Mathematics · Year 13

Active learning ideas

Projectile Motion: Basic Principles

Active learning helps Year 13 students grasp projectile motion because it transforms abstract concepts into observable phenomena. Students see how initial speed and angle affect trajectories when they physically measure and graph motion, making the independence of horizontal and vertical components tangible.

• National Curriculum Attainment Targets
• A-Level: Mathematics - Kinematics

• 25–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Simulation Game
• 45 min · Pairs

Pairs: Ramp Launch Challenge

Pairs build ramps at 30, 45, and 60 degrees using metre sticks and books. They launch marbles, measure range and height with rulers, then plot data to identify maximum range angle. Compare results to equation predictions.

Explain why we can treat horizontal and vertical motion as independent components.

Facilitation Tip

During Ramp Launch Challenge, position ramps so that students can see the ball’s horizontal motion clearly; place timers at 0.5 m and 1.0 m marks for accurate speed calculations.

What to look for

Present students with a scenario: A ball is kicked with an initial velocity of 20 m/s at an angle of 30 degrees to the horizontal. Ask them to calculate the initial horizontal and vertical components of the velocity. Then, ask them to state the acceleration acting on the ball in both the horizontal and vertical directions.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Simulation Game
• 50 min · Small Groups

Small Groups: Trajectory Mapping

Groups video a thrown ball from side view, use free software to track path and extract coordinates. Separate horizontal and vertical motions on graphs, calculate accelerations. Discuss independence with class.

Analyze how the initial velocity and angle of projection affect the range and maximum height.

Facilitation Tip

For Trajectory Mapping, provide graph paper with pre-marked axes so students focus on plotting data rather than setting scales.

What to look for

Pose the question: 'If you launch two identical projectiles with the same initial speed, one straight up and one at a 45-degree angle, which one will travel further horizontally, and why?' Facilitate a discussion where students explain the independence of horizontal and vertical motion.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Simulation Game
• 30 min · Whole Class

Whole Class: Prediction Relay

Project scenarios with given velocity, angle, height. Students predict range, height, flight time individually, then relay answers in chain; verify with live demo or simulation. Adjust for discrepancies.

Predict the time of flight for a projectile launched from a given height.

Facilitation Tip

In Prediction Relay, circulate with sticky notes to capture student reasoning before revealing outcomes, then use these notes to guide whole-class discussion.

What to look for

Provide students with a diagram of a projectile launched from a cliff. Ask them to write down the equations they would use to find the time of flight and the horizontal range, identifying each variable they would need to know.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 04

• Simulation Game
• 25 min · Individual

Individual: Desmos Graphing

Students input parametric equations in Desmos, vary velocity and angle sliders. Trace range, height; export graphs for portfolio. Note patterns like symmetry at 45 degrees.

Explain why we can treat horizontal and vertical motion as independent components.

Facilitation Tip

During Desmos Graphing, require students to label each graph with equations and initial conditions before sharing with partners.

What to look for

Present students with a scenario: A ball is kicked with an initial velocity of 20 m/s at an angle of 30 degrees to the horizontal. Ask them to calculate the initial horizontal and vertical components of the velocity. Then, ask them to state the acceleration acting on the ball in both the horizontal and vertical directions.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

A few notes on teaching this unit

Teachers should start with hands-on measurement to build intuition, then introduce equations as tools to explain what students observe. Avoid rushing to formulas before students see how changing angle or speed alters the path. Research shows that letting students test predictions with real objects reduces misconceptions about gravity’s role in horizontal motion. Use peer discussion to surface assumptions, such as assuming symmetry in all trajectories, and address them with targeted experiments.

Students will confidently resolve velocity into components, predict range and height from given data, and explain why 45 degrees maximises range from ground level. They will also adjust predictions when launch height changes, using evidence from their measurements.

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Watch Out for These Misconceptions

• During Ramp Launch Challenge, watch for students who assume horizontal velocity decreases over time.

  Ask them to measure the time the ball takes to travel each marked horizontal distance; the constant time intervals will reveal that horizontal speed is unchanged, reinforcing the concept of independent motion.

• During Trajectory Mapping, watch for students who draw symmetric paths for projectiles launched from heights.

  Have them compare the time to reach maximum height with the time to descend to the ground using their plotted data; asymmetry will become clear through measurement.

• During Prediction Relay, watch for students who claim that a 90-degree launch yields maximum range.

  Use the angle-variation data from the ramp launches to plot range versus angle, showing the peak at 45 degrees and prompting students to explain why vertical launch produces zero horizontal displacement.

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Methods used in this brief

• Simulation Game