August 24, 2010

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The Similar Triangle Rocket project is a group activity that focuses on the application of right and similar triangles as applied to rocket flight.

- Mathematics > General

- Grade 6
- Grade 7
- Grade 8

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**Introduction:** The Similar Triangle Rocket project is a group activity that
focuses on the application of right and similar triangles as applied to rocket
flight.

**Timing:** This project requires 60 minutes of class time to construct
the rocket and 60 minutes to complete the activity. Break it up over four periods.

**Group Size:** Group and Individual

**Learning Objectives:** The objective of this activity is to:

a) Review right and similar triangles

b) Use students’ understanding of triangles to investigate path a rocket

c) Integrate a creative and competitive component into a traditional math lesson

**Guiding Questions:**

How can various types of linear equations be incorporated into a flipbook?

**Materials:** There are two components of this project: rocket
construction and the similar triangle activity.

Rocket Construction – 2-Liter soda bottles, box cutter, scissors, cardboard, hot glue gun and glue sticks, duct tape, manila folder, scotch tape, markers and paint for decoration.

Similar Triangle Activity – Inclinometers (constructed by students), trundle, bottle rocket launcher, tire pump w/psi gauge, water container, graduated beaker, ruler, and protractor

Photocopy enough activity sheets for each student and enough inclinometer construction sheets for each group.

**Ordering Resources:**

Trundle

Launchers1) ?

- Easy to use, but not particularly stable and you will swamp out a spot

2) ? - This is what I use. Very easy to set up and use.

**Procedures:**

This project is really three parts: rocket construction, rocket firing and the similar triangle activity. The procedure will look at each section individually:

*Rocket Construction:*

Building the rockets will require two 45-minute blocks, including the initial presentation. As a class, discuss the basics of rocket construction. The PowerPoint presentation covers the bare minimum for designing a functioning rocket. An Internet search of “soda bottle rockets” will provide a multitude of information on how to build and design these things. The main points are the weighting, the nose cone, and fins. Weighting the rocket is crucial. If the center of mass is not higher than the center of pressure, the rocket will tumble. A good rule of thumb is somewhere between 100-200 grams in the nose cone. The nose cone can be a simple cardboard, or you can get really creative and use a reshaped bottle called a guppy. Most students choose to just use the nozzle end of a cut 2-L bottle as the nose cone. Pictures of the various designs can be found in the PowerPoint presentation. The fins can really be any shape as long as they are not upward sweeping. Symmetry and spacing is the key with fins. There are obviously other parameters to consider, but for the purposes of this activity, we are just shooting for a functioning rocket.

The PowerPoint includes the contest component of the rocket activity. This could be removed, depending on your learning objectives. The contest adds a bit more excitement to results of the standard math activity. It is a great way to get wider range of students to shine.

At some point in time during the construction time, the group should build its inclinometer.

*Rocket Firing:*

Choose your site wisely. Football fields are great. Rockets go pretty high up, so make sure there are no cars and not much pedestrian traffic in your location. On firing day, immediately have students fill their rockets all the way up to the top with water before heading to your launch site. You will need to bring a bucket and a few measuring cylinders. When you get to your launch site, have students empty their rockets of water into the bucket and refill to their desired firing level with the measuring cylinders. A good rule of thumb is 700 mL. The extra water is there is case of a misfire. Each group should have constructed its inclinometer. It can be a challenge to keep everyone engaged when firing the rockets. My students typically work in groups of four, so they will have two rockets to deal with and different roles during the launching. One group member will pull the cord and retrieve the rocket, one will use the trundle, one will be recording the data collected during the firing on the activity sheet, and the fourth is an inclinometer reader. The inclinometer reader is one of many. Each group has one, so there may be a total of five-10 inclinometer readers in the class, depending on your numbers. They all take readings and we usually throw out the high and low values and keep the middle three. The inclinometer readers should stand at least 40 meters away from the launch area and have a clean line of sight for the rocket’s launch. Using the inclinometer is pretty straight forward, just sight on the rocket until it reaches its highest point, hold it in that position until the washer is no longer moving, place a finger on the string to hold the measurement, and read it. The trundle user is going to measure the base of the right triangle created between the rocket’s highest point and the inclinometer readers. The trundle reader should find the mid-point of the rocket’s flight by trundling from the launch area to where the rocket landed, dividing that distance by two, and trundling back to the mid-point. From there, they will trundle to the middle-most inclinometer reader and record this distance as the base of their triangle. The three angles and the base of the triangle are the only readings that need to be taken during the launch.

Firing the rockets is the most exciting part, but it is also the trickiest. Have students practice pulling the cord before the actual launch. They need to give a sharp low pull along the axis of the launching pin. MAKE SURE THEY CANNOT PULL THE ROCKET TOWARDS THEM DURING LAUNCH! The bottles can be pressurized up to 100 psi, but this gets very dangerous. I fire at 40 psi with younger students.

*Note: Rockets can be dangerous. Spend some time testing the firing
process before launching with students, never over-pressurize, always wear and
have students wear goggles, keep students out of the landing area, and don’t
let students sit down (in case they need to run).*

*Similar Triangle Activity:*

Read through the opening sections as a class. This part of the activity is individual, so students may have varying levels of competence with right and similar triangles.

Using the graph paper provided, students must choose an appropriate scale for the base. Try and have them maximize the use of the graph paper by choosing the largest appropriate scale. After they draw their base, they must use the launch angle (q) to construct a right triangle. Once the triangle is constructed they should measure the height and convert it to meters using the graph scale. They now need to add in the average eye level of the inclinometer readers. This is the total vertical height of the rocket. We study a little bit of trigonometry, so I have them check their results with the tangent function. Not a normal topic for Pre-Algebra, but certainly within their grasp.

**Assessment:** Student’s Similar Triangle Rocket project should be graded
based the correctness of their similar triangle graph and how well their calculated
height matches up with the trigonometric height.

**Answer Key:** Each group’s Similar Triangle Rocket project will be
different, so an answer key would be of no use. Comparing group member’s results against each other could be
helpful, since they have the same readings.

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