Year Three - Thinking Around Shapes
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About this Big Idea
In this Big Idea students explore perimeter through bodily movement and visualisations so as to develop deep understanding of this fundamental mathematical concept.
Understanding Goals:
Students will understand:
- the concept of perimeter and know that it is a linear measure.
- why different shapes might have the same perimeter
Background:
It is important that students have a clear understanding of the distinction between perimeter and area. 'Perimeter' is derived from the Greek words that mean to measure around the outside: peri, meaning 'around', and metron, meaning 'measure'. The concept of area is developed later in "Tiling to Understand Area".
Core Content from the Syllabus:
Working Mathematically
Length
- measure lengths and distances using metres and centimetres
- use scaled instruments to measure and compare lengths
- recognise the features of a three-dimensional object associated with length that can be measured, eg length, height, width, perimeter
- use the term 'perimeter' to describe the total distance around a two-dimensional shape
- estimate and measure the perimeters of two-dimensional shapes
- describe when a perimeter measurement might be used in everyday situations that students will encounter (Communicating)
Language:
- length, distance, metre, centimetre, millimetre, ruler, measure, estimate, perimeter
Connected to:
Mindset Mathematics Learning Activities
Visualise
Students build the concepts of perimeter as the "distance around" by finding objects they can surround with a piece of string, and making lots of useful mistakes along the way. - See page 53
Questions for reflection:
- What surprised you?
- What estimates did you make that you were surprised to find didn't work? Why?
- What did you notice from analysing your "Useful Mistakes" sheet that helped you?
- What makes it hard to estimate the distance around (or perimeter)?
- When might finding the perimeter of something be useful? Why?
- When might you need to find or estimate the perimeter of something? Why?
Play
Play
Students construct rectangles and other rectilinear shapes with a perimeter of 36 units. The class investigates patterns in shapes with the same perimeter. - See page 59
Questions for reflection:
- What did you notice?
- What changed when we were no longer looking for rectangles? How did you use patterns in the rectangles to help you create new shapes?
- Do you see any patterns?
- How might we find the perimeter of a shape?
Investigate
On geoboards, students try to construct the shape with the longest perimeter possible, and explore how to find the perimeter of irregular shapes. - See page 65
Extension opportunities are provided in the book starting page 69
Questions for reflection:
- What makes perimeter longer? What makes perimeter shorter?
- Do you think we could make a shape with an even longer perimeter than the one we found? How would we do it? Or why not?
- What kind of shapes have a long perimeter? Why?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
