In the previous blog post I talked about the most fundamental ideas about counting and how we can help children develop cardinality. Until children have grasped this understanding, there is nothing else to be learned in mathematics. Nothing. They need to know the names of numbers, the order they come in, and that the last number names the quantity. However, we don’t want a child’s mathematical development with numbers to get stuck in counting. It is important in the beginning but we want them to develop a rich understanding of numbers apart from counting. I will share more about that later.
Here are some other kinds of counting that you can do with your children as their knowledge of numbers develops.
Counting Up and Back
Counting up to and than immediately back down from a target number can be a rich exercise. It can be done with movement (such as clapping, jumping, air fist-pumping, etc.) in a rhythmic manner. Or you might move a set of objects from one line to another as you chant, “ 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, …”.
Another version is to count up and back between two numbers such as 8 and 13. As before, keep a rhythm.
What about counting between numbers such as 28 and 37? That raises the difficulty level again.
Counting On
Counting on is the practice of starting the counting sequence from a number other than 1.
WITH COUNTERS: Give your child a collection of small counters and have them line them up. Then have them count a few of them, hide them under their left hand and count from that number. For instance, if they have 10 counters, you might have them hide 4. Point to the hand and ask how many are there under the hand. (Four.) Then say, “Let’s count like this: four (pointing to the hand), five, six, …”.
Instead of covering the counters with a hand, you can use a piece of paper, a small bowl turned upside down, or something else that is handy. The important idea is to know how many are hidden (because they were counted first) and continue “counting on” from that number.
Older children can practice counting by 1’s from other larger numbers such as 37, 142, etc.
Other ideas for counting:
Most kindergarten-aged students can also practice
counting by 5’s and 10’s. I have found it very useful to use hand motions for these. For instance, when counting by 10’s you can flash all 10 fingers every time the next multiple of 10 is said, thus illustrating the increase by 10 each time.
Similarly, when counting by 5’s, flash the fingers of one hand each time a number is said. Students may or may not have full understanding of the concept of “tens and ones” here, but still practicing the counting sequence of words is useful.
Counting by 2’s and 3’s are both useful exercises. These can be done using counters and/or by looking at numbers on a 100 chart.
IMPORTANT: Count past 100!
When you are counting up to 100 by 1’s, 2’s, 5’s or 10’s
do not stop counting (as may be your instinct) at 100. I have asked dozens of children what comes after 100, and their answer is almost always “200” no matter what they were counting by. It is very important to continue the counting sequence past 100:
…97, 98, 99, 100, 101, 102, 102, …
…96, 98, 100, 102, 104, 106, …
…85, 90, 95, 100, 105, 110, …
…70, 80, 90, 100, 110, 120, …
Happy counting!
Mathematically yours,
Carollee
