What happens when a child has no addition strategies to help them add two numbers successfully?
We've all seen these kids. They're the ones who secretly add on their fingers, putting their hands under the desk so no one can see.
Then they struggle when those two numbers add up to equal more than 10 because they don't have enough fingers.
I'm not saying it's wrong to add on fingers but when these kids see their peers adding quickly in their heads, it increases their own sense of failure. Confirmation in their belief that they're ‘not good at math'.
How can we give them the strategies to add successfully and confidently? How do we build addition fact fluency?
To ensure success, it's recommended that the addition basic facts are taught using a sequenced approach. By sequenced, I don't mean learning to add on 1 first followed by 2, 3, 4, 5, 6, 7, 8 and 9. A sequenced approach to learning the basic facts involves learning thinking strategies in a particular sequence.
The importance of teaching a few powerful, yet simple thinking strategies to teach basic facts cannot be overemphasized. If efficient strategies are not taught, children will use or invent their own inefficient strategies, usually related to counting.
Booker, Bond, Sparrow & Swan 2014
The Mental Math Strategies
1. Making 10
We introduce the mental math strategies by looking at two numbers that add together to make ten. Addition to ten has been taught in kindergarten so in first grade, it becomes a nice introduction into the use of strategies.
The addition facts for ten are known by different names. Some teachers call them the rainbow facts or making a ten. Others call them partners of ten or friends of ten.
0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 and their turn arounds (using the commutative property we turn 3 + 7 around to become 7 + 3) are all addition facts for 10.
Whatever you call them, they're a prerequisite for gaining an understanding of friendly numbers which can be used when adding two digit numbers.
2. Counting on 1, 2, or 3
The next addition strategy to learn is to count on 1, 2 or 3 and 0. Counting on any more than 3 can lead to difficulties and there are better strategies to use. To count on, students put the larger number in their heads and count on the next 1, 2 or 3 numbers. They calculate the answer to 9 + 3, students start with nine and count up 3 more – 9 …10, 11, 12. Watch to make sure they're not including 9 when they're counting up and getting 11 as their answer – 9, 10, 11.
It can seem obvious to us that adding to zero or adding zero to a number doesn't change the number but it's important to make sure that your students actually understand this. It's easy to demonstrate with manipulatives.
3. Doubles Facts
Once the count on facts have been taught and your students have had plenty of time for meaningful practice, teach the doubles next. This is simply doubling a number – 1 + 1, 2 + 2 etc. The doubles don't have a strategy as such so we use images as a memory trigger.
Would you love some doubles posters for your class? Grab them here.
When children are confident and fluent with the doubles facts it's time to move on to near doubles – doubles plus one and two.
4. Near Doubles – Doubles + 1
Near doubles are two numbers that are close to a double.
6 + 7 is a near double. It's actually a doubles + 1. To answer it, we double the smallest number and add one more.
5. Near Doubles – Doubles + 2
6 + 8 is a doubles + 2. We get the answer by doubling the smallest number and adding two more.
Or we can look at it as a counting pattern with the number in the middle missing. To get the answer we can double the missing number.
This means we would double 7 to make 14. 6 + 8 = 14. This mental math strategy is called monkey in the middle too because to get the answer we double the number that would be in the middle – 6, _, 8.
6. Adding 10
Once children have become familiar with their teen numbers, adding ten becomes easy. Children become aware that 17 = 1 ten and 7 ones, therefore 10 + 7 = 17.
7. Adding 9
Using counters and two tens frames to show the number fact, students begin to see that we just need to move one counter across to make a ten. 9 + 3 becomes 10 + 2. And because they've already had lots of practice adding 10, this number fact is quickly mastered.
Practice the Facts
One addition fact can have different strategies. To answer 7 + 9 we can think of it as an adding 9 fact and use a ten to help us or we can see it as doubles + 2 and double the 7 and add 2 more. Having fact fluency means using the strategy the student prefers, one that gets them the correct answer.
Thinking strategies can't be taught in isolation. Students need plenty of opportunities for practice to master them. Games, of course, are my preference and you'll find the games above in the Addition Facts Strategies Bundled Pack or the pack can be purchased separately HERE or by clicking on the pictures below.
Booker, G., Bond, D., Sparrow, L., and Swan, P. 2014. Teaching Primary Mathematics. NSW: Australia
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