The Common Core- Counting & Cardinality Pt. 2

The second Domain in the area of Counting & Cardinality is divided into 2 main standards as described below.

Count to tell the number of objects.

  • CCSS.Math.Content.K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
    • CCSS.Math.Content.K.CC.B.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
    • CCSS.Math.Content.K.CC.B.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
    • CCSS.Math.Content.K.CC.B.4c Understand that each successive number name refers to a quantity that is one larger.
  • CCSS.Math.Content.K.CC.B.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

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This entire domain is something I think most early childhood teachers focus on.  We count with children all of the time looking for opportunities throughout the day for children to develop this skill.  There are some interesting specific expectations here that I think are worth exploring- things you might not be thinking about, but should be.

The first part of this standard refers to “one-to-one correspondence” even thought the authors are not calling it this.  When a child counts one object to one number and understands that each object represents “1” and only 1 number name and quantity.  So when children set the table we ask that they put one napkin at each chair, and one plate, and so forth.  You may periodically have the children count aloud when putting each item in its place, to reinforce the concept of one item = one number.  The last number they arrive at is the total number of items they distributed.  So, if there are 5 chairs at a table and the child distributes 5 napkins and 5 plates, there are a total of 5 places for children to sit and eat.  That number is the same no matter what chair they started from.  Sometimes, you can be explicit about this by asking, “How many kids can sit at this table?” or “How many napkins did you pass out?” Follow this up with a prompting question, i.e., “If you put 5 napkins out, how many plates did you put out?  Why is it the same number?”  Explaining this, or putting it into words is going to be a work in progress, but the questions will encourage mathematical thought and exploration.

The next part sub standard is a much, much harder concept for most children.  Many children 3 and up, can tell you that 5 is more than 3, or 10 is bigger than 2, but understanding that there is an actual algorithm that 6 is one unit bigger than 5… that is highly complex.

So, let’s break this down.  If I can count, “1,2,3,4,5… and so on, I have memorized a specific set of words in a specific order that describes a mathematic algorithm of

1+1+1+1+1+1…. and so on.

That means that I have to possess an understanding of the concept of “1” or in other words, the “oneness” of something so that I can then make the leap to the larger principle that counting by ones is based on the addition of “1” to the previous number.  This is also true when we ask children to count by 2s or 5s or 10s.

As adults, it is hard to break down a concept that is seemingly very simply and something that we have had known for what seems like our entire lives, into this highly complex process.  Many teachers think that if children can count then they understand number.  That is patently untrue and is a disservice to them.

Simple addition will support this concept and by simple I mean adding 1 to other small numbers.  Put two fingers up on one hand and put one finger up on the other.  Have the children add the fingers together.  This clear and consistent approach to adding “1” will reinforce the eventual understanding that 1 more, means the next number in the sequence of numbers.

Keep those kids counting….whenever you can as often as you can.

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