# Paper planes: Level 2

Purpose

This unit uses the context of making paper planes to develop understanding of metre and centimetre measures.  Students investigate a variety of paper airplanes designs, experiment to see which planes fly the furthest, and decide winners by measuring and comparing results.

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
GM2-2: Partition and/or combine like measures and communicate them, using numbers and units.
Specific Learning Outcomes
• Estimate using metres and centimetres.
• Measure to the nearest metre and centimetre.
Description of Mathematics

This unit is suitable for students who have had plenty previous experience with non-standard units and have had the concept of standard units introduced. It provides a good context for practising the use of metres and centimetres. In the second unit, Paper Planes L4, students create scatter plots of the distance their planes travel when a variable is changed.

When students can measure lengths effectively using non-standard units, they are ready to move to the use of standard units. The motivation for moving to this stage, often follows from experiences where the students have used different non-standard units for the same length. They can then appreciate that consistency in the units used would allow for the easier and more accurate communication of length measures.

Students' measurement experiences must enable them to:

1. develop an understanding of the size of the standard unit
2. estimate and measure using the unit

The usual sequence used in primary school is to introduce the centimetre first, then the metre, followed later by the kilometre and the millimetre.

The centimetre is often introduced first because it is small enough to measure common objects. The size of the centimetre unit can be established by constructing it, for example by cutting 1-centimetre pieces of paper or straws. Most primary classrooms also have a supply of 1-cm cubes that can be used to measure objects. An appreciation of the size of the unit can be built up through lots of experience in measuring everyday objects. The students should be encouraged to develop their own reference for a centimetre, for example, a fingertip.

As the students become familiar with the size of the centimetre they should be given many opportunities to estimate before measuring. After using centimetre units to measure objects the students can be introduced to the centimetre ruler. It is a good idea to let the students develop their own ruler to begin with. For example, some classrooms have linked cubes which can be joined to form 10 cm rulers. Alternatively pieces of drinking straw could be threaded together.

The correct use of a ruler to measure objects requires specific instruction. The correct alignment of the zero on the ruler with one end of the object needs to be clarified.

Metres and millimetres are established using a similar sequence of experiences: first construct the unit and then use it to measure appropriate objects.

There are many websites that give instructions for folding paper airplanes.

This unit can be differentiated by altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. In particular, have students measure length using non-standard measures, such as hand spans or foot lengths, if they are not ready to progress to using metres and centimetres.

An alternative context for this unit is Manu tukutuku – Māori kites. Information about Manu tukutuku is readily available online, and the Te Ara website provides a useful overview. Within this context, students could design and make simplified Manu tukutuku to use for the measurement tasks, with the work culminating in a kite day, rather than an air show.

Required Resource Materials
• A4 paper
• A variety of measuring instruments: 30 cm rulers, metre rulers, measuring tapes
• Instructions for a variety of different paper planes: see useful sites or have a range of books available
• Paper and pens for recording
Activity

#### Getting started

1. Make a simple paper plane. Show students your plane and ask if they have ever tried making paper planes. Discuss the different designs they have tried.

2. Have students work in pairs to make a simple paper plane of their own design. Alternatively they could make a plane the same as the one you have shown them.

3. Have students experiment with their planes to see how far they fly. Discuss:
How could we measure the distance our planes fly?
What could we use to measure how far our planes have travelled?
What would we need to be careful of when measuring?

4. Discuss the use of non-standard measures and the need for a standard unit to allow comparison.

5. Show students a variety of measuring tools and discuss these.
Which of these measuring tools do you think would be best to measure the distance of our plane’s flight? Why?
What other things could we use?

6. Emphasise the importance of an accurate starting point for the flight and accurate use of the measurement tools to the closest cm.

7. Have students experiment with a variety of measurement tools to measure the flights of their paper planes. As they work encourage estimation and reinforce the correct use of measurement tools to ensure measurements are accurate to the nearest metre and cm.

8. Students can find the dfference between their estimate and the measured length.

#### Exploring

1. Tell the students that at the end of the week there will be an air-show. Explain that they will all participate in the show by making and flying planes and there will be a competition to see whose plane can fly the furthest.

2. Over the next few days have students work in pairs or small groups to try out some different designs for paper planes. As a starting point for their designs, find instructions for a selection of planes online or in books.

3. As students try different designs have them measure the lengths of their flights. Encourage them to record their trials in a table similar to the one below to help them keep a track of which planes fly the best. This will help them decide which plane they will use in the air-show at the end of the week.

 Plane Flight 1 Flight 2 Flight 3
4. Start each session with some ideas they might like to consider when making their planes. You may like to include the following points.

• Planes with longer wing spans and larger surface areas for their wings will tend to fly further than planes with shorter wing spans and smaller surface areas. As paper is not very strong it can be difficult to lengthen the wingspan.
• For planes to fly a long way they need to be stable in flight. A symmetrical plane is more likely to be stable.
• Weight near the bottom of the plane may increase its stability and allow it to fly further.

5. As work progresses you may need to set criteria for the planes. These can be discussed with students and may include the size of paper to be used and limits to the other materials that may be included, for example the number of paper clips, sellotape, glue or staples. How the planes are to be thrown may also need to be discussed.

6. As students work help them with their measurements and discuss these with them. Encourage estimation. Ensure that accurate starting points are used and measurements are made to the nearest cm.

7. Conclude each session with a discussion of the planes and how far they have flown.
How far did the plane you made today fly?
How do you think you could improve your plane?
What do you think you will try tomorrow?

8. Reinforce the correct use of measurement tools to allow accurate measurements.
What did you use to measure the distance of your plane’s flight?
What steps did you take to ensure your measurements are accurate?

#### Reflecting

1. To conclude the work on paper planes, hold an air-show. Conduct a competition to see which of the planes flies the longest distance.

2. Students can work in groups to measure the distance their planes fly with one plane from each group going through to the final. This will give students maximum practise at measuring distances. Encourage the use of estimation before measurements are made.

3. At the conclusion of the competition reflect.
What was the difference between the first and second place getters?
Which planes went the furthest?
Why do you think they flew so well?
What did we need to be careful of when we were measuring?
Which tools do you think were most useful for measuring? Why?