Paper Planes: Level 4

Purpose

In this unit, students investigate changing one variable to see if they can make a paper plane fly the longest. They will need to define what is meant by the longest.  They use scatter plots to establish a possible relationship between variables, then use what they have found to make a paper plane to enter a class competition.

Achievement Objectives
GM4-1: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
Specific Learning Outcomes
• Design an investigation.
• Measure accurately using length and time.
• Record data in tables.
• Use scatter plot graphs to display paired numerical data.
Description of Mathematics

In this unit students plan and carry out their own statistical investigation to find out what makes a paper plane fly the longest. 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.

Variable

A variable records characteristics of individuals or things. There are two types of variables - categorical and numerical.

Categorical variables

Categorical variables classify individuals or objects into categories.  For example, the method of travel to school; colour of eyes.

Numerical variables

Numerical variables include variables that are measured e.g. the time taken to travel to school, and variables that are counted e.g. the number of traffic lights between home and school.  Measured numerical variables are called continuous numerical variables.  Counted numerical variables are called discrete numerical variables.

Scatterplots

A scatterplot is a display for paired numerical variables. For example, a sample of students from CensusAtSchool was taken and their heights and arm spans graphed.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

• providing a paper plane template to use and direct as to the variable to adjust
• the type of data collected; categorical data can be easier to manage than numerical data. For example, this unit focuses on collecting measurement data about paper planes. One way to adapt it would be for students to research paper planes online and identify the different ways they are classified, collect this information, and display it. For example, paper planes can be classified by airtime/time aloft, speed, distance, stunts/aerobatic, easy through expert to make, category of plane e.g. dart, fighter jet etc.
• the type of analysis – and the support given to do the analysis
• providing prompts for writing descriptive statements
• teacher support at all stages of the investigation.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

• the statistical enquiry process can be applied to many topics and selecting ones that are of interest to your students should always be a priority
• this investigation focuses on paper planes, but other similar investigations can be carried out for paper helicopters, see examples here.
Required Resource Materials
• Instructions for a variety of different paper planes, search online or have a range of books available
• Stopwatches
• A variety of measuring instruments, 30 cm rulers, metre rulers, measuring tapes
• A4 paper
• Paper and pens for recording
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, and measured time using minutes and seconds. They should also know the relationship between metres, centimetres and millimetres and between minutes and seconds.

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 to see which plane can fly the longest. 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 the longest.
What might be meant by the longest? Is this the longest distance, or the longest time, or some other longest?
What features would a plane that can fly a long way have/ fly for a long time have?
If you were to make a plane to fly a long way/long time 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 or time a plane will fly. Discuss these features and introduce the word variable.
• Identify the different numerical variables that could be involved in the activity.
• how far the plane flies
• how long the plane flies for
• the length of the plane
• the wingspan of the plane
• the number of paper clips on the plane.
• Identify the response or outcome variable that we will be measuring, either length of flight or time of flight, and then discuss how we will measure it (groups might want to do both and the class competition could include both, with their places in each combining to get an overall winner)
• e.g. flight time starts from when the plane leaves the throwers hand to when it lands on the ground, Which units of seconds, minutes or hours would be most appropriate for time? Why?
• e.g. flight length – throwers must be behind a line, the place the plane touches the ground is identified (not where it ends up after skidding along the ground), the distance from the line to the where the plane touches the ground is measured. Which units of measure, millimetres, centimetres or metres would be most appropriate for distance? Why?
• Identify the possible explanatory variables (the feature of the plane that we will change) and then discuss how they will be measured
• e.g. wingspan – measure from tip to tip
3. 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?
4. 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.

Investigation Steps

1. Make an assertion (a thoughtful statement) on a variable that will affect flight distance/time.
2. Choose a basic design for your paper plane; then modify (change features of) the variable for this design to provide a variety of different models, based on your assertion.
3. Decide on how to test each plane, e.g. how many times will you throw the plane at each distance, how will you decide which outcome measure best represents for the variable (feature) chosen
4. Collect data by trialling each plane and recording the distance/time it flies alongside the variable (e.g. wingspan, plane length) you are testing. This can be done by recording the data in a spreadsheet or in a table in a statistical software package such as CODAP.
5. Plot data on a scatterplot to establish whether there is a relationship between the variables you are investigating. This can easily be done using CODAP or spreadsheet software, see Cars for ideas on plotting scatterplots using CODAP.

Example Investigation

1. Assertion: a longer wingspan will help a paper plane fly a greater distance.
2. To test the assertion about wingspans several planes with varying wingspans are required.
3. Decided to test each plane three times and record the middle measurement.
4. Data collected as below
 Plane Wingspan Middle 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
5. Data plotted as below
6. As the wingspan increases so does the distance flown.

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 (in science they use 3-5 trials, pragmatically because of time constraints, but this is usually sufficient to see if there are any outliers, in higher levels they also take the mean, but for this level we will use the middle value when placed in order (median)).
• The best way to record and plot the data.
• Is all data plotted or an average e.g. the middle value (median) for each different set of trials.

Reflecting

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

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?