Counting does not always have to start at the beginning!

I was not planning on writing a post today, but I was so excited during my two minutes of math with Katie that I felt the urge to document and share the experience right away.

Recently I introduced Katie to the concept of multiplication (something I will write more about in a later post) and today we were computing 5 times 7.  I was laying out the chips in rows of five, and Katie was counting after each row.  In the past, whenever we had some number of objects already on the table and we added a few more, Katie would always count all of the objects from the beginning.  But today, after each successive 5, Katie continued counting from where we left off.  And this was not a consequence of me laying them out very quickly; after each row I would point out to her that now we have 5 times 2, 5 times 3, etc.

I am fairly certain that Katie did not realize that she had a revelation and was doing something differently from the way she did it in the past.  I would not even be too surprised if next time she went back to counting from the beginning again.  Nonetheless, it feels like a definite step forward :-).  As usual, I would love to hear about other people’s experiences with this!


About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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6 Responses to Counting does not always have to start at the beginning!

  1. Kathy says:

    David started doing this recently — while playing Sum Swamp, actually — and I was so excited too :-). By the way, since you mentioned using chips, we have a set of base 10 blocks and I’ve found it super helpful for the kids while they’re figuring out arithmetic, place value, borrowing/carrying, etc.

    Do you set aside time each day to do math with Katie? Do you plan out little lessons/ideas ahead of time? I kind of want to be more deliberate about doing math with our kids.


  2. aofradkin says:

    We currently do not set aside time each day to do math but do it rather sporadically. I would like to do something in a more structured fashion, but that probably wouldn’t be on a daily basis. I like doing math spontaneously, even if briefly. For example, if we finish playing a game that has chips or pegs I will usually try to then use the pieces to give Katie an arithmetic problem or play with symmetry. Sometimes I do think of ideas ahead of time; for example, that was the case when I introduced functions to her. I wanted to make sure that I make them sound fun and not scary :-).


  3. I am sure Katie will not look back. It is one of these little steps with big consequences. I stil think you should introduce an abacus to her. This will help her to learn faster to work with relatively big numbers.


  4. We’re not quite there yet BUT Ari stopped counting fingers on his hands – he now knows there are five!


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