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Reasoning

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Triangular array of billiard balls, five on each side and 15 in total.

Billiard balls.
Source: James Barker/Freedigitalphotos.net

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Teacher recording observations of student working.

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Row of eight small squares matched to row of five large squares. Student response to questions comparing the areas, explaining reasoning.

Row of squares task.

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A long box divided into eight square sections. Below it, a second box divided into five sqaure sections. Box long boxes measure 10 cm in length. 10

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Student drawing of the 5 dice faces, explanation that double 8 is 16 then counting on 5 more gives 21.

A learning story about addition reasoning.

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Each of the triangular numbers 6 and 10 is modelled with rows of squares. Then one shape is rotated 180 degrees so that the two triangular numbers fit together, creating a 4 by 4 square.

Proof by modelling.

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Student work; picture of human bones; text; length of paper streamer, predominantly white with a thin strip of black.

Mungo Man poster.
Source: © 2012 MathsIsFun.com

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Four triangles of different sizes, each labelled with two interior angles.

Similar or not?

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Lines on a rectangle showing that it is to be folded in half and half again, to make a smaller rectangle. Then a triangular notch is cut out of one of the folded edges.

One example of paper folding.

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Screen grab showing an isosocles triangle with a single line of symmetry.

Screen grab from L7803 Finding symmetry: one line: city.
© Education Services Australia, 2011

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