Assessing Reasoning: Year 4 Exemplars


These exemplar tasks are part of the special topic on “Assessing Mathematical Reasoning”. The exemplars are designed to provoke students’ mathematical reasoning and to assist teachers engage in formative assessment of students’ abilities to analyse, generalise and justify. Each exemplar is aimed at Year 4, with adaptability to other years. Students analyse the task situation, form or test conjectures, and explain their thinking to others. Lesson materials include task information with suggested reasoning prompts and further activities, along with multiple annotated work samples illustrating the assessment rubric. 

Read the Teachers’ Guide (also included in the download) before using these materials.  


Exemplar: The Magic V (Year 4)

The Magic V task affords an opportunity to explain the reasons why a conjecture is true. Students begin by creating Magic Vs by trial and error, but come to see constant features. By manipulating numbers, analysing totals and recording their ideas, students will come to see why the properties of odd and even numbers are relevant. The main purpose is to develop students’ capacity to analyse situations, to find reasons and develop logical arguments.

Exemplar: Matchsticks (Year 4)

Students explore making rows of squares from matchsticks. The patterns can be described pictorially, numerically and symbolically. Students learn to work systematically and keep a record of results that assist them to develop and test conjectures. As the students describe and explain patterns, they will begin to move from additive to multiplicative reasoning. By changing from rows of squares, the task is easy to adapt to other year levels.

Exemplar: Shapeshifter (Year 4)

Shapeshifter is based on a picture story book. Students find a rule for using a straight line to dissect a polygon to make a polygon with one more side. The content foci are naming shapes and their components. The reasoning foci are especially Analysing and Justifying – seeing and explaining when and why cutting off a corner increases the number of sides.


Last updated December 18 2018.