| In part one of this article, you read about | | | | value blocks until there are enough smaller |
| representing and adding numbers using base | | | | place value blocks to remove. The resulting |
| ten blocks. Once these two skills are | | | | piles after the subtrahend is removed |
| mastered, it is time to move onto many a | | | | represents the difference. |
| child's nightmare: subtraction. Subtraction, | | | | |
| as you may have heard, is essentially | | | | In the example, begin by representing 234 |
| addition in reverse. It can be an arduous | | | | with 2 flats, 3 rods, and 4 cubes. The goal |
| task on paper, but it can be quite easy with | | | | is to remove 187 or 1 flat, 8 rods, and 7 |
| base ten blocks. | | | | cubes from these piles. Removing one flat is |
| | | | simple enough, but 8 rods and 7 cubes are |
| Recall that there are four different base ten | | | | difficult to remove if there are only 3 rods |
| blocks: cubes (ones), rods (tens), flats | | | | and 4 cubes! To solve this problem, trade in |
| (hundreds), and blocks (thousands). Groups of | | | | one flat for 10 rods, and one rod for 10 |
| ten base ten blocks can be regrouped or | | | | cubes. The result would be 1 flat, 12 rods, |
| traded for equivalent amounts of other base | | | | and 14 cubes. Removing the subtrahend - 1 |
| ten blocks; for instance, ten cubes can be | | | | flat, 8 rods, and 7 cubes - at this point |
| traded for one rod because both are worth | | | | would leave no flats, 4 rods, and 7 cubes. |
| ten. For subtraction, it is useful to know | | | | The difference is whatever is left after |
| how to trade down rods, flats, and blocks. | | | | removing the subtrahend, so the difference is |
| Trading down means converting larger place | | | | 47. |
| value blocks into smaller place value blocks. | | | | |
| For instance, one flat can be traded for ten | | | | For beginners, it would be wise to start with |
| rods since they are both worth 100. | | | | subtraction that does not require trading. |
| | | | For example 1954 - 1831 would require no |
| Before describing the subtraction procedure, | | | | trading because there are enough blocks in |
| let's go over some vocabulary . . . | | | | the minuend to remove the subtrahend. For |
| | | | more advanced students, questions that |
| Minuend - The amount from which you are | | | | include zeros can present a bit of a |
| subtracting. | | | | challenge. For example, 4000 - 3657 would |
| | | | require several trading steps all starting |
| Subtrahend - The amount that you are | | | | with four blocks. has several thousand free |
| subtracting. | | | | math worksheets including subtraction |
| | | | questions with no regrouping (trading). One |
| Difference - The answer. | | | | of the nice features of this website is that |
| | | | answer keys are provided, so students can get |
| In the equation, 234 - 187 = 47, the minuend | | | | feedback on their results. |
| is 234, the subtrahend is 187, and the | | | | |
| difference is 47. Most people don't bother | | | | With enough experience, students learn |
| with the terms minuend and subtrahend, but | | | | subtraction on a conceptual level and are |
| they are useful in describing the subtraction | | | | better equipped to apply it to pencil and |
| procedure using base ten blocks. | | | | paper methods later on. Students who only |
| | | | learn the paper and pencil method don't |
| To begin, represent the minuend with base ten | | | | always develop a conceptual understanding of |
| blocks. Try to keep the blocks in order from | | | | subtraction and are less able to identify |
| largest to smallest as this will help to | | | | errors in their work. |
| transfer knowledge and skills to paper and | | | | |
| pencil methods later on. Remove from the | | | | Base ten blocks are not limited to just |
| minuend piles, enough blocks to represent the | | | | addition and subtraction of whole numbers. In |
| subtrahend. If there aren't enough blocks | | | | part III of this series, several other uses |
| available, trade some of the larger place | | | | of base ten blocks will be explored. |