Number Sense Strategies for Addition

The following is taken from a post by Shelley Grey titled “Mental Math Addition Strategies” and is available by clicking the title. There are many websites that describe “number sense” strategies, but Shelley does a great job describing these strategies for addition. I encourage you to visit her website for more information about math strategies.

1. Counting On – Counting On is generally the first mental math strategy that should be taught, as it is the easiest for most students. Chances are that some or many of your students are already using this strategy without knowing it. Counting on means that you start with the biggest number in an equation, and then count up. For example, in the equation 5+3, you want students to start with the “5” in their heads, and then count up, “6, 7, 8.” This is to discourage students from counting like, “1, 2, 3, 4, 5…..6, 7, 8.” Students also need to be taught that if an equation looks like this: “2+6,” they still should start with the bigger number in this case “6” and count up “7, 8.”

2. Doubles – Doubles is the next strategy that I recommend teaching, as it usually comes quite easily to students. Doubles are all around us; think of fingers and toes – 5+5, wheels on a car – 2+2, or the eggs in a carton – 6+6. When students know their doubles well, they should no longer have to think about the equation to solve it. Rather, the answer becomes automatic. This means that the student has developed automaticity. For example, when a student sees the equation 8+8, he should know that it equals 16 without even stopping to think. Building a strong foundation of doubles will help students with the next strategy, Doubles Plus One.

3. Doubles Plus One – This strategy is a natural progression from the doubles. It includes using a known fact and building on it. For example, in the equation 5+6, a student could think, “I know that 5+5 makes 10, and one more makes 11.” This strategy will likely require a bit more teaching than the previous two, but it will be well worth it; when students know their doubles and doubles plus one facts, they know 25% of the addition table!

4. Making Ten – The making ten strategy involves memorizing the number combinations that add to ten. This includes 7 and 3, 8 and 2, & 5 and 5. Again, it is important that students develop automaticity with regards to these facts so that when they see a combination, they quickly know that it is a making ten combination. Once students begin to use this strategy, “counting on” becomes unnecessary in some circumstances.

5. Making Multiples of Ten – This strategy is a natural follow-up to making ten, as it uses the same number combinations in a different way. When teaching this strategy, students will learn to use the making ten facts in equations such as 27+3. In this case, students will see the ones digits and realize that 7 and 3 make 10, so 27 and 3 makes 30.

6. Front End Addition – This is perhaps one of the most powerful mental math strategies out there. Front end addition involves adding numbers from left to right, eliminating the need for carrying. Don’t dismiss the importance of teaching this strategy if it is an appropriate curricular expectation for your students! It will transform the way that they add, making them efficient and effective. Although many parents and some teachers are unfamiliar with this type of addition, it can transform people into believers pretty quickly! I have written another blog post all about front end addition, which you can see by clicking here.

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