How to make a square

Stage 1 to 3 – A thinking mathematically targeted teaching opportunity focussed on creating a square from a piece of paper


Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023


  • MAO-WM-01
  • MA1-GM-03
  • MA1-2DS-01
  • MAO-WM-01 
  • MA2-GM-02 
  • MA2-2DS-01 
  • MA2-2DS-02
  • MAO-WM-01
  • MA3-2DS-01

Collect resources

You will need:

  • 5 sheets of A4 or A5 paper
  • a pair of scissors.


Watch the How to make a square video (2:05).

Two methods to create a square from a sheet of paper.

[Text over a blue background: How to make a square from a piece of paper.
Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the white waratah of the NSW Government logo.

A title on a white background reads: You will need…
Bullet points below read:

  • a pair of safe scissors
  • some paper

On the floor is a rectangular yellow sheet of paper. Above the yellow paper and on the top left corner are more sheets of different coloured paper. On the yellow paper is text: method 1.

The lecturer holds up 1 finger. They pull up the bottom right corner of the yellow paper, aligning the right side of the paper to the top. They fold the paper down, creating a triangle. They turn the paper so the long side faces down. They fold the right side of the paper at the edge of the triangle. They open the fold. They flip the paper. They fold the paper up at the crease. They open it up. They flip the paper and open up the triangle. They take a pair of scissors. They cut the paper at the new crease. They create a square and a long rectangle. They take the shapes away.

Text appears: method 2.

The lecturer holds up 2 fingers. They move the sheets of paper from above and place them side by side. They are both rectangular, slightly longer on the side than top. On the left side is the blue paper, on the right is orange. They turn the orange paper on its side. They align its bottom left corner with the blue paper’s bottom left corner. They turn the papers to the right so that the section of the blue paper that is showing is on the right. They take the scissors. They hold the paper up. They cut the blue paper at the edge of the orange paper. They flip the papers as they put it down on the table. With the blue paper, they create a square. They hold up the yellow square paper next to the blue one. They place the blue square over the yellow square, on the table. They flip the squares, then flip them back.

In large font is text over a blue background: Have fun making your 5 squares you will need. Maybe you will find another way to make a square from a piece of paper? Below the text is another line of text: Over to you, mathematicians!

Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.] 

[End of transcript]


Follow the steps in the video to make 5 squares and keep them for Pentominoes.

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