Not quite right...
There are two methods you can use, one is to use a series of comparators and connect the outputs to the LEDs. The comparator switches state when the voltage on one of it's inputs exceeds the other. You connect the voltage from the rheostat to one input of all the comparators and a stepped voltage level to each of the others. For example, you put 1V on the first comparator, 2V on the second, 3V on the third and so on. As the voltage from the rheostat reaches each of these voltages, the matching comparator turns its LED on. The good news is there are several dedicated ICs for doing just this so it is a relatively trivial task.
The second method is more versatile but a little more difficult to implement. You use a cheap micro-controller (for example a PIC) with a built in ADC. The ADC measures the voltage and software does the comparison with fixed levels you have chosen. Then, as each level is exceeded, you turn on one more pin of the processors port to light an LED. This method probably costs less than using comparators and it uses fewer components (possibly only one, plus the LEDs and their series resistors) but it would involve writing a very simple program.
Brian.