The counting on addition strategy is a great mental math strategy used to build number fact fluency. To put it simply, counting on involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
What we want to achieve when teaching counting on, is for children to understand that they will start with the larger number in the addition sentence and count on 1, 2 or 3.
We don’t want them counting up to the larger number, for example, 5 + 3 – 1, 2, 3, 4, 5, … 6, 7, 8. We simply want them to start at 5 and then count 3 more – 5 … 6, 7, 8. This is much more efficient and when we start looking at larger numbers 22 +3, for example, it is crucial they have this basic understanding.
To be successful in counting on, two prerequisite skills are required:
- Students should be able to count forward in ones from a given number (instead of having to begin at 1) and;
- Students should understand the communicative property.
Teaching the counting on strategy with addition facts to 10
Before introducing the strategy, students need to be able to count on from any given number. Begin counting in ones to a number of your choosing, stop and have a child give the next number. When children are successful with this, introduce counting on one as an addition sentence.
To count on, students need to identify the largest number in the equation and count on from it. This means they need to understand the communicative property (turnarounds or flip-flop facts).
Children must understand that 1 + 5 = 5 + 1. If they haven’t got the basics first, you’ll find them starting with 1 and then counting up five more. This won’t lead to a quick recall of their number facts.
The more opportunities children get with identifying the turn-around fact, the easier count on facts will become.
To help children really understand the concept of counting on from the larger number have them circle it first.
Difficulties with the counting on addition strategy
Some children can find the counting on addition strategy a little bit tricky. Watch for students who include the circled number in their counting on. For these kids, you will find that instead of counting on from the number given, they start counting with that number so that 5 + 3 becomes 5, 6, 7 … 5 + 3 = 7.
If you are finding this is a problem for some of your students, take them right back to using concrete materials.
Have a container with a number in it. Students roll a die with the numbers 1, 2 or 3 on it and drop that number of counters in the container counting as they go. You should hear them say 6 (the starting number), 7, 8 (as they drop the counters in). Have them record the equation on a personal whiteboard.
Counting on 2
Once you know that your students can successfully count on one, introduce counting on two and then three.
They already know the commutative property but it’s important to continue to reinforce it.
Counting on 3
Before introducing counting on 3, use activities that just focus on counting on 1 and 2.
Then it’s time to count on 3 …
then mix them together.
Consolidating counting on with addition facts to 20
Once your students have shown continued success with counting on 1, 2 or 3 to numbers to 7, extend them by introducing adding to teen numbers. If they understand the strategy, this will be an easy next step.
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