Base Blocks Decimals

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.

Blocks representing positive numbers are colored blue. Negative numbers are displayed using red blocks.

Decimal places

A unit may represent 1, or 1/10, or 1/100, or 1/1000, depending on the number of decimal places indicated. For example, with 3 decimal places showing, a unit represents 1/1000, a long represents 1/100, a flat represents 1/10, and a block represents 1. With 2 decimal places showing, a unit corresponds to 1/100, a long is 1/10, a flat is 1, and a block is 10. With just 1 decimal place, a unit represents 1/10, a long is 1, a flat is 10, and a block is 100. Up to 3 decimal places can be displayed.

Canceling blue and red blocks

If you place (click-hold-drag with the mouse) a blue block on top of a red block of the same size they will disappear or "cancel" each other out. The same thing happens when you place a red block on top of a blue block of the same size.

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 10, you can "lasso" ten units to make a long or you can lasso ten flats to make a block. The newly grouped object can then be dragged into the next column.

Addition and subtraction exercises

When this virtual manipulative first loads, you are asked to complete either an addition or a subtraction problem using base blocks. The number of decimal places is indicated.

You will need to use the exchange, grouping, and canceling procedures to perform the addition and subtraction operations. As you complete these procedures, the subtraction algorithm is updated at the far right of the workspace, column by column. That is, when the blocks in the right-most column represent a number, that number appears in the sum or difference at the right. Continue with each column until the addition or subtraction is complete.

Click Next Problem to obtain a new exercise.

Create your own problem

You can build and solve your own addition and subtraction problems. Click Create Problem, select the number of decimal places, and then use the blue and red buttons at the top to enter blocks above and below the dashed line. As long as you have two numbers correctly represented, the problem will appear on the left. To solve it, click Begin Problem.