The responses y'all gave were excellent, and were similar to those students give when they first encounter Number Talks! They ranged from counting one by one, to recognizing the pattern from previous experiences, to coming up with strategies for how to see patterns within the larger figure. None of these responses are better or worse than another, and we will spend the rest of this blog examining each type of response to help you recognize the merits of each.
Some of our students will automatically count the dots one by one. If your students do this, encourage them to find another way to determine the number of dots.
Some people saw the vertical line of 3 dots, then added the remaining two to get a sum of 5. Others might have seen the vertical line of 3 dots, then added the remaining two. The ability to quickly identify the number of items in a small set without counting is called subitizing. Recognizing the pattern as being similar to that found on a dice or from other sources is memorized subitizing.
Other people saw the two lines of three cross, and either added 3+3 or multiplied 2x3. Then they realized that the middle dot was counted twice in this process, and subtracted it from the total to end up with 5.
One person noticed the square formed by the outside dots, then added the middle dot. This geometric way of seeing will come more naturally to some than others.
Because many of our students haven't ever been asked to go beyond the algorithm or been encouraged to question the memorized methods, it might take a while for them to feel comfortable visualizing things in a different way. This is ok. It's also important to have these commonly used methods mentioned so that students can make connections between their method and the standard algorithm.
I'm going to have a Number Talk every Friday, with the responses discussed on Monday. Thank you all for participating in our very first one!
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