Home > Reasoning > Downloads


'Above and below the line' ideas, F–6

This document suggests a range of F–6 content, with curriculum descriptions, where an 'above and below the line' activity could be used.

'Bad apples': Extension ideas for secondary students

The Bad Apples activity can be extended for use up to year 9. This document suggests three possible extensions.

Addition of Odd and Even Numbers video transcript

This document contains the transcription of the video which explores a student's reasoning of why the addition of two odd numbers is always even.

Compare and contrast: Content descriptions

Finding similarities and differences between numbers and between objects is a vital skill in mathematics. This documents suggests areas of the curriculum where comparing and contrasting are used.

Insects and spiders: An avenue for if-then thinking

This problem sets up processes for if-then thinking. There are suggestions for modifying the activity to suit various year levels.

Jan’s train

Jan's train is an example of a relatively open problem that encourages mathematical reasoning. It is easily adaptable to many year levels.

Max's statements

A year 7 scenario illustrates various levels of student reasoning.

Other covering shapes

This document suggests shapes that can be used to cover sections of a number or algebra chart, suitable for students from F–10.

Problem solving versus reasoning

Reasoning is not problem solving. This table highlights the differences between the two and references the Australian Curriculum.

Reasoning statements

This document presents some propositions to use with years 5–10 students and statements to use with years 1–4 students, asking questions such as "Is this true?"

Sample response to quadrilateral tessellation

One student's response when asked to consider the proposition that 'any quadrilateral will tessellate' and whether this is true some of the time, all of the time, or not true.

Some milestones in the development of mathematical reasoning

Reasoning develops throughout the curriculum. This document outlines that development from Foundation to year 10 with extracts from the Australian Curriculum.

Some W question starters

Teachers and students can use this list of questions to promote the use of reasoning.