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Binomial Cube

Materials

A box with:
- One red cube and three red and black matching prisms.
- One blue cube and three blue and black matching prisms.

All the pieces, once assembled, form a cube of a binomial (a+b)3
The square of the binomial is painted on the lid.

Presentation
Before the presentation, check the box to make sure it has been put back correctly.

Introduction

Invite the child to come and work with you. Show him the Binomial Cube box and tell him its name. Have him bring it over to the table and place it near the top left corner of the table.

Procedure
- Remove the lid and place it on the diagonal of the box and so the painting is facing up.
- Pull down one side at a time.

- Carefully and gently take out all of the prisms, keeping the top level together and the bottom level together.
- Bring the child’s attention to the red cube.
- Replace it into the back left corner of the box.
- Slide it into place.
- Point to one of the red sides of the cube and then look for a prism that also has a red side.
- Place the correct prism in front of the red cube.
- Replace the first level by working your way from the back left corner to the front and then from the right side to the front.
- Replace the second level in the same manner so you are placing the blue cube in last.
- Close the box, one side at a time and then replace the lid.
- Invite the child to work with the binomial cube.

Exercises

Exercise 1
The child works individually with the binomial cube as shown in the presentation.

Exercise 2
Invite the child and set up the box as done for the presentation. Remove all of the prisms and place them all together to the right of the box. Then close the box and place it to the side. Build the binomial cube as in the presentation, but this time without the help of the box. Once done, mix the prisms and have the child build it outside of the box, as you had done.

Exercise 3
Repeat the building of the binomial cube as in Exercise 2. Once it has been built outside of the box, separate the cube in half (height wise). Turn them so the child can see that they are the same. Then replace the halves together to reform the cube and carefully take off the top layer and place it next to the bottom layer to show that these too look the same. Replace the layers and have the child separate them.

Language
No language is given with this material.

Purpose

Direct
To build the cube.

Indirect
Preparation for mathematics: the cube of a binomial.
Preparation for the cube root.
Introduction for algebra and preparation for the proof of the formula (a+b)3 at Elementary Level.

Control of Error
The first exercise: the box itself.
The second and third exercise: visual.

Age
3 to 3 1/2 years

Video
This Montessori Video shows how to present a child with the Binomial Cube.

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