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Area and surds inquiry

Inquiry Maths

Link to the Inquiry Maths website

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Inquiry Maths

Inquiry prompt

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Inquiry Maths

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Inquiry Maths

Inquiry prompt

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Inquiry Maths

Regulatory cards for a guided inquiry

Link to the Regulatory Cards

Ask the teacher

to explain.

Decide if the prompt is true.

Explore other cases.

Make a generalisation.

Find connections.

Practise a procedure.

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Inquiry Maths

Link to the Regulatory Cards

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Inquiry Maths

Alternative prompt

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Inquiry Maths

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Inquiry Maths

Preliminary task

Find the area of each polygon by splitting it into parts.

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Inquiry Maths

Preliminary task

Find the area of each polygon by splitting it into parts.

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Inquiry Maths

Lines of inquiry

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Inquiry Maths

Decide if the prompt is true.

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Inquiry Maths

Decide if the prompt is true.

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Inquiry Maths

Ask the teacher

to explain.

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Inquiry Maths

Ask the teacher

to explain.

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Inquiry Maths

Ask the teacher

to explain.

Using Pythagoras’ theorem

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Practise a procedure.

Inquiry Maths

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Practise a procedure.

Inquiry Maths

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Inquiry Maths

Lengths of line segments that can be drawn on a grid.

Practise a procedure.

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Inquiry Maths

Explain how to draw rectangles with a given (whole number) area on a grid.

Explore other cases.

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Inquiry Maths

Explain how to draw rectangles with a given (whole number) area on a grid.

Instructions	Example
1. Choose an area to explore.
2. Find the factor pairs of the square of the area.
3. Decide if the factors are square numbers or if you can express them as the sum of two squares.
4. Draw the line segments on the grid and decide if they are perpendicular.

Explore other cases.

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Explore other cases.

Inquiry Maths

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Make a generalisation.

Inquiry Maths

Area of rectangle	Number of rectangles that can be drawn on a grid.

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Make a generalisation.

Inquiry Maths

Area of rectangle	Number of rectangles that can be drawn on a grid.

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Area of rectangle	Number of rectangles that can be drawn on a grid.

Make a generalisation.

Inquiry Maths

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Make connections.

Inquiry Maths

Spiral of Theodorus

You can draw line segments for the square roots of all positive whole numbers (up to 17) by creating this spiral on blank paper.

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Make connections.

Inquiry Maths

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Make connections.

Inquiry Maths

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Inquiry Maths