UNIT PLAN: Paper Airplanes and Flight
NYS Mathematics, Science, and Technology Learning Standards Addressed
Standard 1: Students will use mathematical analysis, scientific inquiry, and engineering
design, as appropriate, to pose questions, seek answers, and develop
solutions.
Standard 6: Students will understand the relationships and common themes that connect
mathematics, science, and technology and apply the themes to these and
other areas of learning.
Standard 7: Students will apply the knowledge and thinking skills of mathematics,
science, and technology to address real-life problems and make informed
decisions.
Need to link carefully to specific math and science standards that apply to your grade
level. See Power Point presentation for rationale and skills developed.
Unit Objectives
1.
Students will explore methods of folding paper airplanes.
2.
Students will discover/recognize/identify mathematical concepts utilized in folding
(parallel, perpendicular, angle, symmetry, …).
3.
Students will fly various folded airplanes. (3 trials for each of 2 designs per team)
4.
Students will observe, measure and assess aspects of flight (speed, distance traveled,
length of time aloft, direction of travel).
5.
Students will perform activities to discover and name basic forces that act on a plane in
flight (thrust, lift, drag, gravity) as well as how to counteract common instabilities (roll,
pitch, yaw) which hinder flight.
6.
Students will determine which flight characteristic they want to optimize in the design of
the plane, redesign, refold a new plane.
7.
Students will fly redesigned airplanes, collect measurements and record observations.
(3 trials for one optimal design, per team)
8.
Students will analyze and present results.
Materials
Paper (unlined photocopy paper)
Folding Instructions and/or the book Championship Paper Planes, Paul Jackson, 1988, ISBN 07607-2185-8, Barnes & Noble Books by arrangement with Michael O’Mara Books in London.
Scissors
Paper clips
Tape
Markers
Stop watches
Rulers
Yardsticks
Posterboard
Tissue Paper Strips
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Cheri Boyd
Anticipatory Set
Have you ever folded paper to make something? We will be creating paper airplanes
using our own designs, and also by following diagrams and reading written instructions for some
interesting designs. You’ll make and see geometry as you fold.
Then we’ll fly the planes and investigate which designs produce different flight patterns.
Your job will be to modify the design of your plane to produce better flight.
Lesson Body (Guided Inquiry)
Essential Questions
Q1: What ideas from geometry are present (inherent) in folding paper airplanes?
Q2: Explain three important elements of flight.
Q3: How can you optimize flight?
Q4: How is the scientific method used in this project?
Here are my detailed planning notes from our workshop, including expected/hoped for input
from students:
Geometry and Paper Airplane Design
Sequence of Learning Activities:
9:30 – 9:45
1) Prewriting Questions: (Free write first (3 min), then add any mathematical or scientific
words you think relate or apply (2 min). Share with partner (2 min). Share with entire
group (5 min). Record shared thoughts on board.)
What makes a “good” paper airplane?
folded neatly/evenly/symmetrical/balanced
flies well/far/high/long
flies in interesting paths
flies reliably/doesn’t crash
sturdy even after bumping into objects
Why might a paper airplane not fly well?
bulky/too heavy/too light (wrong materials, drag)
not balanced (faulty design or faulty construction)
not folded carefully (faulty construction of good design)
doesn’t stay together/needs tape or support (faulty design, drag)
front heavy (dives down)/back heavy (rear sinks down) [pitches]
veers left or right
rolls (barrel rolls on x-axis)
flat spins [yaws]
error in launch motion (thrust issues)
additional uncontrolled variables (wind speed, wind direction)
9:45 – 10:25
2) Fold an airplane (written instructions provided)
Brief introduction to folding terminology 9:45 – 9:55
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Cheri Boyd
They fold individually, help one another, we wander and discuss 9:55 – 10:25
Active discovery and investigation of geometrical concepts (see separate handout) inherent
in folding Use geometry vocabulary throughout the lesson.
Skills developed:
Read a blueprint/diagram
Follow written and/or verbal instruction
Collaborate
Create a model that will be used to study specific properties and concepts
10:25 – 10:35
3) Reflect in Scientific Notebook:
What geometry terms or examples did you notice while folding?
Explain something you learned while folding.
Describe a problem you had while folding.
What would you try to fix the problem?
(Continue in Scientific Notebook)
10:35 – 10:45
Which plane will fly best? (see all models they made, additional folded models provided)
Why? (visual observation, predict, hypothesize)
Each team choose two different models for experiment.
10:45 – 10:50 Teach launch motion to entire group
4) Fly them in the halls
10:50 – 11:05
If time and interest, measure and record 3 flights for each of 2 planes. Make launch
motion consistent. Have meter sticks laid out in hallway along wall. Provide stopwatches.
One team start at each doorway at top of stairwells and head in (4 groups). One team start
at each end of center hallway and aim in (2 groups).
Otherwise, just fly them several times and visually decide which plane “flew better”.
If time: Identify variable you want to measure. How do you define “flew better”?
