Strategies for Addition and Subtraction
(Facts up to 20)
In second grade, we focus on the memorization and application of addition and subtraction facts up to 20. After these skills are embedded, we tackle the task of learning how to use regrouping to solve more challenging 2 and 3 digit-problems. By exploring the patterns in our math system, we equip students with strategies that can be generalized to solve tougher problems. Each strategy can be extended to offer enrichment and meet individual student needs. As we introduce strategies, students learn a common language to use to explain their problem solving. Encouragement is provided to solve problems in as many ways as possible, building confidence in the manipulation of numbers.
We teach “Fact Families” to stress that addition and subtraction are related and opposite functions. For instance, if we know that 3+7 = 10, we also know that 10 – 3 = 7. Three, seven and ten are members of a Fact Family. We also use “Turn Around Facts” to explain the relationship between numbers. 3 + 7 and 7 + 3 are examples of Turn Around Facts. Below are specific math strategies that your child will be using to solve problems and explain their math thinking.
Doubles: (1 + 1 = 2 and 2 – 1 = 1, 5 + 5 = 10 and 10 - 5 = 5)
Students learn most of the doubles quickly. If I know that 6 + 6 = 12, then 7 + 7 is two more and that’s 14. Also, 60 + 60 = 120 and 70 + 70 = 140. All doubles equations have an even sum.
Near Doubles: (7 + 8 is 7 + 7 + 1)
Once the students have a firm memory of the doubles, then the near doubles are the next strategy to learn. These are always 1 number away from the doubles. If I know that 6 + 6 = 12, then 6 + 7 is one more and that’s 13. Or, if I know that 6 + 6 = 12, then 6 + 5 is one less and that’s 11.
Make Ten: (1 + 9, 2 + 8, 3 + 7, and 10 – 1, 10 – 2, etc.)
These facts follow a structural pattern. Once students have a good understanding of these then they can use this information to solve harder problems. If I know that 3 + 7 = 10 then 30 + 70 = 100 and so on.
10 Plus: (10 + 1, 10 + 2, 10 + 3, and 11 – 1, 12 – 2, etc.)
These are among the easiest facts for children to learn. They follow a basic pattern and can be memorized rather quickly.
9 Plus: (9 + 1, 9 + 2, 9 + 3, etc…)
To solve these types of problems students can say…” If I am trying to solve 9+6, I can steal 1 from the 6 and add it to the 9 to make 10. Then I have 5 left and 10 + 5 is 15.
Some combinations belong to more than one group: 9 + 8 is a 9 Plus and also a near double. Students can use whatever works best for them. Children work together and individually to show their math thinking using pictures, manipulatives, numbers and words. Multiple solutions are a critical part of math mastery. As the year progresses, we will send more on math strategies and problem solving.
If a student can learn the above strategies, then there will only be 8 single digit addition combinations that do not fall into any of the categories above. The following facts should be practiced EXTRA hard because they seem to be the most difficult for kids.
5 + 3 6 + 3 7 + 4 7 + 5
8 + 3 8 + 4 8 + 5 8 + 6
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