The purpose of this activity is to support students using an informal unit to measure and compare the area of two or more shapes. An informal unit is self-chosen by the students and may or may not be recognised by others.
- Copymaster
- Variety of flat objects to be used as measurement units (counter, square tiles, beans, spiral or tubular pasta, small shells, recycled plastic bottle tops)
Note: This lesson starts with discussion around forest fires. It could complement learning around global warming, or could be adapted to draw on a different context that involves area.
- Find a video about a recent forest fire online. Discuss how fires are becoming more common due to global warming, especially in hot countries like USA and Australia.
Why might we be worried about forest fires?
Students might suggest that people and animals could get killed, trees get ruined, and other negative consequences.
- Show the students page 1 of the Copymaster.
I have an aerial photograph of two burnt areas. What is an aerial photograph?
Students should say that an aerial photograph is taken from an aeroplane or helicopter.
Which patch of burnt forest has the most area?
Let the students discuss their ideas and how they might tell which area is greatest. Some might suggest cutting out the areas and overlapping them.
- I will give each pair of you a copy of the photograph and I want you to find out which area is biggest, without cutting the patches out and overlapping. I have some things to help you.
Show students the flat objects they can use.
Give each pair of students an A3 (enlarged) copy of page 2 of the Copymaster. Let them work, in appropriate groupings and using appropriate means of expression, at finding the greatest area. Roam as they work and look for the following:- Do they choose a single unit to work with?
- Do they try to make the units the same size?
- Do they fit the units together without gaps or overlaps?
- Do they use groupings to count the number of units?
- Do they fill one burnt patch then transfer the object to the other patch?
- If they use two different units, do they have a way to count in one unit?
If possible, take photographs of students’ strategies for comparing the areas.
- After a suitable time gather the group to discuss their strategies. Use the bullet points above to focus the discussion. Display any photographs you have taken and ask students to explain what they are doing.
Use Pages 2-5 of the Copymaster to show some examples of other students trying to solve the problem. Use the slides to create a set of guidelines about how to measure areas with units.
Page 2
What unit have Kelly and Min used to measure the areas of the burnt patches?
Is there anything they can do to improve their measurement?
These questions should provoke an agreement that the units should fit together as closely as possible to minimise the lost spaces.Page 3
What units have Tevita and Aria used? Are the units the same?
Tevita says the left-hand patch has less area because only 13 squares fit in. The right-hand patch has 21 squares. Is Tevita right?
These questions should provoke a discussion about using identical units, wherever possible, so the comparison is fair.Page 4
Josie says the left-hand area is smaller because it holds 13 squares, and the right-hand area holds 32 squares. Is she right?
This question should provoke a discussion about consistency, since the left-hand area only has squares that fit inside it, but the right-hand area has a lot of ‘overlap’ that is not burnt.Page 5
Can Daniel and Kayla compare the area, even when they used two different units? How?
Some students may use the ratio idea that three beans are equivalent to a square.- Provide students with an A3 copy of page 6 that has three different burnt patches. Ask them to work out which burnt area is the largest. Consider which learning partnerships will best suit your class for this activity, and which means of action and expression will be most appropriate for presenting their learning.
Next steps
- Give students open-ended challenges involving area like this:
Create three shapes that have an area of about 20 square tiles (any unit is fine).
Compare the shapes visually, without measuring.
Do the shapes look like they have the same area?
- Investigate areas in real life.
Where do we use area?
Students might look at situations like areas of walls, floors, or land.
Look at occupations in which people use area, such as painting, plastering, building, curtain-making, advertising, engineering, etc.