Take 36 cubes of equal sizes (i.e., length of each cube is same). Arrange them to form a cuboid. You can arrange them in many ways. Observe the following table and fill in the blanks.

What do you observe?

How will you arrange 12 cubes of equal length to form a cuboid of smallest surface area?

Ask your friend to fill the following table and find the ratio of his age to the corresponding age of his mother . What do you observe?

Arrange 64 cubes of equal size in as many ways as you can to form a cuboid. Find the surface area of each arrangement. Can solid shapes of same volume have same surface area?

Take a clock and fix its minute hand at 12. Record the angle turned through by the minute hand from its original position and the time that has passed, in the following table : What do you observe about T and A ? Do they increase together ?

When we add zero to any whole number we get the same whole number Zero is called the additive identity for whole numbers .Is it an additive identity again for integers also Observe the following and fill in the blanks (i) (-8)+0=-8 (ii) 0+(-8)=-8 (iii) (-23) +0= (iv) 0+(-37)=-37 (v) 0+(-59)=... (vi) 0+...=-43 (vii) -61 +....=-43 (vii) -61 +...=-61 (viii) ..+0= ..... The above examples shows that zero is an additive identity for integers . you can verify it by a adding zero to any other five integers . In general , for any integer a , a+0=0+a=a