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Assessment Resource Centre (ARC)

  1. Stage 3
  2. Mathematics
  3. Activities
  4. Changing rectangles
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Changing rectangles

Grade Work Samples
Midway through Stage 3 (end of Year 5) End of Stage 3 (end of Year 6)
Grade A Huong  
Grade B Casey   Dale   Jessie  
Grade C Tai   Chris   Robyn   Lesley  
Grade D Indra   Courtney   Lou  
Grade E Drew  

Foundation Statement strands

The following strands are covered in this activity:

Working Mathematically, Measurement and Data

Description of activity

Students respond to a given scenario about the perimeter and area of a rectangle with changing dimensions. They then justify their answers.

  1. The students are presented with the following scenario:
    Sarah said ‘If I change the dimensions of a rectangle but keep the perimeter the same, the area is always the same.’
  2. Teacher poses the question:
    Is Sarah correct? Why?
    Students give examples to justify their answers.

The suggested time allocation for this activity is 20 minutes.

Suggested materials

Blank paper, pens, square grid paper

Prior learning

Students have investigated, measured and recorded the perimeter and area of various shapes. They have explored and discussed the relationship between perimeter and area. They have had experience making generalisations about findings and recording them in words.

Board of Studies NSW, Mathematics K–6 Syllabus, pp 95, 99
Board of Studies NSW, Mathematics K–6 Sample Units of Work, p 139


Length (MS3.1)
Selects and uses the appropriate unit and device to measure lengths, distances and perimeters
Area (MS3.2)
Selects and uses the appropriate unit to calculate area, including the area of squares, rectangles and triangles
Applying Strategies (WMS3.2)
Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations
Communicating (WMS3.3)
Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions
Reasoning (WMS3.4)
Gives a valid reason for supporting one possible solution over another

Criteria for assessing learning

Students will be assessed on their ability to:

  • calculate perimeters and areas of rectangles
  • use problem-solving strategies to investigate the relationship between perimeters and areas of rectangles
  • justify conclusions using mathematical reasoning and terminology


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