Numerical Fluency Tips – Addition/Subtraction Facts

The first few times a child looks at addition and subtraction problems can be a confusing experience. It is very important for children to be able to effortlessly recall reliable methods to answer number facts.

One excellent method is Filling in the Gap. Take a look at the following example.

8 + ___ = 13

To find the missing number, we can fill in the gap between 8 and 13 by solving:

8 +___ = 10       and      10 +___ = 13

Once the two easier problems are solved, adding the two answers together will give the child the desired result. Take a look.

Since 8 + 2  = 10 and 10 + 3 = 13, the “gap” is 5 (2 + 3).

Check the result: 8 + 5 = 13.

And in words…

How far is it from 8 up to 10 (2) — how far is it from 10 up to 13 (3)? From 8 up to 13 is 5 (2 + 3) so 8 + 5 = 13.

Now try this:

7 + ___ = 16

7 + ____ = 10 and 10 + ____ = 16

7 + ___ = 16  
Since ____ + ____ = ____, the “gap” is ____.

So, 7 +____ = 16

The ability to use this “up to and over 10” method relies on the student knowing a series of prerequisite skills.  Here is a list of those skills.  When mastered, these skills will enable students to have effortlessly recall of addition and subtraction facts.
For each tip, I will also provide practice problems.

ADDITION TIPS

1)    Doubles

5 + 5 =                                             9 + 9 =

2)    Doubles plus/minus 1

5 + 6 = 5 + 5 + 1 =                        8 + 7 = 8 + 8 – 1 =

3)    Counting on (start at x and count up by y)

7 + 2 =                                              8 + 3 =

4)    Breaking down numbers

6 + ___ = 9                                        7 + ___ = 11

5)    How far apart are two numbers? (How far is it from x up to y?)

How far apart are 6 and 10?

How far is it from 9 up to 12?

6)    Combinations that make 10

8 + 2 =                                              6 + 4 =

7)    10 plus a number

10 + 7 =                                           10 + 9 =

8)    10 plus what number?

10 + ___ = 16                                  10 + ___ = 19 

SUBTRACTION TIPS

1)    How much is left?
Use the notion of “how much is left” when the numbers are fairly far apart, and count down.
For example, 12 – 3 is best thought of as “counting down from 12 by 3.”

2)    How far apart are the two numbers (how far is it from the smaller number up to the bigger number)?
Use the notion of “how far apart are the two numbers” when the numbers are fairly close to each other, and count up.

For example, 12 – 9 is best thought of as “how far is it from 9 up to 12.”

For the following examples, decide which method you would use: How much is left or How far apart

100 – 98 =                       100 – 3 =                          100 – 87 =                       100 – 15 =

Stay tuned for my next Blog posting to learn some more tips to effortlessly recall number facts.