This unit provides opportunities for students to order and compare objects according to their area.
- Directly compare the area of 2 objects by superimposing.
- Cover a shape with smaller shapes.
It is important that students experience activities in which they compare and order attributes as these extend their understanding of the attribute and introduce informal measuring processes. Begin by comparing identical shapes of different size so that one shape fits inside the boundaries of others. Most classrooms have attribute shapes that are ideal for this purpose, however digital shape models (e.g. on a slide deck) could also be used.
The next step is to compare different-shaped objects, where it is possible to lay one object on top of the other. For example, a circular card can be placed on a sheet of paper.
Shapes which cannot be put together can be compared indirectly by cutting paper to cover one surface and then comparing the (size of the) paper with the surface of the second shape.
After comparing two areas students should be given the opportunity to order three or more areas. The process of ordering three or more areas is not a simple extension as it involves thinking that if A is larger than B and B is larger than C then A is larger than C.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
- explaining and modelling each task, before allowing students to work independently. Provide secondary modelling and more targeted support to students, as necessary
- providing opportunities for individual, grouped, and paired work
- strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
- working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities (e.g. accurately tracing a hand or footprint).
The activities in this unit can be adapted to make them more interesting by adding contexts that are familiar, or of interest to your students. For example, you may include a task ordering the size of the footprints of the teachers at your school, the footprints from other members of your local community, or even celebrity footprints. Consider how connections might be made to other curriculum areas (e.g. ordering the size of native bird's tracks, the size of footprints belonging to characters from a recent shared book).
Te reo Māori kupu such as horahanga (area), nui (big), and iti (small) could be introduced in this unit and used throughout other mathematical learning.
You could also encourage students, who speak a language other than English at home, to share the words related to size that they use in their home language.
- Station One: paper, crayons, glue
- Station Two: Copymaster of footprints of a variety of sizes, paper, crayon
- Station Three: Books, brown papers
- Station Four: Paper, crayons, glue, leaves
- Station Five: 3 cardboard shapes to represent the top of birthday cakes: square, rectangle and circle, smaller coloured paper shapes to represent lollies to ice the cakes, large sheets of paper, glue, crayons
This unit is organised as 5 stations. You could choose to explore one or more of these per day, as a whole class, or you could have students explore all stations over one or two extended sessions. Ensure that you carry out sufficient modelling and explicit teaching before allowing students to explore the stations. Students should be prepared enough to enable their effective participation in the learning at each station.
Station 1: Whose hand makes the most mess!
In this station we draw around our hands and work out whose would make the biggest mess on the new "table cloth". To further engage students in this station, you could provide the handprints of other relevant peoples (e.g. the prime minister, school principal, Guinness World Record holder) for students to compare their handprints to.
- Draw around your hand.
- Cut around the outline you have drawn.
- Now pretend your hand was covered with paint. Work with a friend to find out whose hand would leave the biggest mark on the new "table cloth"
Can you think of a way to find out whose hand would leave the largest mark? (Placement of the paper hands one on top of the other or direct comparison could be used.)
Whose hand takes up the most space?
Whose hand covers the least space?
How can you tell which hand covers the most space?
- Paste both of your hands onto a piece of paper and record whose hand takes up the most space, and whose takes up the least.
Station 2: Whose footprint is this?
In this station we consider a number of different footprints that we have found outside in the farmyard (Copymaster). We guess who they might belong to and put them in order. Note, if you want to compare students' footprints with those from the Copymaster, you will need to enlarge the prints from the Copymaster. You could change the context of a farmyard to be more relevant to your students (e.g. the footprints of native animals found in the forest, footprints of New Zealander's at the opening of the Olympic games, the footprints of characters we have met in a story).
- Present the students with a variety of outline footprints you have already prepared. Make sure the prints cover a variety of areas.
- Discuss the outlines with the students and place them in order from least to greatest area covered. Which footprint takes up the most space?
Which footprint covers the least space?
- Have the students draw around one of their feet and cut out the outline.
- Pick out one of the students’ footprints and compare it with the others you have been working with. Place the student’s print into the correct place in the order you have created.
Which footprints take up more space than Tony’s?
Does the dog’s footprint take up more or less space than Tony’s?
- Have all the students estimate where their footprint would fit into the order you have established and check some of these visually to see whether their estimations are correct. Jamal where do you think your footprint would fit?
(It covers more space than the dog's print and takes up less space than the horse's print.)
Station 3: Book Covers (Dust Jackets)
In this station we make book covers for a large and a small book. We think about which took more paper.
- Show the students two hard cover books (perhaps a book that you have recently read as a class, or a new book for the class library). Explain that they need book covers to protect them. All the students are to choose one of the books and make a cover for it.
- Discuss with the students how they are to make their covers. They will be using stiff paper. Remind them the cover goes around the front and back, which will need to be the same size. It will also need a flap at the front and the back to fold in. Show the students a cover on another book.
- Observe as the students make their book covers.
- How have you made sure the book cover will be the right size?
Is your book cover the same size as the one Ari is making?
How can you tell?
Can you find somebody that is making a smaller / larger book cover than you?
- As the students finish their book covers have them try them against the books.
Which book fits your book cover best?
- Make two piles, one for the book covers for the large book and one for the smaller book covers. Compare the book covers for one of the books and see if they are all the same size.
- Get the students to record what they have done, drawing the book cover they have made and writing about which book it fits.
Station 4: Collecting leaves
In this station we collect leaves from outside and discuss which covers the most space (area).
- Collect leaves from outside and bring these back to discuss as a group.
Which leaf covers the most space?
Which leaf is the smallest?
Who has a leaf that covers more space / less space than this one?
- Explain to the students that they are now going to draw the outline of a tree and cover it with the leaves they have collected. They will need to leave space in their tree for the leaves to be pasted on. As they work discuss the trees they are drawing:
Will your tree have more or less space for leaves than Kiri’s?
Can you find somebody else whose tree has the same space for leaves as yours does?
- Paste the leaves onto the trees and compare the space the leaves take up.
Whose tree has more leaf space than this one?
Can you find a tree with less space for leaves than this tree?
- In groups of two or three students can then compare whose tree has the most leaf space and order them.
Station 5: Birthday cakes
In this station we "ice" birthday cakes and think about which one uses the most icing. this could be adapted to look at designing a tuktutuku panel, a panel featuring Tongan kupesi patterns, or a cover for a new class cushion. Consider what context will be relevant and engaging for your students.
- Show the students 3 different shapes of birthday cake (square, rectangle, circle). Explain that they are to design the icing for one of these cakes.
- Students choose one of the cakes and draw around the outline of it onto a sheet of paper. They then paste the smaller pieces of coloured paper onto their cake to create the icing.
- Discuss the icing patterns the students have designed, comparing the area of the cakes.
Which cake has the most space for icing?
Which cake has the least space for icing?
- As a group order the 3 cake shapes from smallest to greatest area.