Counting Collections in Grades 1-2

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Although I have worked with outliers in every elementary grade, most of my classroom experience has been in grades 1 and 2.  Counting collections has seemed like a valuable activity for kinders and first graders.  After all, there are a lot of foundational concepts developed through rational counting:  number word sequences, one-to-one correspondence, one more, the cardinal principle, just to name a few. About halfway through first grade, we brought out bags of small items for the students to count.  Initially, the children counted by ones from one.  Over time, they started organizing the collections into groups of ten – developing ideas of efficiency as well as understandings about our number system.

The recently published book, Choral Counting and Counting Collections, does a beautiful job of not only addressing the early learning of number concepts but also making a compelling case for using collections all through elementary. There are quite a few ideas to take the act of establishing quantity to new levels:

  • Provide children with  5 or 10 frames to help with organizing objects as they count.
  • Provide children with a choice for tools (frames, cups, hundred grids, egg cartons, etc) for organizing the objects as they count.
  • Provide children with a recording sheet to not only write their total but also to record how they counted.
  • Provide children with materials that are packaged in amounts that would support the development of strategies for solving multiplication tasks or perhaps multidigit addition.

One of the blessings of a job like mine is that I get to spend time in a lot of classrooms. A few weeks ago, I happened to be in Sam’s room for a second grade math lesson.  The task for the day was to determine how many lima beans were in the teacher’s bag.

Sam asked the children to estimate first.  Yay!  Estimation experiences help children develop ideas of reasonableness and quantity.  The estimates ranged from 50 beans to 1 trillion beans.  

Next, the children worked in pairs to count their portion of the whole bag.  When partners were done, they brought their work back to the circle to be combined with the work of others.  

As Sam and the children counted the cups from all the groups, he periodically asked them what estimates they could rule out.  This class of 7 and 8 year olds was engaged in meaningful mathematics the entire lesson because there was an entry point for every student and the task felt worthwhile. 

Below are some examples of how children could organize collections as they count.  The first picture illustrates how a common classroom tool could be utilized in another context.  The organizing tools in the next two pictures came from dollar store:  miniature red plastic cups and a cupcake holder with 9 depressions.  What do you notice?

The dollar store just might be my favorite place to shop.  I found packs of gum that come in packages containing 5 sticks each and these amazing clear plastic vials. 

 We put 12 pennies in each container and wrote 12 cents on the lids.  The rule:  You can NOT open the lid.  Children who need to, can count each individual penny as they are all visible.  However, that’s not easy.  The conditions of the task push children, who are ready,  to chunk the quantity out.  Here you see 4 vials with 12 pennies in each vial.  One could predict that some children would break the 12 into 10 and 2 to find the total.  Others might go with repeated doubling.  

Here is a challenge for you.  Look carefully at the buttons in the picture.  What expressions could you use to describe the number of buttonholes?   The group to the left has one hole in the back of the button.  The middle five groups have 2 holes each.  The three groups on the right have 4 holes each. 

How many different expressions can you create?

There are many, many ways to use collections that will support content and process standards.  I challenge you to investigate these opportunities for yourself.  In addition to the book mentioned above, you may also be interested in this website, where you will find a plethora of resources, including video examples of the ideas shared:   https://tedd.org/mathematics/

Thanks for all you do every day for our students!

Margaret Williams

MCTM Elementary VP