Math Fact Strategy Guide:
Addition and Subtraction
(based on Teaching Student-Centered 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.
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 three-more-than, however students may have more efficient strategies for these facts.
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.
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.
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.
9 + 2
8 + 3
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 “think-addition” 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 “finger-counting” or “head-bobbing” to count.
Subtraction as Think-Addition
(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.