(i) Working with a classmate, discuss what you already understand about balance.
(ii) Next, balance a ruler on a pencil, as shown. Place a small item (e.g. a paper clip) at one end of the ruler. What do you observe?
(iii) What would you need to place on the other end of the ruler to balance it again? (iv) Try your solution. (v) Repeat this with identical pairs of small items.
(vi) Place two different items at both ends of the ruler, e.g. a paper clip and a push pin at one end, and a push pin and a paper clip at the other end. Now remove a paper clip from one end. What would you need to do to the other end to restore balance?
(vii) Repeat this with different items, adding and taking away items from the ruler before restoring balance each time.
(viii) Can you come up with a general rule for how to make the ruler balanced again, if items are added or removed from either end?
Solving for unknown values in an equation
The equals sign in a mathematical equation indicates that the left-hand side (LHS) is equal to the right-hand side (RHS).
A fundamental rule Whatever operation you do to one side of an equation (add subtract, divide, square, etc.) you must also do to the other side. This means the left-hand side and the right-hand side remain equal. We use this rule to fi nd the value for solutions to linear equations.