(farthest distance, longest time in the air, fastest speed, most interesting flight path,
consistent flights, …)
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Cheri Boyd
11:05 – 11:25
5) Analyze what happened. What went wrong?
What flight problem(s) did you observe?
How could you correct one problem? (Provide tape, paper clips, scissors, rulers)
Add paper clips or tape to adjust balance.
Create more flaps.
Refold more symmetrically and/or more cleanly (less bulk)
Make one change to one plane. Refly that plane 3 flights. Compare results to original
data.
11:25 – 11:30
Document (include before and after sketches) the design changes and flight results in
your Scientific Notebook.
11:30 – 12:10
6) Investigate forces that effect flight.
11:30 – 11:35
Prewrite about these after flying experience. What descriptions can students make on
their own? What vocabulary do they use? Can they draw diagrams for any specific
situations they observed?
Experiments:
lift
(at seats) 11:35 – 11:45
- blow above strip of paper to lessen air pressure there
- greater air pressure below strip cause paper to rise, creating lift
- provide diagram of airplane wing with moving air streams, they label
- this is Bernoulli’s Principle
- bending tips of airplane wings up or down slightly can assist lift and
significantly improve flight
- similar to adding flaps
- write about lift (1 min)
gravity
-
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(at seats) 11:45 – 11:55
design must create enough lift to overcome effects of gravity
drop heavy and light objects from same height at same time, should
land at same moment (unless large difference in objects allows
significant air resistance) They choose objects from room. Have things
available.
Cheri Boyd
-
-
drag
This is Galileo’s experiment, orange vs. grape
Planes with greater mass need greater thrust
Extension: Connect to real world data, have students research
materials used in airplane construction and power of engines. Look for
newspaper announcements of contracts awarded defense contractors to
develop new style of aircraft
Lift from wings must be greater than pull of gravity
Write about gravity (1 min)
11:55 – 12:05
- race with one person holding a piece of posterboard in front of them
- poor folding (and some designs) can create drag on paper airplanes
- look at front profiles of folded models
- write about drag (1 min)
thrust
-
what serves as thrust for a paper airplane? (arm, wind)
forward thrust must be greater than drag
Write about thrust (1 min)
12:05 – 12:20
It would be nice if they came up with these “plane instabilities” (below) in prewriting, sharing.
Probably no time, so draw out in quick discussion familiar problem flight motions below – pitch
is most common.
Demonstrate with plane in hand – terms and diagrams on screen. Ask them how to counteract the
problems.
pitch
(nose dives down, or rising nose causes rear to fall to earth)
How could you counteract nose dive pitch? (bend rear corner wing tips up)
How could you counteract nose up pitch? (bend rear corner wing tips
down) Try this! This is valuable and often used information 
roll
(as in stunt flying, dip wing down and keep doing barrel rolls)
- horizontally flat sturdy paper will roll when “flown”
- counteract roll by making a center crease/angle between the wings
(the dihedral angle)
- with this angle, the plane can rock from side to side and still resist the
roll
yaw (flat circular spin as in horrific weather)
- counteracted by vertical fuselage (body of plane, vertical height of
main center crease)
- counteracted by rudders (vertically fold up entire outer edge of each
wing parallel to center crease)
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12:20 – 12:25
Draw a flat rectangle in perspective – three of them.
Have teachers draw a linear axis and a circular arrow to show the differences between:
pitch (turning/rotation about side to side axis – commonly the y-axis in 3D)
roll (turning/rotation about the front to back axis – commonly the x-axis in 3D)
yaw (turning/rotation about the up to down vertical axis – commonly the z-axis in 3D)
12: 25 – 12:30
Reflect on the morning in your notebook.
What ideas or practices might you use with your students?
Closure
Geometry is all around you. Take the time to notice, use and appreciate it.
Recognize and use the optimization process (design, test, observe, measure, analyze, modify) in
all you do. Constant and never-ending improvement! Be realistic about constraints.
Accommodations for IEP
1. Have pairs of students teach each other how to fold a plane.
2. Pair classes of fifth graders and kindergartners to fold and fly together.
3. Use different level instructions for folding several planes, increasing from simple to
intermediate to advanced folding techniques.
Homework/Assessment
1. Individual students fold a new design.
2. Students identify geometrical objects and concepts occurring at each specific stage or
motion in folding.
3. Students create written instructions and labeled diagrams (step by step) to allow others to
fold a plane they design themselves. Have another student read and fold.
4. Students will describe a new understanding they had while folding (a key moment, how a
problem was solved).
5. Students describe and demonstrate forces involved, principles of flight, and flight
instabilities.
Extensions
Gliders, airfoils (flying wings)
Mechanized flight (private, commercial, military airplanes)
Cost of flight and design of new planes
Classifying things that fly
Historical timeline of human flight
Literature about flight– fantasy, myth, non-fiction, technical manuals
Resources
02/12/16
See last slide of Power Point
Cheri Boyd
02/12/16
Cheri Boyd