Binomial Cube



4 years approx.
Montessori Lesson


The binomial cube is a wooden box with a cover and two adjacent hinged sides, containing 8 wooden blocks that fit together to form a cube with the same pattern on each side and in the middle. The cube has a visual representation of the algebraic formula (a+b) (a+b) (a+b) or (a+b) 3
Control charts


To help develop the child’s visual perception of three-dimensional patterns.


To prepare the child for later work in Maths, especially algebra.
To aid the child’s fine motor.
Eye- hand co-ordination.
To prepare the child for writing.


  1. Individual exercise done at a table on a work mat.
  2. Show the child how to carry the box and how to open and remove the box’s lid. Show the child how to lower the two adjacent hinged sides gently towards yourself. Show the child how to place the lid into the angle made by the opened sides, with the red square in the corner next to the box.
  3. Place the control charts beside and slightly in front of the box.
  4. Remove the top layer of blocks and place them onto the lid, starting with the cube nearest the open side. Then remove the one to the left of that then the one to the right of that. Place them on the appropriate colour of the control lid. Feel that they are all the same height by placing your hand gently onto the layer of cubes.
  5. Place the next layer of cubes directly on top of the previous layer.
  6. Now, remove the top layer of cubes and place it on the furthest (a) control charts that you have placed in front of the cube. Place your flat hand on the cubes again to make sure that they are all the same height.
  7. Repeat this removal for the next layer placing them on the control chart closer to you (b) again feeling that they are all the same height.
  8. Beginning with the red cube, that is, the cubes on control chart (b) place the SHORTER dimension cubes back onto the lid of the box. Feel that they are all the same height.
  9. Now place the TALLER cubes, on control chart (a) back onto the layer of cubes that are already on the lid of the box.
  10. Beginning with the red cube from the top layer of cubes, replace them into the box wrapping the other cubes around the red cube. Place the blue cube in last. Feel with your flat hand that they are all the same height. Do the same for the second layer of cubes.
  11. Once the cubes are all back, fold up the sides of the box and draw attention to the fact that the pattern of the cubes inside the box resembles the pattern on the lid.
  12. Invite the child to have a turn.


The child can build the Binomial cube in exactly the same way but outside the box without the control 2harts.


  1. One day, after the cube is built outside the box, show the child that all the cube’s faces have the same pattern on them. Turn the cube around to show the child that the back faces are the same too. Place both hands around the cube and lift it, to show the child that the bottom also has the same pattern on it.
  2. Show the child that the 6 inside faces have the same pattern. You will be able to do this by splitting the cube three ways, horizontally, vertically, and back to front. This will expose each face with each split.


The control charts
The child feels that all the blocks have the same dimension.
The colours of the cubes.