Base Blocks

Base blocks consist of individual "units," "longs," "flats," and "blocks" (ten of each set for base 10). They can be used to show place value for numbers and to increase understanding of addition and subtraction algorithms.

Enter base block pieces

Click on the blue icons at the top of each column to enter units, longs, flats, or blocks.

Set the base and number of decimal places

You can work with base blocks for any of the bases 2, 3, 4, 5, or 10. The default setting is base 10. Click the up or down arrow buttons to change the base. All problems and numbers are represented in the base shown. The default is whole numbers (no decimals shown), but changing the number of decimal places changes the meaning of each column. Thus with Dec. place = 1, the right-most column represents the number of tenths (in base 10), etc.

Representing numbers in the selected base

The number represented by the entered base blocks is automatically updated and shown at the left of the workspace. If you move base blocks into a wrong column, say a long in a flat column, or if there are too many blocks in a column to represent a number in the specified base, then the number representation at the left is blanked out. It reappears when you make changes that define a number.

Exchanging and grouping pieces

You may drag a base block into a column to the left or back to its appropriate column, but when you move a block one column to the right, it breaks apart to show that you have made an Exchange (as, for example, a 10-long is exchanged for ten units, or a 5-flat is exchanged for five 5-longs). To group pieces to make an exchange the other direction, click and hold the mouse key down while dragging a rectangle to "lasso" the pieces. Thus, in base 5, you can "lasso" five units to make a long piece or you can lasso five flats to make a block. The newly grouped object can then be dragged into the next column.

Show problem and next problem

Click the Show Problem button to be given an exercise in the specified base. There are two types of exercises, those that ask you to enter base blocks to represent a particular number, and those that ask you to rearrange the given blocks to represent a number.