Teaching Sequence

15 minutes – Part A: How big are those values really?
25 minutes – Part B: How much space is that?
25 minutes – Part C: How many football fields is that?
15 minutes – Reflection: Where did most of the paper go?

Work through this resource material in the following sequence:

Part A: How big are those values really?

Step 1.

Begin the lesson by projecting the following graphic where all students can see it (image also available on the Student Worksheet):

(Image source: Visy, 2021)

Invite students to analyse the image with a SEE THINK WONDER routine that uses the following questions:

Engage students in a class discussion around their ideas. Through your discussion explain to students that the values represented in the image are measured in tonnes. Invite the class to share what they know about large numbers by asking the following questions (questions also available on the Student Worksheet):

Does anyone know how many kilograms are in a tonne?
Can anybody name an animal or object that weighs a tonne?

Ask students to find the amount of paper and cardboard manufactured by Visy in a year, and then convert it to kilograms. This is approximately 1.56 million tonnes of paper and cardboard. Students should write:

1 560 000 tonnes
1 560 000 000 kilograms

Step 2.

Now invite students to just focus on 1.56 million tonnes of paper and cardboard. Ask the class to think about how much 1.56 million tonnes really is. Although students will understand that this figure is big, they may not comprehend just how big it is. To help students visualise the size of this number, it may be useful to make comparisons with large animals. Ask questions similar to the following:

How much is 1.56 million tonnes really?
How many hippos or elephants would that equate to?
How many blue whales?

Ask students to work this out by using the information box (below and on the Student Worksheet) containing the weight in tonnes of hippos, African elephants and blue whales. Students could work independently or in pairs to answer these questions.

Answers below:

Once complete, invite students to share their answers with the class and ensure all students understand the calculations and large numbers represented.

Part B: Investigation – How much space is that?

Step 1.

Now that the class has some concept of how much 1.56 million tonnes of paper is (in weight), we would like them to think about how much space this might take up. To encourage students to think about area, ask the class questions similar to the following:

How many sheets of standard copy paper would equate to 1.56 million tonnes?
How much space would that take up?
How much paper would it take to cover our classroom?
How much paper would it take to cover a football field?

Students will now begin an investigation in a location of their choosing with sheets of paper. You will be covering a measured area with sheets of paper to obtain an understanding of space and size. Possible locations could include:

A classroom or a section of the classroom (the length and width of a classroom is sufficient)
A small outdoor area, weather permitting (e.g. the length and width of a cricket pitch, handball court, bus stop shelter).

A regular sized classroom could easily use up a ream of paper so try not to choose an area that is too big! Try and use paper from the recycling box to avoid wastage.

Mark out the area you intend to use and ask students to begin laying sheets of paper on the ground to cover the space. Ensure students are using weights, rocks or thumbtacks to keep the paper in place.

Step 2.

Once the area is covered, invite students to measure the dimensions of the area and count the number of sheets of paper and record their responses under Part B of the Student Worksheet. Students can then be directed to pack up the investigation.

Step 3.

Now ask students to calculate the area of the space. Students may need some guidance with area formulas if the space used is a composite shape. Students can record their responses under Part B of the Student Worksheet.

Part C: How many football fields is that?

Note: Now that students have investigated the weight of paper and how much space it takes up, they will now bring the two concepts together to work out just how much paper there is in 1.56 million tonnes.

Step 1.

To complete this section students will need the following information. Depending on the time you could simply provide this information to students or you could direct students to undertake research online to find out this information. Source links have been provided below:

A sheet of paper weighs approximately 5 grams or 0.005 kg (Source: https://www.papersizes.org/weight-of-sheets.htm)
You could also weigh a ream of paper and divide by 500 sheets to obtain a more accurate figure.
Dimensions of a football field. Choose a field you feel will interest your class.
- An NRL and Rugby Union football field is 68 m wide and 100 m from goal line to goal line (Source: https://www.dlgsc.wa.gov.au/sport-and-recreation/sports-dimensions-guide/rugby)
- A soccer field is 75 m wide and 110 m long (Source: https://footballnsw.com.au/wp-content/uploads/2017/06/Field-Markings-and-Equipment.pdf)
- An AFL oval is 165 m long and 135 m wide (Source: https://www.dlgsc.wa.gov.au/sport-and-recreation/sports-dimensions-guide/football-(australian-rules))

Area will need to be found using the ellipse formula which is not frequently taught as a normal shape. This option may be better suited to extension or high ability students/classes.

