The problem said, "How much money?" It showed two circles with N in them (for nickel) and three circles with P in them (for penny). It said ____ cents. The student was supposed to fill in the amount of money showing. This student wrote a 5 above each nickel representation and a 1 above each penny representation. Below this, she wrote 10 + 3. She filled in 13 cents. This student currently understands how to identify the value of different coins. She also can translate this value to a numeral by writing the value of individual coins. She was also able to write a sum of the nickels and a sum of the pennies when she showed 10 + 3. I currently do not see gaps in this students understanding of the value of coins from this homework assignment, however, I will take a closer look into how she completes other coin combinations and their values. The only gap that I can see is in her ability to count up to find the value of the coin. She wrote 10 + 3, but may not have been able to count the coins by saying "5, 10, 11, 12, 13." She has not shown her thinking in this way before, so if I could ask her a question, I would ask how she thought to write 10 + 3 to find her total. A way to advance her thinking might be to mix up the coin combinations so that some pennies are mixed in with nickels instead of all just in order so that she could decide how to determine the amount. Another way that I could advance her thinking is to give her a handful of pennies and nickels to count in whichever way she thought was best. This would allow her to either organize the coins by nickels and pennies, or attempt to count the coins by adding onto her total value each time she picks up another coin. A future math task that may be beneficial for her is to explore with dimes, as well as, pennies and nickels so that she can see the connection between all three coins.
What do other students think / understand in regards to this type of problems? What types of patterns do you see among them? These might be valuable questions to ask in planning future lessons (e.g., how might you group students together? What types of questions might you ask students? Which students might you want to have explain their strategies to the class?). Part of answering these questions involves an analysis of student work across all of the students in your class (of course, I don't expect that for this post, but I am just trying to advance your thinking).
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