Required skill: fluent addition by counting the first group of objects quickly without pointing at every object, as described in my last post, fluent rote counting starting at any number (not just at 1.)
In my last post, I talked about how you can build fluency with the skill of adding by counting the first group of objects quickly. Since this skill builds on a child’s mental models of addition and quantity, it tends to be retained well with practice. You’ll know that the skill has become second nature if a child can reliably use it to put numbers together without having to think; occasionally forgetting and starting from 1 is not a problem, but a child should be able to quickly change course when reminded. This stage can be reached in anywhere from a few days to a few months.
Once this stage is reached, getting to “traditional” counting on is usually straightforward. Here’s how it goes, using the example of adding 6 and 1. This can be done with or without counters, depending on a child’s preference. (If the below dialogue doesn’t work without counters, definitely try it with counters.)
Parent: Can you tell me what 6 and 1 make together? Remember, you can count the first group quickly.
Child: 1, 2, 3, 4, 5, 6. Then there’s one more, so that’s 7. The total is 7!
Parent: Now I’m going to teach you an even faster way to do it! You counted the first group quickly, and you said 1, 2, 3, 4, 5, 6. So you said the number “6” last.
Wait a minute… we didn’t even need to count that group! We already know that when we count it, we’ll say the number 6 last, because that’s the total number of items in the group. So really, we can just say that number and keep counting from there. That means that we could have said 6 for the first group, then counted a 7 to add on the last 1.
Here’s another example. Say we’re putting together 7 and 2. When you count the first group, what’s the last number you’ll say?
Child: I’ll be counting 7 things… so the last number I’ll say is 7.
Parent: Now keep going! Remember, we want to count the 2 we’re putting together with the 7.
Child: I already got to 7, so now I say 8, 9. The total is 9!
Usually, once a child is fluent in the previous stage of counting on, this stage is not particularly tricky. One possible issue can be a child who understands the idea but is not sufficiently familiar with the counting sequence to starting counting at a number other than 1. In that case, you should continue practicing counting on via fast counting until the counting sequence is absorbed.
To practice this skill, you can use any of the ideas from my previous post, except that this time you will tell the child not to count the first group at all and will instead ask them what the last number they’d say if they had counted it fast would be.
In my experience, this stage transitions smoothly to kids being able to quickly add 1 or 2 to any number. Counting on also opens a lot of doors to mental manipulations of numbers, as we’ll see in later posts!
This is the fourth and final entry in a series of posts about counting on. Here are the first, second, and third entries in the series. These lay out precisely how I teach counting on, as well as my motivation for teaching it like this.