A sheet of paper is usually about 21 cm wide and 29.7 cm long (Source: https://papersizes.io/a/) or 0.21 x 0.297 m

You could ask the class, or select volunteers, to measure these dimensions rather than provide them.

Step 2. Calculate areas:

Referring to the Student Worksheet, now invite students to use area formulas to find the area of a sheet of paper and the area of the football field. Remind students to use metres as the units for both areas since this will help to prevent conversion errors later. Approximate answers:

Sheet of paper	NRL	Soccer	AFL
A = l x w A = 0.21 x 0.297 A = 0.0624 m²	A = l x w A = 68 x 100 A = 6800 m²	A = l x w A = 75 x 110 A = 8250 m²	A = πab A = π x (165/2) x (135/2) A = 17 494.5 m²

Step 3. Calculate the number of sheets:

Where possible, allow students the time to solve this step on their own but allow scaffolding and/or explicit teaching where necessary:

NRL	Soccer	AFL
6800 / 0.0624 = 108 974.36 ~ 108 974 sheets	8250 / 0.0624 = 132 211.54 ~ 132 212 sheets	17 494.5 / 0.0624 = 280 368.59 ~ 280 369 sheets

Step 4. Calculate the weight of the sheets:

NRL	Soccer	AFL
108 974 x 0.005 = 544.87 kg	132 212 x 0.005 = 661.06 kg	280 369 x 0.005 = 1401.85 kg

Step 5. Calculate the number of football fields:

NRL	Soccer	AFL
1 560 000 000 / 544.87 = 2 863 068.25 ~2 863 068 fields Or almost 3 million fields	1 560 000 000 / 661.06 = 2 359 846.31 ~2 359 846 fields Or over 2 million fields	1 560 000 000 / 1401.85 = 1 112 815.21 ~ 1 112 815 ovals Or over 1 million ovals

Reflection

Step 1.

Now that the class has worked out the number of football fields 1.56 million tonnes of paper could cover, encourage them to think about the amount of paper that is not being recycled, and going into landfill instead.

Invite students to read the following quote, also available on the Student Worksheet:

Source: https://irp-cdn.multiscreensite.com/ed061800/files/uploaded/cleanupaustraliapapercardboard_factsheet-2017.pdf

Ask students to respond to the Reflection Questions on the Student Worksheet, and allow them to discuss their thoughts with the class or a peer.

Note: Students can work in pairs to discuss this question; however, each student is responsible for recording their own ideas in their own words.

Step 2.

Explain to the class that although it is common knowledge that paper is recyclable, much of it is still being thrown away as rubbish. Ask students to suggest reasons as to why we may be throwing away paper. You may prompt the class with the following ideas:

One person throwing away a sheet of paper might feel insignificant, but if you considered the whole population throwing away a sheet of paper each, this figure would be huge! What about if we all threw away more than one sheet, every day?
Perhaps people are throwing away sensitive or personal information, like bank statements.

Take It Further

By this stage, your class has investigated the sheer size of paper usage and the importance of recycling. Encourage students to think about meaningful ways that they could prevent paper from ending up in landfill, and reduce their usage. Allow them to discuss with the class or a peer, and record their ideas.

Differentiated Learning

Extension – This lesson can be extended by reducing the amount of scaffolding (particularly in Part C) or by choosing a more complicated field or space in which to use for Part C. The AFL field is more complicated due to the use of the ellipse formula but a highly able student could also consider using the surface area of a building or landmark (e.g. internal or external surface area of the classroom).

Provisions for Learning Support – Depending on support requirements, students requiring learning support could work in a pair or group, be provided with partial solutions and/or be given extra scaffolding to complete tasks. The teacher could also adjust the field or space used in Part C to be of particular interest to the student (e.g. a cricket field), or round the provided figures in this lesson (e.g. use 0.2 x 0.3 for the area of a sheet instead of 0.21 x 0.297).

Teacher Reflection

Take this opportunity to reflect on your own teaching:

What did you learn about your teaching today?
What worked well?
What didn't work so well?
What would you share?
Where to next?
How are you going to get there?

The information and statistics included in this document are approximate and have been simplified for educational/illustrative purposes. They should not be relied upon for any other purpose.

Visy Education - Football Fields of Paper

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