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Understanding area


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Last updated 26 October 2012 15:28 by NZTecAdmin
Understanding area (PDF, 40 KB)

Measurement progression, 2nd–3rd steps

In this activity, the learners develop an understanding of area as a description of the number of square units needed to cover a shape. They do this by finding the area of rectangles, initially by counting square units, and then by imaging the number of square units.

The teaching points

  • The area of a region is the number of square units needed to cover that region. (In this activity initially squares with sides other than 1 centimetre are used to encourage the learners to develop a conceptual understanding of area rather than use already known formulae.)
  • For a rectangle, working out the number of squares in one row and one column and considering how many rows and columns are needed to cover the region is a faster way of calculating area than counting each square.
  • Metric units for area are squares with sides of 1 centimetre and 1 metre and have the symbol cm2 and m2. (There are more: mm2, hectare (10,000 m2), km2).

Resources

  • Paper or cardboard rectangles (20 centimetres x 30 centimetres) and square units (5 centimetres x 5 centimetres and 2 centimetres x 2 centimetres) for each pair of learners. Image of rectangles and square units.
  • One square centimetre.
  • Rulers including metre rulers or measuring tape.

The guided teaching and learning sequence

1. Give each learner a rectangle of paper (20 centimetres x 30 centimetres) and a square unit (5 centimetres x 5 centimetres) and ask them to find out how many squares cover the rectangle.

2. Ask the learners to share the results. Draw attention to the area of the paper being described by the number of square units needed to cover it – in this case 24 square units.

3. Discuss the method used. Some learners may move the square around and count the number, others may draw squares on the paper, others may count the number in one row and one column and multiply the two together.

4. Ask:

“Was it necessary to draw all 24 square units to determine that it would take 24 units to cover the rectangular region?”

Reinforce the idea that after finding the number of square units in one row and one column, the total number of squares can be obtained by considering how many rows and columns of squares will be needed to cover the region. (For example, if there are 4 squares in a row and 6 columns, there will be a total of 24 squares (6 x 4).)

5. Give each learner a square unit (2 centimetres x 2 centimetres) and ask them to find the area in terms of this square unit.

6. Ask the learners to share the results, emphasising the area as 150 square units, and the efficiency of counting squares in one row and column and multiplying the two together.

7. Ask the learners to discuss what units of measurement are commonly used for area. Listen for and reinforce ‘square centimetre’ and ‘square metre’. (If acres are given, explain that this is not a metric measurement and that m2 and hectares are the metric measurement used for land area.)

8. Show the learners a square with sides of 1 centimetre. Ask them how they could find the area of their piece of paper in square centimetres without using the centimetre square. You may need to prompt the use of a ruler to measure the length of the sides.

9. Ask them to find the area of the 20 centimetre x 30 centimetre paper in square centimetres, share the methods used, and record the result as 600 square units, 600 square centimetres and 600 cm2. Draw attention to the unit and symbol.

10. Point out a large rectangle in the room (for example the door or a table) and ask the learners to estimate its area in square centimetres. Ask them to consider whether square centimetres are an appropriate unit to use to measure the rectangle’s area and to suggest alternatives. Listen for ‘square metres’.

11. Discuss with the learners what a square metre might look like. Ask each learner to make a square metre out of newspaper. Emphasise that a square metre is a square with sides of 1 metre with the symbol m2, from 1 m x 1 m. Emphasise that it is the unit used to describe the area of larger shapes.

12. Ask the learners to estimate the area of a large rectangle in the room (floor, door or table) in square metres and share their estimations. Ask them to check their estimations using square metres. Discuss that fractions of the square metres may be necessary to cover the shape – “You would need 3 square metres, 2 whole square metres and 2 half square metres”. Keep away, at this stage, from calculating the area to confirm estimates unless your learners are competent with multiplying fractions!

Follow-up activity

Ask the learners to choose small and large objects in the room, decide which metric unit of measurement they would use to describe the area, and give an estimation of the area of the object in that unit.

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