Using unit cubes for learning math

We at "Planet Infinity" are using Unit cubes for making our teaching/learning of cubic algebraic identities in a different way.The first question which comes in the mind is what is a unit cube?
A unit cube is nothing but a cube all of whose sides are 1 unit long as shown below.

• We say its dimension is 1 X 1 X 1.
• The volume of a 3-dimensional unit cube is 1 cubic unit.
• By joining unit cubes we can form cubes and cuboids of varied dimension.

In our “Planet infinity” we have designed the activities using the unit cubes. We have 500 wooden unit cubes in our laboratory which were prepared by the help of the carpenter in our school.It is necessary to arrange the unit cubes first.You can purchase plastic unit cubes from a toy shop also. I believe that "Where there is a will there is a way".

We have designed the following activities for the students of grade 8 and grade 9.
1) the formation of cubes and cuboids using unit cubes.
2) Verification of algebraic identities
i) (a+b)^3 = a^3 +3a^2b +3ab^2 +b^3
ii) (a-b)^3 = a^3 -3a^2b +3ab^2 -b^3
iii) a^3+b^3 = (a+b)(a^2-ab+b^2)
iv) )a^3-b^3 = (a-b)(a^2+ab+b^2)
Firstly, I will discuss the formation of cubes and cuboids using unit cubes.
(a)To make a cuboid of dimension 2 x 1 x 1 ,we need 2 unit cubes.Place the two unit cubes adjacent to each other.You will observe that the shape which is obtained by joining 2 unit cubes is not a cube,but a cuboid whose length is 2 units ,breadth is 1 unit and height is 1 unit as shown below.

Children love to do this activity because of two reasons ,one,they are able to do this on their own which motivates them for further learning and second,they are able to visualise the concept of 3-dimension in mathematics.
(b)To make a cube of dimension 3 x 3 x 3,we need 27 unit cubes.Firstly,try to get the length by joining 3 unit cubes,then try to get the breadth 3 units by adding more unit cubes.By doing this a base cuboid of dimension 3 x 3 x 1 will be formed.Now ask the students to add unit cubes to get the heigth 3 units.Thus a cube which is obtained is of dimension 3 x 3 x 3 .

Like this you can get cubes and cuboids of varied dimensions using unit cubes.
In my next post I will share with U "how we are verifying the cubic algebraic identities using the unit cubes"?