Year Three - Thinking In Equal Groups

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About this Big Idea

In this Big Idea students explore area through tiling visualisations so as to develop a deep understanding of this fundamental mathematical concept.

Understanding Goals:

Students will understand:


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'. Area relates to the measurement of two-dimensional space in the same way that volume and capacity relate to the measurement of three-dimensional space.

Core Content from the Syllabus:

Working Mathematically



Connected to:

Mindset Mathematics Learning Activities


Students use geoboards and square tiles to develop an understanding of area as covering with square units. Students make shapes on the geoboard to figure out, "How big is this shape?"- See page 101

Questions for reflection:



Students play with area by building pixelated letters out of square units to see what letters could have an area of 4, 5, 6 and up to 12 square units. - See page 111

Railway Station Matrix Display Board

Questions for reflection:

Digital Technology Extension

Students can apply their knowledge of letter area and designs to the challenge of displaying letters on small LED displays such as that on the BBC MicroBit. Students will need to use their knowledge of the area required for each letter and translate this to the 5 x 5 grid of LED's on the MicroBit or similar display.

BBC Microbit with 5 x 5 LED Display

Image - BBC MicroBit - an easily programmed system on a chip computer with LED display.

Design & Production Extension

Students could investigate how a display board could be made using coloured paper, cardboard and craft supplies. Students would need to consider the size of the matrix they would need to display all letters and numbers and devise a method for changing the display by perhaps flipping pixels over or covering unused pixels. Displays could be back lit by placing on a light box or by attaching to a window.


Students create rectangles with the same area and look for patterns opening the door to connecting area and multiplication. - See page 119

Questions for reflection:

Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012



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