find the side and angle measurements, as covered in [url=https://www.geogebra.org/m/vmhhd5vj][b]Activity 1.1[/b][/url][b][/b].[/*][/list][b]2. Guided Exploration: The Side Story (10 minutes)[/b][list][*]Instruct students to open [url=https://www.geogebra.org/m/zfvycwdt][b]Activity 1.2[/b][/url][b][/b].[/*][*]Pose the challenge: "Your first mission is to build a triangle where all three side lengths are exactly the same. See if you can do it!" Give them a minute to try.[/*][*]Discuss the term [b]Equilateral[/b].[/*][*]Repeat the process for [b]Isosceles[/b] ("exactly two sides equal") and [b]Scalene[/b] ("no sides equal").[/*][*]Use the open-ended questions from Activity 1.2 to spark a brief class discussion. For instance, ask: "When you made your equilateral triangle, what did you notice about its angles?" This subtly previews the next topic.[/*][/list][b]3. Guided Exploration: An Angle on Things (10 minutes)[/b][list][*]Direct students to [url=https://www.geogebra.org/m/rmhxds7k][b]Activity 1.3[/b][/url][b][/b].[/*][*]Pose the next challenge: "Now, let's ignore the sides and focus only on the angles. Can you create a triangle with a perfect 90-degree angle, like the corner of a piece of paper?"[/*][*]Discuss the term [b]Right Triangle[/b].[/*][*]Repeat the process for [b]Acute[/b] ("all angles less than 90°") and [b]Obtuse[/b] ("one angle greater than 90°").[/*][*]Use a key question from Activity 1.3 to check for understanding: "Try to make a triangle with two obtuse angles. Can it be done? Why not?"[/*][/list][b]4. Synthesis & The Final Challenge (15 minutes)[/b][list][*]Explain that every triangle has two names. Give an example on the board: "This triangle is [b]Right[/b] (angle name) and [b]Scalene[/b] (side name)."[/*][*]Direct students to [url=https://www.geogebra.org/m/pcv3h9xc][b]Activity 1.4[/b][/url][b][/b] and present it as the "Final Boss Challenge."[/*][*]Task them to build the specific combinations listed (e.g., Right Scalene, Obtuse Isosceles).[/*][*]Circulate the room, providing support and asking probing questions.[/*][*]Bring the class together for a final discussion. Ask: "Were there any combinations you could [i]not[/i] build?" Use this to lead a conversation about why an [b]Obtuse Equilateral[/b] or [b]Right Equilateral[/b] triangle is impossible, referencing the fact that equilateral triangles always have 60° angles.[/*][/list][b]5. Wrap-Up & Exit Ticket (5 minutes)[/b][list][*]As an exit ticket, project a new triangle on the board using the applet.[/*][*]Ask students to write down its full classification (e.g., Acute Isosceles) on a slip of paper and explain how they know. This provides a quick formative assessment of their understanding.[/*][/list][b]Differentiation[/b][list][*][b]For Support:[/b][list][*]Encourage students to work in pairs.[/*][*]Provide a printed handout with definitions and diagrams of each triangle type.[/*][*]Focus on mastering one classification system (sides or angles) before combining them.[/*][/list][/*][*][b]For Extension:[/b][list][*]Challenge students to discover the [b]Triangle Inequality Theorem[/b] by trying to create a triangle where two short sides don't "reach" each other.[/*][*]Ask them to investigate the relationship between the longest side and the largest angle.[/*][/list][/*][/list]