Mathematics

Supercubes: numeracy and hands-on learning

Making ‘supercubes’ is a great way for children to explore cube numbers, and what happens when numbers are increased by the ‘power of three dimensions’

At times I see my granddaughter Daisy playing on her own, completely immersed in her imaginary play. At other times, she likes an adult to join her in the play: they are invited to adopt a role, or are involved in creating the setting.

I’ve found the most special and rewarding play is generally inspired by Daisy’s questions. This is when the play takes a new direction and, as grandparents or parents, we enable Daisy to learn through play, experimenting and looking for an answer through hands-on learning.

Recently Daisy was watching a Numberblocks episode about ‘supercubes’, in which Numberblock Two made its supercube ‘to the power of the three dimensions’ (2x2x2). 

Daisy turned to her Daddy and asked if they could make supercubes together with her set of Mathlink cubes. A cube is a prism with six faces all of the same size. Each Mathlink block is a cube. By joining these cubes together it is possible to create different shapes including larger 3D shapes.

Daisy, with her Daddy, constructed supercubes in order of size, starting with a supercube for 1, then 2 and 3. 

Daisy made supercubes of 1, 2 and 3

Curious cube numbers

Out of curiosity, Daisy wanted to keep going and asked if they could make a Supercube for 4. She’s familiar with square numbers and she and I have frequently played with the Mathlink cubes and we had previously made number 4 squares (along with many other numbers) so the start of making the supercube was easy.

A 4x4 square made of Mathlink Cubes
Daisy has made a number 4 square with Mathlink Cubes before

Daisy joined together 4 Mathlink cubes and then kept adding more Mathlink cubes until she had made a number 4 square. Once the first square was constructed, Daisy (with support from Daddy) was able to work out that she needed a total of 4 of these square numbers to make a supercube for 4.

Most of their remaining Mathlink cubes were required to construct the supercube for 4.

Daisy and Daddy lined up their supercubes and took a photograph.

A set of Numberblocks Mathlink cubes arranged into a set of supercubes - 1, 8, 27, 64
Daisy made four supercubes – but how many cubes were used in total?

In the Numberblocks supercubes episode, each supercube displays the total number of blocks as a ‘numberling’ above its head. Having created the supercube for 4, Daisy really wanted to know how many cubes it contained. 

This is the rare occasion when subitising skills simply aren’t applicable! 

It was complicated then because Daisy couldn’t see inside the cube to count all of the other Mathlink cubes that she had used. To count all of the cubes, Daisy would need to undo the supercube!   

Adding it all up

At this stage, Daddy was able to provide some technical support. Instead of taking the supercube apart and counting each individual Mathlink cube, Daddy suggested that they could use the calculator on his phone. (Daisy has already found the number functions on the phone and created some impressive numbers.) 

Daisy was able to count each of the Mathlink cubes that she could see on one side of the supercube and correctly told Daddy that there were 16 Mathlink cubes on that side. She remembered that they had made 4 square numbers and joined those together to make the supercube. Daddy explained that there were 16 Mathlink cubes in each of those square numbers to add together. 

Daisy has just started to learn about ‘addition’ at school and learned about the + symbol.  Using the calculator with Daddy, Daisy tapped in 16 then added + and with Daddy’s support they added 16 and repeated + 16 + 16 and Daisy pressed = to find the answer was 64.   

This was the easiest way for Daisy to find an answer to the number of cubes. She is just starting to do simple addition at school and doesn’t yet know about multiplication.

And then the two supercube constructors decided to just find out how many cubes they had used that afternoon in their play. Together they used the calculator to add together the numberlings for each supercube: 1 + 8 + 27 + 64. They had used 100 cubesa memorable number on which to finish the activity.

Granny Smith says…

  • In most cases, the best hand-on learning or learning-by-doing happens when a child has plenty of time to play. 
  • Daisy has a set of Mathlink Cubes. There are other connecting cubes available and small wooden cubes which could be used to create supercubes.

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