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Triangular numbers inquiry

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Link to the Inquiry Maths website

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Inquiry prompt

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Inquiry prompt

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Inquiry Maths

Link to the Regulatory Cards

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Extend the pattern

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Pattern number	Number of black squares	Number of grey squares	Total number of squares

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Pattern number	Number of black squares	Number of grey squares	Total number of squares

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Connections

What are the connections between the black, grey and total number of squares?

What is the connection between triangular and square numbers?

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What are the connections between the black, grey and total number of squares?

What is the connection between triangular and square numbers?

The sum of two consecutive triangular numbers is a square number.

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Connections

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Position to term rules

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Pattern number	Number of black squares	Number of grey squares	Total number of squares

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Proof

The sum of two consecutive triangular numbers is a square number.

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Patterns on a multiplication grid

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Inquiry Maths

1. Fill in the multiplication grid

2. Shade the square and triangular numbers.

3. Describe any patterns you notice.

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4	8	12







			144

Inquiry Maths

1. Shade the square and triangular numbers.

2. Describe any patterns you notice.

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4	8	12







			144

Inquiry Maths

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Other patterns

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Explore the tile patterns.

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Inquiry Maths

Pattern number	Number of black tiles	Number of grey tiles	Total number of tiles

Pattern number	Number of black tiles	Number of grey tiles	Total number of tiles

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Explaining the position-to-term rules

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Grey tiles

Add two grey tiles to the next pattern.

Black tiles

Rotate the blue tiles to form a square.

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Explaining the position-to-term rules

Inquiry Maths

Grey tiles

Add four grey tiles to the next pattern.

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Explaining the position-to-term rules

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Black tiles

Rotate the blue tiles to form two squares.

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Inquiry Maths

Explore the tile patterns.

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Explore the tile patterns.

Pattern number	Number of grey tiles in the centre	Number of grey tiles on the corners	Number of white tiles	Total number of tiles

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Proof

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Patterns in three dimensions

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Number of cubes

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Number of cubes

Pattern number	Number of cubes

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Inquiry Maths