Moment 1: Introduction to Quadratic Functions (Estimated: 5 minutes)
Start the class by briefly introducing the concept of quadratic functions and their significance in mathematical modeling. Provide a real-world example where quadratic functions are used, such as the trajectory of thrown objects. Use simple language to ensure comprehension and engage students with questions like 'Where have you seen objects follow a curved path?' to activate prior knowledge.

Moment 2: Explaining Parabolas Through Visual Aids (Estimated: 5 minutes)
Utilize visual aids such as graphs or videos that illustrate the shape of a parabola and its properties. Highlight key aspects such as the vertex, axis of symmetry, and direction of opening. Encourage students to note how these features appear in real-world objects like bridges or satellite dishes. It's important to allow them to ask questions during this section to clarify any doubts.

Moment 3: Theoretical Background on Quadratic Equations (Estimated: 5 minutes)
Provide an overview of quadratic equations, discussing their standard form (ax^2 + bx + c = 0) and how they translate onto a graph. Introduce vocabulary such as 'roots' and 'coefficients'. Prompt students to identify and discuss the role of each in determining the graph's shape and position. Evaluate comprehension through quick verbal assessments or asking them to illustrate an example on the board.

Moment 1: Setting Up the Experiment (Estimated: 5 minutes)
Begin by dividing students into small groups of four or five, ensuring that each group has access to one catapult and lightweight balls. Instruct students to clear their workspace and organize the materials. Provide a brief demonstration on how to safely use the catapult. Emphasize the importance of measuring accurately, as well as recording data consistently. Allow students to ask any clarifying questions before proceeding.

Moment 2: Conducting Object Launches (Estimated: 10 minutes)
Guide students to position the catapults on a flat surface and begin launching the balls. Instruct them to launch the balls at different angles and measure the distance and height reached by each ball. Encourage students to repeat the experiment several times for consistency, and record their observations diligently. Walk around the classroom to offer assistance, remind students of their roles in recording the data, and prompt them with questions to enhance their analytical thinking.

Moment 3: Initial Data Review and Clean-up (Estimated: 5 minutes)
Once the experiments are completed, direct students to organize their data in a clean table format. Encourage a brief discussion within groups about their findings, focusing on any patterns or anomalies observed. Prompt them to consider factors that might have influenced the trajectory. Assist groups in reconciling any discrepancies in recorded data. Finally, ensure that students clean up their workspace, returning all materials to their designated spots.

Moment 1: Analyzing Collected Data (Estimated: 10 minutes)
Guide students to work within their groups to organize and analyze the data collected during the experiment. Ask them to transfer their observations onto graph paper and try plotting the measured trajectory points for each ball's launch. Emphasize the importance of identifying trends and patterns and fitting a quadratic curve that traces the trajectory. Move between groups to provide guidance, prompt critical thinking with questions like 'What does your graph tell you about the nature of the ball's path?'. Evaluate the ability to plot data accurately and interpret patterns as indicators of understanding.

Moment 2: Group Discussion and Interpretation (Estimated: 10 minutes)
Lead a class discussion where each group shares their findings. Encourage students to compare their plotted graphs and discuss any similarities or discrepancies. Introduce terminology related to quadratic functions (e.g., vertex, axis of symmetry, roots) to help them articulate their observations clearly. Highlight groups that demonstrate strong collaborative skills and thoughtful interpretations. Ensure participation by asking different students to speak and address any misconceptions detected during presentations. Assess learning by observing the clarity of explanation and peer-to-peer interactions.

Moment 3: Connecting Findings to Real-World Applications (Estimated: 5 minutes)
Facilitate a brief discussion to help students relate their experimental findings to real-world scenarios. Give examples such as the trajectory of a basketball shot or the path followed by fireworks. Prompt students to brainstorm other real-life applications of parabolic trajectories. Encourage them to propose new scenarios where understanding quadratic functions is beneficial. Wrap up the session by reinforcing the significance of mathematical modeling in understanding and predicting real-world phenomena. Evaluate engagement and comprehensive understanding through questions such as 'How might the knowledge of parabolic paths assist in sports strategy?' or 'What professions might utilize these mathematical concepts in their work?'.