Stage 4 - space and geometry – 2D space

Strategy

Students can:

  • Use a formula to find the circumference of a circle
  • Identify that a fraction of a circle comprises a sector
  • Calculate the perimeter of a figure
  • Correctly round a calculation to a given unit

Activities to support the strategy

Students need to have confidence in using a formula to find the circumference of a circle, understand that sector is a fraction of a circle and have a well-developed understanding of perimeter. Review of each of these areas is encouraged before they are combined in more challenging perimeter problems.

Activity 1

1. Review the use of formula to find the circumference of a circle. Students need to apply either of the formulas below to calculate the circumference of a circle with confidence, given a particular radius or diameter. At this stage students should also have modelled concepts around rounding. It should be noted that π is an irrational number and answers can be given rounded to a given number of places or in exact form (in terms of π). Appropriate use of approximations of π and the calculator should also be discussed. Formulas and examples are shown below.

Calculate the circumference, given radius = 6 cm.

  • Use π on your calculator and answer to 1 decimal place.
  • c=2πr
  • c=2×π×6
  • c=18.849555…
  • ∴ Circumference is 18.8 cm (1 d.p.)

Calculate the circumference, given diameter = 10 m. Leave your answer in exact form

  • c=πd
  • c=π×10
  • c=10π
  • ∴ Circumference is 10 π m

2. A number of examples demonstrating the perimeter of more complex figures involving circles and in particular the perimeter of a sector need to be presented. Students should also be given the opportunity to practice a variety of questions to build their understanding.

Calculate the perimeter.

  • Take π=3.14 .

The perimeter of this figure is made up of a half-circle and the base. Using formula c=πd

  • P=12 ×3.14×4+4
  • P=10.28
  • ∴ Perimeter is 10.28 cm

Calculate the perimeter.

  • Leave answer in terms of π

The perimeter of this figure is made up of a quarter-circle plus the two straight sides. Using formula c=2πr

  • P=14 ×(2×π×3)+3+3
  • P=3π2 +6
  • ∴ Perimeter is (3π2 +6)  cm

Calculate the perimeter. Use π on your calculator and answer correct to 2 decimal places

The perimeter of this figure is the two straight sides plus the curved fraction of the circle. Since there are 360° in a full revolution, the curved part of the perimeter is 50360 ×2πr

  • P=(50360 ×2×π×4)+4+4
  • P=11.49065…
  • ∴ Perimeter is 11.49 cm (2 d.p.)

Activity 2

Teachers should review the TIMES teacher guide on circles. A number of examples and teaching techniques are provided for measuring the perimeter of circles and more complex figures involving circles.

Activity 3

Students and teachers can review the activities provided on Supporting Australian Mathematics Project - Circles. The resource may be useful in helping students achieve that element of the year 8 achievement standards that refers to students naming the features of circles and calculating areas and circumferences of circles.

References

Australian curriculum

ACMMG197: Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference

NSW syllabus

MA4-12MG: Calculates the perimeters of plane shapes and the circumferences of circles

Student resources

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