When Will We Reach One Half?

Working with a hundreds chart, how many numbers can be covered that contain only the digit 1? If we used the digits 1 and 2, how many numbers could be covered that contain only the digits 1 or 2, or both? By following this pattern:

How many digits are needed before the hundreds chart is half covered?

First grade students became deeply engaged in this open problem.  They explored patterns, made conjectures (predictions) as to what digit they would be on when half the 100 board would be covered. They discussed and defined what one half would mean on the hundred chart.  In the process of solving this interesting problem, they discovered other numeration concepts along the way. They learned the meaning of a “digit” versus a number. They also gained reinforcement and practice in recognizing, sequencing, writing, and saying numbers up to 100.