Math Fact Strategy Guide:
Addition and Subtraction
(based on Teaching StudentCentered Mathematics,
2006)
An efficient strategy is one that
can be done mentally and quickly. An
efficient strategy is most useful to students when it is their own, built on
and connected to concepts and relationships they already own. When students do not yet own efficient
strategies, implementing premature drill and/or timed practice introduces no
new learning and encourages students to resort to inefficient practices (such
as counting on fingers). Premature drill
and practice is a waste of time and frustrating for students. The vast majority of instructional time spent
on math facts should be spent helping students to develop efficient strategies,
and then learn to select and retrieve appropriate strategies based on the math
facts to be solved. Brief daily strategy
development instruction (5 minutes a day) is the best contributor to math fact
mastery. Every student should be
required to understand each strategy; however different students will adopt
different strategies for the same collection of facts.
Addition
Strategies
 
Strategy

Example

Explanation

One/TwoMoreThan
(Counting Up)

6 + 1
2 + 6

Count on from six.
*As students count on from the larger addend instead
of counting all, they are ready to practice this strategy. This strategy can be extended to
threemorethan, however students may have more efficient strategies for
these facts.

Zero

7 + 0
0 + 4

Seven plus zero is still seven.
*Some children may overgeneralize the idea that
addition answers are always bigger than the addend. This strategy is a good
time to address this misconception.

Doubles

2 + 2
7 + 7

*These ten facts (0+0 through 9+9) are fairly easy
to learn and serve as anchors for many other facts.

NearDoubles
OR
Using Doubles

4 + 5
6 + 4

Double the smaller number and add one.
Compensate addends to double the middle number (6+4=5+5)
*Some students may also double the larger number and
subtract one. This strategy may be
extended to doubles plus two or three.

MakeTen
Or
Using Ten

9 + 2
(Think 9+1+1)
8 + 3
(Think 8+2+1)

Start with the larger addend, build partial sum up to ten,
then add on the rest.
*Before using this strategy, students should own a
variety of ways to compose and decompose 10.

As students learn and apply addition strategies, related
subtraction facts should be addressed as a part/part/whole relationship. If “thinkaddition” is to be used effectively
with students with subtraction, it is essential that related addition facts
must be mastered first. Research
shows that children learn very few, if any, subtraction facts without first
mastering the related addition facts.
If children are not thinking addition, they are most likely using
inefficient practices such as “fingercounting” or “headbobbing” to count.
Subtraction
Strategies
 
Strategy

Example

Explanation

Subtraction as
ThinkAddition
(selecting and/or
combining appropriate addition strategies)

9 – 4
14 – 9
15  6

*Students must previously own efficient strategies
for related addition facts to use this strategy effectively.
What goes with four to make nine?
Build up through ten: Nine and one more makes ten and four
more (makes five) to get up to fourteen.
Back down through ten: Fifteen take off five gets you down
to ten and take off one more to get to nine.

Taken from CCPS Basic Facts Resources.
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