One dime is ten cents and tens cents is one dime.
We continued to work on building a flexible understanding of ten as a unit. We read Only One and talked about the big idea that one thing could be many things. They seemed to understand this idea in the abstract, and it gave us a point of reference when talking about tens and one. “Oh, you mean a dime is the SAME AS ten cents!�
Emilio and Jack both solved problems in ways today that showed me they are building this understanding. I was especially happy to see Jack draw this:
to represent 5 dimes with 20 cents subtracted out. In my sessions with him before today, he has been representing tens with ten tally marks or something similar, so to use one circle to represent 10 things was a real advance! I was hoping that a dime would have for the children a “one-nessâ€? and also a “ten-nessâ€?. But the problems I wrote may not help children develop this understanding if they don’t know money denominations
What’s so hard about these problems?
Both Daniella and Sunny struggled with these problems. In fact, Sunny didn’t solve a single problem. She represented the 5 dimes in problem 1 with 5 cubes. We talked about how much 20 cents was; she knew it was 2 dimes. But when I left her to work on the problem, she took all of the tens she had (unifix cubes) and broke them into ones to represent the stars in the sky that Emilio, in the story problems, had decided to buy. Daniella seemed confused about dimes and cents as different units, and how they related. She wrote Emilio “has 0 mony now� bec 5 of something take away 20 of something leaves you with, at most, 0. Interestingly, she represented the dimes in this way:
which shows she knows at some level that 1 dime is 10; but she didn’t seem able to use that knowledge to solve the problem.
I think these problems were just right for Jack and Emilio, but too hard for Sunny and Daniella.
For children whose understanding of dimes and, more generally, multiples of 10, isn’t automatic, these problems must seem like multistep problems with one of the steps left out! Like this: Henry has 4 packages. He eats 6 cookies. How much food does he have left? It doesn’t make much sense without the crucial information of how many cookies in one package.
Looking forward.
What should we do next? It is clear to me that simply telling or showing these children that one ten is the same as ten ones is not enough to help them learn to use this knowledge in problem solving. It is a difficult concept for young children, although of course if you understand it, the fact that it is a sophisticated mathematical idea isn’t obvious. So this is what’s on the agenda: more problem solving and more explicit discussion of how they are using tens. And once we get those norms for listening developed, more comparisons of each other’s strategies and the differences and similarities in how tens are used.
Posted in Case Study: Four Second Graders, Jack, Uncategorized | Comments (0)
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