This document provides information about a Montessori mathematics project on trinomial cubes. It includes an acknowledgement, aims and objectives, introduction, materials, layout, and exercises for building a trinomial cube using wooden cubes and prisms. The project aims to help children visually understand the trinomial formula (a+b+c)3 through hands-on manipulation of the cubes and prisms to rebuild the cube structure. The document outlines the different layers and sizes of cubes/prisms used to represent the terms in the expanded trinomial formula.

1. TRINOMIAL CUBE
MONTESSORI METHOD
Prepared By: Rani Priyadarsini
Student, PSTTI

2. ACKNOWLEDGEMENT
I would like to express my special thanks of gratitude to the
Montessori Teacher Mrs. Prathima as well as our Principal Mrs.Sadaf
who gave me the golden opportunity to work on wonderful project on
Trinomial Cube. I am happy to take up and successfully complete this
project for Montessori Mathematics.
I also like to thank my family for supporting me in completion of the
project. Have taken the help from infomontessori.com in finishing this
project within the available time period.
This project has provided me knowledge in understanding the visual
concepts of Trinomial Formula.
I am thankful to all of them from PSTTI who have helped me directly or
indirectly in completion of the project.

3. AIMS AND OBJECTIVES

The purpose and aim of Trinomial Sensorial work is for the child to
acquire clear, conscious, information and be able to then make
classifications in their environment

Montessori saw the importance of the manipulation of objects to aid
the child in better understanding of the environment.

Through the child’s work with Sensorial material, the child is helped
to make abstractions, making distinctions in their environment.

The child is given the knowledge not through word of mouth, but
through their own experiences.

At the Primary level these are presented as puzzles that challenging
for child.

4. INTRODUCTION
TRINOMIAL CUBE
Meaning of Trinomial cube is :
(a+b+c)3 =a3 +b3 +c3 +3a2b+3a2c+3ab2+3b2c+3ac2+3bc2+6abc
Importance is expanding and clearly understanding the equation
with touch and eye contact

5. MATERIALS
A box with:

3 wooden cubes:
1 red, 1 blue, and 1 yellow.

6 red and black prisms,

6 blue and black prisms,

6 yellow and black prisms,

6 all black prisms.
All the pieces, once assembled, form a cube of a trinomial (a+b+c)3
The square of the trinomial is painted on the lid.

6. LAYOUT

7. THE SIZES OF CUBES ARE:

First layer of cubes size is : 4*4*4

Second layer of cubes size is :3*3*3

Third layer of cubes size is :2*2*2
TOTAL 27 PRIMS IN TRINOMIAL CUBE.

All the size of 4*4 faces are in RED.

All the size of 3*3 faces are in BLUE.

All the size of 2*2 faces are in YELLOW.

All non-square faces are in BLACK.

8. FIRST LAYER

9. SECOND LAYER

10. THIRD LAYER

11. INVITATION
Invite the child to come and work with you. Show him the
Trinomial 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.
PREPERATION
Before the presentation, check the box to make sure it has been
put back correctly.

12. PRESENTATION

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 each 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 and third level in the same manner.

Close the box, one side at a time and then replace the lid.

Invite the child to work with the trinomial cube.

13. POINT OF INTERSET
The moment at which the last piece is placed in building the cube.
CONTROL OF ERROR
If the cube is not formed.
LANGUAGE
No language is given with this material.

14. EXERCISES
Exercise 1
The child works individually with the trinomial cube as shown in the
presentation.

15. 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 trinomial cube
as in the presentation, but this time without the help of the box.
Then isolate each layer as you had done for the binomial cube. The
child can isolate each layer by building one layer at a time.

16. Exercise 3
Repeat the building of the trinomial cube outside of the box. Then,
disassemble the cube and line each prism by colour: the reds
together, the blues together, the yellows together, and the blacks
together. Then, mix them up.
Place each cube in a row but with space between each. Ask the
child to find a prism with the same height as the red cube (it can be
of any colour). Line up every one in a line in front of the red cube.
Find the same for the blue cube and the yellow cube (you can also
use the prisms from the other lines). Notice that there are always 6
prisms left.

17. DIRECT AIM
To build the cube.
INDIRECT AIM
Preparation for mathematics: the cube of the trinomial .Introduction
for algebra and preparation for the proof of the formula (a+b+c)3 at
Elementary Level.
AGE
4 Years.

18. THANK YOU