# Focus on Math

## Helping children become mathematicians!

### Basic Facts: Subtraction May 3, 2011

The subtraction basic facts are those that are the “reversals” of the one-digit + one-digit addition facts. Ideally students are working on  the subtraction  facts right along with the addition ones, making the connection between the two operations of addition and subtraction. They are  intimately linked. As with addition, we want children using efficient, mental strategies rather than counting on fingers, tapping with a pencil, or other such inefficient methods.

First and foremost the “think addition” strategy is useful. Thus if a child is faced with the fact 9 – 5 = ?, he can use addition and think ” 5 + ? = 9. This fact is easily visualized on a ten frame card (the nine card has a row of 5 dots and a row of 4) and thus the child has a way of actually figuring out the fact from things he already knows. Most of the subtraction facts which begin with a number 10 or less can be solved by visualizing an appropriate ten-frame cards or using a “think addition” approach.

The 36 “Hard” Subtraction Facts

Facts with a minuend (start number) that is greater than 10 are generally harder for children. For some of these (such as 12 – 6) think addition is appropriate.

Several other strategies can be developed with children:  bridging to 10 with adding; bridging to 10 with subtraction; and subtracting from the (place value) “ten”. All of these rely on the number 10 as a reference point, combined with the whole-part-part relationship.

The relationship between addition and subtraction is important in bridging to 10 wiht adding. A child faced with 16 – 7 = ? can think 7 + ? = 16. By visualizing (either on a 10-frame or a blank number line*) a jump of 3 to get to ten, realizing there is still a jump of 6 to get to 16, putting those together results in a “large jump” of 9, the difference. This can be practiced with children recording the first jump so as not to forget it. This works particularly well with +7, +8, and +9.  (* Using a blank number line is important. If a regular, marked number line is used, students will generally count.)

Bridging to 10 with subtraction is done in a similar fashion. It truly is “take away” and not think addition. The anchor of 10 is again used, this time the student begins (using the above question) at 16, jumps down 6 to ten, and then goes three more to get to 7. The part of 6 and 3 are put together for the actual difference.

Subtracting from the “ten” is also a true “take away”. In this case the student considers the minuend in its base 10 components (e.g., 16 is 10 + 6, then takes the amount away fully from the 10. The remainder is combined back with the ones value that was totally untouched.

Please note that some students will be comfortable with a particular strategy such as think addition and use it exclusively. Others may have use different strategies for different questions. Both are fine, as long as the strategies being used are based in logically reasoning. Counting as a strategy is not efficient and should be discouraged.

Mathematically yours, Carollee