# Origami cube

Stage 2 and 3 – A thinking mathematically targeted teaching opportunity focussed on creating a cube using paper folding

## Syllabus

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
• MA2-3DS-01

• MAO-WM-01
• MA3-3DS-01

## Collect resources

You will need:

• 6 paper squares

• observation skills

• you may also need some patience.

## Watch

Watch the Origami cube video (4:40).

Create an origami cube with 6 squares.

### Transcript of Origami cube

[Text over a navy-blue background: How to make an origami cube. In the lower left-hand corner is a white waratah logo of the NSW Government. In the top left-hand corner is small font text which reads: NSW Department of Education.

New slide: Dark text on white background: You will need…

· 6 square pieces of paper (you can see our video on how to make this if you don’t have square paper)

· good observation and noticing skills

On a table is a square piece of blue paper. A pair of hands folds the paper bottom edge to top edge to make a firm crease. The paper is unfolded. The paper is folded again from the bottom edge to the middle fold and another firm crease is made. The paper is unfolded. The paper is then folded from the top edge to the middle to make another firm crease. The paper is unfolded. The top edge and bottom edge are now folded together so they meet in the middle crease. The paper is turned horizontally to vertically.

In the vertical position, the paper is folded bottom edge to top edge to make a square. The square is firmly creased. The square is unfolded, and the paper is held horizontally.

The top left corner is folded to the middle of the bottom edge and held in place. The bottom right corner is then folded to the middle of the top edge. Both folds are then unfolded.

On the right hand edge a small triangle of paper stands up. The right hand grabs the triangle and uses it to life up the top half of the paper. The triangle is then folded inward, so that the top corner points to the bottom-left. The process is repeated with the bottom half of the paper, with the bottom left triangle’s top corner pointing towards the top right.

The top half of the paper is folded back to the middle crease. From the top left corner, a triangle is made with the top corner reaching the vertical middle crease. The bottom half of the paper is then folded over the triangle, halfway up the paper and back to the horizontal crease.

In the top right half of the current folded position, a trapezoid is slightly lifted to reveal space underneath. The bottom right corner is folded inward, with the corner tucking under the space made by the trapezoid to reach the top-most point of the vertical line. An even parallelogram has now been created.

The parallelogram is flipped over so that the folded parts of the paper is hidden and held horizontally. The right-hand points to the top right corner and then the top left corner. The paper is then folded from top-right corner to top-left corner. A firm, vertical crease is made along the fold. The process is then repeated with the bottom edge, with the bottom left corner folded into the centre to make a square. The last two folds are then slightly unfolded so that two right triangles of paper stick up in the air.

Five identically folded blue pieces of paper are placed on the table.

Dark text on white background: Watch very carefully.

The left hand collects all six folded pieces of paper, stacked on top of one another vertically with the folded side facing up.

Four of the folded papers are left on the table. One piece of paper is held in the left hand. The parallelogram is held vertically and in such a way that the top corner is on the right. The folds have made a square in the middle of the paper, equally segmented in to four triangle shapes. The right-hand points to a fold that runs from the top right corner of the square, which is also the middle of the right hand edge of the entire shape, to the middle of the square. That fold can be lifted so that paper can be slotted in underneath.

The right hand takes the other piece of paper and holds it so that it looks identical to the paper in the left hand. The right-hand paper is then held horizontally so that the corner which was in the top right is now facing to the left. That corner is then slotted into the space made by the fold in the left-hand paper. The two pieces of paper are now linked.

The paper is turned so that the square face of the paper that was just slotted is now facing upwards. The right-hand picks up one of the parallelogram papers and slots in the top corner in the same manner.

The semi-completed cube is now turned so that the square face of the recently slotted paper is facing upwards. An over-hanging triangle shape of paper to the right of that face is then slotted in to the fold as has previously been done. There are not three sides on the cube completed.

The half-cube is held so that an over-hanging right angle triangle to the bottom left of the cube. The right hand picks up another parallelogram shape and slots it into the cube in the same manner as before. After slotting in that part of the parallelogram, an overhanging triangle is slotted in to connect all four sides.

The last two parallelograms are connected in the same manner to complete the cube.

The hands place the completed cube on the table, give a thumbs up and then applause.

White text on blue background: Over to you, mathematicians! (You will need 1 or 2 cubes).

The NSW Government logo flashes on screen. Text below reads: Copyright, State of New South Wales (Department of Education), 2021.]

[End of transcript]

## Instructions

Make 1 or 2 (or more if you like) cubes. We will need them for exploring nets later.