Australian curriculum linked lessons.

Marshall, Linda ; Swan, Paul

Continuing the focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum: Mathematics, in this issue we focus on the Measurement strand.

We believe that this small unit of work on Area, leading to investigating the link, or otherwise, between Area and Perimeter would involve the following aspects of the Measurement and Geometry strand. Where appropriate, elaborations are listed beneath each content descriptor, in grey italics.

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Year 2

* Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

** Comparing areas using the palm of the hand or a stone

Year 3

* Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

** Recognising the importance of using common units of measurement

Year 5

* Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

* Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

Year 6

* Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)

** Recognising and investigating familiar objects using concrete materials and digital technologies

We would like to encourage any teachers trying these ideas with their classes to send in a short paragraph explaining what happened. Samples of children's work illustrating how they tackled these tasks would be appreciated. Likewise any assessment schemes that could be shared among colleagues would be welcomed.

Who has the largest hand?

Materials

* Blank paper

* Pencil

* A range of counters, blocks, marbles, stones, shells, etc.

The lesson

Trace your hand onto a piece of paper.

Cover the shape with materials of your choice.

Count how many pieces you have used. This tells you the area of your hand.

Is your hand bigger, smaller or the same size as your partner's hand?

Does it matter whether your hand is open or closed?

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Assessment

* Did the child use the same material to cover his/her hand? (If she/he used a mix of blocks, shells, marbles, etc, she/ he does not understand the importance of using the same unit to compare areas.)

* Did the child use different-sized units of the same material? If she/he used, for example, shells, were the shells a similar size? (As above)

* When comparing areas with a partner, did the child compare like with like? For example, did she/he try to compare square tiles on one hand

to marbles on another?

Variations

* Trace around the hand onto 10 mm grid paper, and then count the squares to find the area. Discussion can arise as the how children deal with part squares. (There are two main methods: count all squares

f larger than half as one and don't count those less than half; or try to match up bits of squares to create wholes.)

* Compare the area of your hand to the area of your foot.

Interesting note

If you multiply the area of your hand/foot by 100, you find the approximate surface area of skin on your body.

Thinking tiling

Materials

* Square tiles

* 10 mm grid paper

The lesson

This square is 1 unit long, and 1 unit wide. Its perimeter is 4 units.

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Ted the Tiler has 9 tiles. He must use all the tiles so that he always has an area of 9 squares.

He has arranged his tiles like this to get a perimeter of 12 units.

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Do the same with your tiles. Make a copy of this floor on your grid paper.

Now help Ted by making 4 more floors with the 9 tiles with:

(a) a perimeter of 14 units

(b) a perimeter of 16 units

(c) a perimeter of 18 units

(d) a perimeter of 20 units

Make a copy of your results on grid paper. Using each shape, write its area and perimeter. Write about your results.

Assessment

* Did the child note that the perimeter had changed even though the area stayed the same?

Taking Tiles

Materials

* Square tiles

* 10 mm grid paper

The lesson

This square is 1 unit long, and 1 unit wide. Its perimeter is 4 units.

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Arrange 9 tiles like this. The area is 9 squares. The perimeter is 12 units.

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Do the same with your tiles. Make a copy of this floor on your grid paper.

Make the perimeter 14 units by removing:

(a) 1 tile

(b) 2 tiles

(c) 3 tiles

(d) 4 tiles

(e) 5 tiles

Make a copy of your results on grid paper. Using each shape, write its area and perimeter. Write about your results.

Assessment

* Did the child note that the area had changed even though the perimeter stayed the same?