Paper Planes

Purpose

In this unit, students investigate one variable to see if they can make a paper plane fly further. They use scatter plots to establish a possible relationship between variables, then use what they have found to make a paper plane to enter into a class competition. 

Specific Learning Outcomes
  • measure accurately using metres, centimetres and millimetres
  • record data in tables
  • use scatter plot graphs to identify relationships between variables
Description of Mathematics

In this unit students plan and carry out their own statistical investigation to find out what makes a paper plane fly further. Like all such investigations it is important to have a good idea of what data should be collected, how much data is needed and what the limitations of the collecting mechanism are. It is also important that students are clear about which variable they will be changing so that all other variables can be kept constant. Key vocabulary will need introduction and discussion.

This unit provides an opportunity to focus on decimal notation and to convert between units of measure. In their investigations students will need to measure accurately using metres, centimetres and millimetres to enable the relationship to be established.  Make explicit for students the relationships between the units of metres, centimetres and millimetres: There are 100 centimetres in a metre. There are 10 millimetres in a centimetre. There are 1000 millimetres in a metre. As the students work with measuring the distances their planes fly, use these relationships to develop student knowledge of decimal notation. For example: If we know there are 100 centimetres in a metre, how many metres are there in a cm?  How would we write one hundredth of a metre? 0.01m.  If the nose section of a paper plane measured 4 hundredths of a metre how would we write that? 0.04m How many cm would that be? 4cm. If a plane measured 27 hundredths of a metre how would we write that and how many cm would that be? 0.27m and 27cm.

Students should be operating at Number Framework Stage 6, Advanced Additive. 

Required Resource Materials

Instructions for a variety of different paper planes, see links below or have a range of books available

Access to computers with Excel or similar

Stopwatches

A variety of measuring instruments, 30 cm rulers, metre rulers, measuring tapes

A4 paper

Paper and pens for recording

Key Vocabulary

centimetres, millimetres, metres, units of measure, dot plots, graphs, dot plots, scatter plots, features, variables, investigations, measures, relationships, limitations, decimals, assertion

Activity

Prior experiences

Before working on this unit, students should have engaged in practical measurement exercises where they measured items of varying length using metres, centimetres and millimetres. They should also know the relationship between metres, centimetres and millimetres.

Getting started

  1. Introduce the topic of paper planes to the students by telling them there will be a competition at the end of the week and they will all be designing their own planes to enter. Encourage them to think about the features of a paper plane that would help it to fly a long distance.
    What features would a plane that can fly a long way have?
    If you were to make a plane to fly a long way what would you need to consider?

  2. Allow students time with paper to carry out initial experiments with planes and then brainstorm their ideas about features that affect the distance a plane will fly. Discuss these features and introduce the word variable.

  3. Facilitate a discussion on how a competition on making a paper plane might be run.
    Which units of measure, millimetres, centimetres of metres would be most appropriate? Why?

  4. Have students work in pairs to experiment with the different units for measurement, and then facilitate a discussion about the units to be chosen for the class competition.
    Which units allow for the greatest accuracy? Why?

  5. Set criteria for the materials to be used to make the planes in the following sessions. These criteria need to include a limit on the size of the paper that can be used and details on the numbers and amounts of other materials that can be used e.g. paper clips, tape or staples.

Exploring

Over the next few days have students work in pairs or small groups to carry out investigations using the following steps. Students may want to research the flight of paper planes before they chose the focus of their investigations. Some of the sites listed above would be useful for this. These sites also provide a variety of planes that could be used as basic designs.

Investigation Steps

  1. Make an assertion (a thoughtful statement) on a variable that will affect flight distance.
  2. Choose a basic design for your paper plane; then modify (change features of) this design to provide a variety of different models, based on your assertion.
  3. Collect data by trialling each plane and recording the distance it travels alongside the variable you are testing.
  4. Plot data on a scatter plot to establish whether there is a relationship between the variables you are investigating. This can easily be done on Excel.
  5. Check your assertion. Was your original idea correct? Modify your plane design accordingly.

Example Investigation

  1. Assertion: a longer wing span will help a paper plane fly further.
  2. To test the assertion about wingspans several planes with varying wing spans are required.
  3. Data collected as below

Plane

Wingspan

Average flight distance

1

5.2 cm

3.2 m

2

7.5 cm

5.6 m

3

10.3 cm

6.1 m

4

14.8 cm

6.4 m

5

18.0 cm

8.9 m

  1. Data plotted as below

graph

  1. There is a straight line relationship between wingspan and distance flown therefore to help make planes fly further the wingspan needs to be maximised.

As investigations are carried out the following points may need to be discussed with the students.

  • For the investigations to be a fair test only one variable can be altered across each of the planes to be tested. The planes need to be the same in every respect other than the feature being tested.
  • The number of trials needed for each plane and the best way to record and plot the data. Should average flight distances be used?
  • Lines of best fit for scatter plots.

Reflecting

  1. Hold a competition to see which plane flies the furthest. Ensure accurate measurements are taken of distances flown.

  2. After the competition reflect on the most successful planes.

    What evidence did we have that those planes would be the most successful?

    If we were going to hold another competition which features could we combine to produce a very successful plane?

 


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