The Arizona STEM Acceleration Project

Let's Play Tanks: A Lesson on Parabolic Paths

Let's Play Tanks: A Lesson on Parabolic Paths

An 8th-12th grade STEM lesson

Author: Karen Larsen

Date: 09/23/23

Notes for teachers

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• The original lesson was taught to 10th & 11th grade students who had already learned about the equations of parabolas but those portions can be easily omitted if you just want to look at the phenomena of projectile motion.

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• Take the time to tryout the lesson before the kids, it’s fun and will help you understand the quirks.

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• Things go a lot quicker and better if you have the grids and a demonstration to show at the beginning of class.

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• You could also use someone throwing a ball to do the same thing without the tanks.

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• Doing Groups of 2-3 students worked best for using the cameras and charting the paths and such.

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List of Materials (1 per group of each item)

• A large grid (I had my students make some on butcher paper with the grids inch by inch 2ft tall by 3ft long the day before) or you can get blankets that have them or white boards or smart board with a picture of a grid or just tape up multiple pieces of graph paper.
• A slow motion camera (we used our class iphones I purchased with the grant and my students iphones 8 or newer)
• Tanks (anything that can launch a small projectile including a child with a ball but I got small cheap tanks from TEMU)
• Target (something you are trying to hit with the projectile)
• A table or the floor if you can get your grid paper sitting on the floor and taped to a wall or something.
• Computer (optional) * only if you want them to use programming to find the equation.

Mathematics

Standards

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N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y=fx and y=gx intersect are the solutions of the equation fx=gx; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

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Dimensions of the Science and Engineering Standards

P3: Changing the movement of an object requires a net force to be acting on it.

U1: Scientists explain phenomena using evidence obtained from observations and or scientific investigations. Evidence may lead to developing models and or theories to make sense of phenomena. As new evidence is discovered, models and theories can be revised.

U2: The knowledge produced by science is used in engineering and technologies to solve problems and/or create products.

U3: Applications of science often have both positive and negative ethical, social, economic, and/or political implications.

NGSS SEPS.4: Analyzing and Interpreting Data

NGSS SEPS.5: Using Mathematics and Computational Thinking

NGSS SEPS.6: Constructing Explanations and Designing Solutions

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Objectives: (1)Show students that parabola’s are phenomena of projectile motion due to net forces and gravity. (2)Help students understand the mathematical terms of zero’s, rates, extrema (maximum) and vertex in real world context.

Today students will see a moving object chart a parabola. Students will interpret the vertex and maxima of this parabola and the meaning of its zero’s. With the aid of an online aid students will find the equation for the parabolic path of their projectile.

Today teachers will help students understand more about the nature of motion and gravity and relate projectile motion and its mathematical computations to real-world concepts.

Agenda (1 or 2) (55 minute classes)

Day 1

• (5-10 minutes) Demonstration (Teacher Demonstrates how the lesson works and the technology)
• (5-10 minutes) Student Set-up
• (25-35 minutes) Students Play Tanks! While recording their results.

Day 2 (Can be Homework or 2nd 55 minute class.)

• (20-30 minutes) Analyze slow-motion videos and recreate the graphs of your parabolas (on computer or on paper)
• (15-25 minutes) report on findings of different parabolic paths (equations, zeroes, maximas and success of the task.)

Lead in: Militaries spend millions of dollars to calculate and execute the most accurate shots and you are already capable of doing this job.

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Today we are going to fire our tanks and break down their motion into a science. This science is actually very common in the physical world for more than just artillery fire. Anytime you watch or play sports, anytime something falls from the sky or even when you jump off the ground, parabolic paths of motion will be there because of gravity.

Hands-on Activity Instructions

• Groups of 2-3 students works well.
• Step by step instructions can be found in the assignment document: Parabola Hands-On

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Here are examples of students shots, hand-drawn graphs and using Geogebra technology to graph.

Assessment

• Quiz on parabolas and their key features.

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• Have them design a similar assignment.

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• Have them identify other places where these concepts could be used and real life and then have them demonstrate how. (we did this with 2-3 minute powerpoints with their partners)

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Differentiation

• Instead of using the little tanks have the students toss a ball to a partner and walk out distances rather than use the graph. (answer questions like how did the ball move, did it go up or down?)
• There are plenty of online tanks games that can do these measurements and maybe having them play the games online rather than having to physically have projectile motion.

Remediation

Extension/Enrichment

• Have the students use two tanks at once and fire on each other and see where their arks overlap.
• Have the students look up slow-motion video clips their favorite sport and have them draw a parabola for the movement of the ball in the sport.
• Here is cool website where I got the background picture on slide 7 that talks a lot more about parabolic paths and their uses that you could check out Projectile Motion .
• Take a field trip to a military base or to Nasa for Rockets or to a sports event or to indoor skydiving.