Equations on a tarazu: finding x
A bag of unknown weight x and some 1 kg weights sit on one side of a tarazu, and weights on the other. Try values of x until it balances, and see the inequality when it tips.
Core concept
In short: Balance a scale to find the hidden number x in an equation.
An equation is a balance: x + 3 = 8 is true only when x = 5; if the left side is heavier, x + 3 > 8, and if it is lighter, x + 3 < 8
Topic: Equation and inequality
An equation says that two things are equal, like a tarazu (balance) that is level. On the left pan there is a bag of unknown weight, x kg, and 3 weights of 1 kg; on the right there are 8 weights of 1 kg. The balance is level only if x + 3 = 8. Finding the value of x that makes it true is solving the equation. If you guess too much, the left side is heavier and the balance tips left: x + 3 > 8 (greater than). If you guess too little, x + 3 < 8 (less than). These are inequalities. One quick way to solve it: take 3 kg off both sides, and the balance stays level: x = 8 − 3 = 5.
What you will learn
- Explain an equation as a balance.
- Solve simple equations of the form x + a = b.
- Use the signs > and < to write inequalities.
- Check a solution by putting it back into the equation.
Before you start
- Know how to add and subtract whole numbers.
Materials
- A simple balance, a closed bag of sand, and some equal small weights
Equipment
- A notebook to write each equation
Procedure
- With x + 3 = 8, try values of x until the balance is level.
- Change to x + 2 = 9 and solve it.
- Try a value of x that is too big, and one that is too small.
How this simulation is simplified
- Every small weight is 1 kg, and x is a whole number of kilograms.