1. Plus zero
This pattern is the Identity Property of Addition. Students should
understand that whenever they add zero to any number the result is the
number. For example, 0 + 8 is the same as 8. Encourage students to use
this strategy by challenging them with large numbers.
2. Counting on
This is the strategy students use most frequently to solve all addition
problems. However, it is only effective when adding 1, 2, 3, and, at times,
4. Students should be encouraged to use strategies that are more effective
when adding larger numbers. Students should always start with the larger
addend and count on the smaller one. Student should be encouraged to count
on in their heads not with their fingers. Some students benefit from
visualizing a number line in their head to help them with the counting.
3. Near Doubles
This strategy requires students to think algebraically because it requires
the decomposition of numbers. It is effective only if the student knows the
doubles facts and understands the relationships between numbers. Students
should be guided to notice that these facts have an outstanding
characteristic - the two addends are near each other on the number line.
For example: 4 + 5 is the same as 4 + (4 + 1) or that 4 + 6 is the same as
4 + 4 + 2.
4. Make ten, add extra
The use of this strategy is essential for quickly and accurately finding
sums greater than 10. Students must know the facts for ten and how to
mentally decompose numbers. To use the strategy, students must take
something away from one of the addends to make the other addend a 10.
Students then add on the extra, or what is left from the first addend to
find the sum. For example: with the fact 8 + 6, students are guided to take
2 from the 6 and add it to the 8 to make a ten. There are 4 left from the
6. This is the extra and it is added to the 10. The strategy will need to
be modeled and practiced frequently for students to become proficient.
1. Minus zero
Students have an intuitive understanding of this pattern but do not apply it
consistently. Students are guided to recognize that if they subtract
nothing from a number, there will be no change in the quantity.
This strategy is used when the numbers being subtracted are equal. Students
should also have an intuitive sense that if they have something and all of
it is taken away zero will remain. However, they do not apply this
knowledge automatically and need guidance to think about what the
mathematical symbols are telling them.
Students can either count backward or count forward to find the differences
between two numbers. The counting strategies work best when the numbers
being subtracted are 4 or less apart or when the number being subtracted is
4 or less. Counting should take place inside students' heads and not on
4. The Nine Trick
This strategy, which is based on 9's relationship to 10, is used for all the
nine facts that involve minuends that are in the teens. If the students add
the digits of the minuend, the sum will be the answer to the problem.
Example: 15 - 9 = ? Students add 1 + 5 to find the difference of 6.
5.Subtract from ten, add extra
Students can use this strategy when subtracting 8, 7, and 6 from a number in
the teens. Students break the number in the teens into a ten and ones.
They subtract the 8, 7, or 6 from the ten and then add the ones. Example:
14 - 8: First, break 14 into 10 and 4. Subtract the 8 from the 10. You
will have 2 left. Add the 2 to the 4 to find the difference of 6.
This strategy involves using known facts to solve unknown facts. Some
students will intuitively use known addition facts to find the differences
for subtraction problems. Others will use number relationships. For
example, if students know that 8 - 4 = 4, they know that 9 - 4 = 5, because
9 is one more than 8. Students who demonstrate strong number sense use
these relationships fluidly. Other students can be taught to use these
relationships with frequent modeling.
Benchmark School, 2005