Author: e200102787

Computation Strategies for Fact Fluency

Addition Strategies
1. Add in Pieces: Example: 8 + 4 equals 8 + (2 + 2) Breaking the 4 into 2 + 2 is more efficient because 8 + 2 = 10 then you add the other 2 to get 12.
2. Sums to 5 or 10: Groupings that get you to 10 are the most efficient groupings.
9 + 7 is the same as 9 + (1 + 6). 9 + 1 = 10 plus the 6 = 16. Other ways to make 7, like 3 + 4 or 2 + 5 are not efficient ways to break down 7 because we need to make the 9 a 10.
3. Make Smart Groups: Example: (29 + 29) Add (30 + 30) which equals 60, then subtract 1, then subtract 1 again to get 58. *This is really another way to look at estimating.
99 + 99 + 99 = (100 + 100 + 100) - 1 -1 -1 = 297
4. Group by Place Value: Example: 14 + 12 This is the same as: (10 + 10) + ( 4 + 2) ; 20 + 6 = 26
5. Find Easy Sums: These are the smartest most efficient groups of all:
9 + 1…..8 + 2….7 + 3….6 + 4….5 + 5
6. Adding Zero: Students can quickly grasp the rule for adding zero; the sum is always the
other number. 8 + 0 = 8, 0 + 4 = 4
7. Counting on by 1 or 2: Students can find sums like 5 + 1 or 6 + 2 by simply counting
on. This thinking strategy allows students to check off 18 of the addition facts.
8. Doubles: For whatever reason, students seem to be able to remember the sums of
doubles. That might be a consequence of skip counting in earlier grades.
9. Doubles Plus One: This strategy overlaps the other strategies of doubles and counting on by one. While more sophisticated, students should be taught to use this strategy when the addends are consecutive numbers. For instance, 7 + 8 becomes 7 + 7 + 1. Another
example, 8 + 9 becomes 8 + 8 + 1.
10. Doubles Plus Two: This method works when the addends differ by two. When this
occurs it is possible to subtract 1 from one addend and add one to the other addend. This
results in a doubles fact that has already been memorized, 7 + 5 becomes 6 + 6. Another
example, 6 + 8 becomes 7 + 7.
11. Nines: It should be pointed out to students that when adding nine, the ones digit in the
sum is always one less than the number added to 9. For example 7 + 9 = 16, the 6 is one
less than 7. Another example, 5 + 9 = 14.
12. Commutativity: By changing the order, 3 + 4 to 4 + 3, it should be pointed out that’s an additional 21 facts the students now know.

Subtraction Strategies
1. Subtract in Pieces: Example: 12 – 5 equals 12 – (2 + 3); 12 – 2 = 10; 10 – 3 = 7
2. Group by Place Value: Example: 65 – 23; 60 – 20 = 40; 5 – 3 =2; 40 + 2 = 42
3. Make Smart Groups: Example: 65 – 29; 65 – 30 = 35; 35 + 1 = 36
4. Count up vs. Count Down: Example: 12 – 8 = Count down; 12 – 4 = Count up
Go the shortest route.
5. Funny Numbers: Teach the “funny numbers” before you begin the concepts of adding and subtracting with regrouping. Then those concepts will make sense to the students.
Addition with Funny Numbers:
T O
30 12 = 42
Subtraction with Funny Numbers:
T O
42 = 30 12
6. Fact families: This strategy is the most commonly used and works when students
understand the relationship between addition and subtraction. When students see 6 – 2
and think 2 + ? =6. However, if this strategy is used with the following strategies,
students will find greater success in a shorter period of time.
7. Zeros: The pattern for subtracting zero is readily recognizable. 5 – 0 = 5
8. Sames: This method is used when a number is subtracted from itself; this is another
generalization that students can quickly identify. 7 – 7 = 0.
9. Recognizing Doubles: Recognizing the fact families associated with adding doubles.
10. Subtracting Tens: This is a pattern that students can pick up on very quickly, seeing that the ones digit remains the same.
11. Subtracting from Ten: Recognizing the fact families for Sums to 10.
12. Subtracting Nines: Again, the pattern that develops for subtracting 9 can be easily
identified by most students. They can quickly subtract 9 from a minuend by adding 1 to
the ones digit in the minuend. 17 – 9 = 8, 16 – 9 = 7.
13. Subtracting Numbers with Consecutive Ones Digits: This pattern will always result in a difference of 9, 16 – 7 = 9, 13 – 4,= 9 15 – 6 = 9 all have ones digits that are
consecutive and the result is always 9.
14. Subtracting Numbers with Consecutive Even or Consecutive Odd Ones Digits: This pattern will always result in a difference of 8. 14 – 6 = 8, 13 – 5 = 8, 12 – 4 = 8.

Multiplication Strategies
1. Commutativity: As with learning the addition facts, order can be changed when learning the multiplication facts. Hence, rather than learning 100 facts, we really only have to learn 55 facts.
2. Multiplication by Zero: Students can easily grasp that 0 times any number is zero.
3. Multiplication by One: Again, the generalization is easy for students to see that 1 times any number is the number.
4. Multiplication by Two: Students should be taught that multiplying by two is the Doubling strategy used in addition. Using the first four strategies, we have learned 27 more facts; only 28 remain to be learned.
5. Multiplication by Five: Students can often be taught the fives by referring to the minute hand on a clock.
6. Squaring: As with the addition facts, students seem to learn square numbers faster than other facts.
7. Multiplication by Ten: This pattern is very easy for students to see.
8. Multiplication by Nine: Patterns emerge when multiplying by 9. One pattern is the sum of the digits in the product is always equal to 9. The other pattern is the ten’s digit is always one less than the factor multiplied by 9. 9 × 6 = 54. Notice 5 + 4 = 9 and the 5 in the product is one less 6, the number being multiplied by 9. Another example, 8 x 9 = 72, the sum is 9 and the tens digit is one less than the tens digit.
9. Distributive Property: Students should feel comfortable breaking numbers apart and using previously learned information. For instance, 7 × 6 might be rewritten as 7(5 + 1). This would allow a student to use the 7 × 5 fact that he knows and add that to the 7 × 1 fact to get 42.
10. Finger Math: Facing your palms of your hands to your face, let the baby finger become the 6 finger, the ring finger the 7, the middle finger the 8, the index finger be the nine finger. To multiply the 7 × 7, place the two ring fingers together. The number of fingers touching and below represent the tens digit. There are four fingers, multiply the fingers above those on each hand to determine the ones digit. That would be 3 x 3. The product is 49. Try 7 × 9 by touching the index finger on one hand answer is sixty something and you now multiply the fingers on top to get the ones digit. That’s 1 x 3, the final answer is 63.

Computation strategies referenced from Greg Tang, 2006 and Hanlonmath.com, 2012.