The following Interactive Activity provides you with some base four blocks you can use to visualize place value in base four operations. The pieces are called flats, longs, and units, and they represent 42, 41, and 40, respectively. Use the blocks to solve Problem C6.
Remember that there are four digits in base four (0 through 3). For addition problems, every time you have four blocks of the same type (a given place value), you need to trade them (or regroup them) for one block of the next-larger place value on the left. So, for example, four blocks representing 40 (four units) would be traded for one block representing 41 (one long). Use the regroup button in the activity to do this.
Similarly, for subtraction, every time you don't have enough blocks in a given place value to do the subtraction, you need to take one larger block from the place value on the left and trade it for four blocks of the next-smaller place value on the right. So, for example, one block representing 41 (one long) can be traded for four blocks representing 40 (four units). Use the regroup button in the activity to do this. Note 3
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, print and cut out several base four blocks PDF to use with Problem C6.