I started teaching about addition and subtraction this week. We spend a lot of time thinking about how we get kids to master basic facts. When students first begin to work with addition, they use concrete objects and need to count all of the objects in the set beginning with one. Eventually they move on to counting up from the first addend. Our ultimate goal is to get them responding automatically to basic facts. The question is, how do we get there?
In helping students work through the operation of addition, we need to help them think about patterns and relationships so that basic facts are derived from number sense and thinking skills. Yes, they do need to be memorized, but I want my students to have a strong sense of number so that if they don't remember a fact quickly, they have some mental strategy for getting there.
To that end I spend a great deal of time reviewing strategies for addition facts. These should all be familiar to you, but there is one that seems to surprise teachers when I share it with them. Here's what it looks like.
I call these the "Two Apart" facts. That line on the addition table represents doubles facts. The "two apart" facts are in the shaded blocks. To use this strategy, students must know their doubles facts. When the addends in a sentence have a difference of two, the sum is the double of the number between them.
5 + 7 = ?
The number between 5 and 7 is 6.
6 doubled is 12.
5 + 7 = 12
This works because we've used compensation to adjust the addends. When we add one to the smaller addend and subtract one from the larger addend, we get two equal addends. This is the doubles fact!
Here are a few more examples.
6 + 8 = 7 + 7 = 14
7 + 9 = 8 + 8 = 16
See? This is simple and elegant and based in a strong understanding of numbers.
I've put together a packet with two versions of a chart for students to track their progress in mastering addition facts by the strategy used. You'll also find an explanation for each of the strategies presented. They are arranged in the order I generally teach these facts/strategies to students.
The ideas presented in the packet are designed to help meet the following Common Core Standards for Math:
- 1.OA.3. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
- 1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
- 1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
- 2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
Download Addition Fact Strategies.
I hope you get a chance to try these strategies in your home or classroom. Please let me know if you try them and how they work!