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Length of an arc inquiry

When the areas of the sector and the triangle are equal, the length of the arc and the height of the triangle are also equal.

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Inquiry prompt

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Inquiry prompt

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Link to the Regulatory Cards

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Find connections.

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Regulatory cards for a guided inquiry

Link to the Regulatory Cards

Prove a generalisation.

Analyse the structure.

Find more examples.

Practise a procedure.

Extend patterns or relationships.

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Lines of inquiry

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Practise a procedure

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Inquiry Maths

Practise a procedure.

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Sector

Triangle

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(b)

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(c)

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(d)

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(e)

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(f)

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Find the missing information in the table, giving your answers in exact form.

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Inquiry Maths

Practise a procedure.

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Sector

Triangle

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(b)

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(c)

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(e)

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Find the missing information in the table, giving your answers in exact form.

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Inquiry Maths

Practise a procedure.

Given information

Further inquiry

Area and radius

  • Look back at your results. What happens to the angle and length of the arc when you halve the area and double the radius? Check another case.
  • What would happen to the angle and length of the arc if you doubled both the area and the radius?

Radius and angle

  • Look back at your results. What happens to the area and length of the arc when you halve the radius and double the angle? Check another case.
  • What would happen to the area and length of the arc if you doubled both the radius and the angle?

Area and angle

  • Look back at your results. What happens to the radius and length of the arc when you halve the area and double the angle? Check another case.
  • What would happen to the radius and length of the arc if you doubled both the area and the angle?

Further inquiry given two pieces of information Choose one pair to explore.

Generalisation Write a generalisation about what you have noticed. Explain why it is always true.

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Generate examples

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Find more examples.

 

 

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Find more examples.

 

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Find connections

Extend patterns or relationships

Analyse structure

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Find connections.

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Extend patterns or relationships.

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Extend patterns or relationships.

 

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Extend patterns or relationships.

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Analyse the structure.

 

 

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Analyse the structure.

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Prove a generalisation

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Prove a generalisation.

Prove that when the areas of the sector and the triangle are equal, the length of the arc and the height of the triangle are also equal.

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Prove a generalisation.

Degrees

Radians

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Prove that when the areas of the sector and the triangle are equal, the length of the arc and the height of the triangle are also equal.

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Inquiry Maths