One piece of work that I examined this week is a homework assignment where students worked with nickels and pennies to determine the amount shown. The problem read "Sabine grabbed 2 nickels and 6 pennies. She had ____ cents." This student said that she had 8 cents. This reveals that she knows how to count amounts of coins, but cannot yet determine the value of the nickels. She knows how to count pennies, assuming that she thought all coins were pennies. She may have thought that all coins are worth the same as a penny. She does not yet know how to count nickels and pennies together.
One way that I might advance this students thinking is by creating a chart for her to visually see the differences between different coins. I can display the faces of each coin and how much it is worth. I can also display the conversion between 5 pennies and 1 nickel. This might help the student to see the difference between pennies and nickels. Another way that I might advance her thinking is by explaining orally the difference between the values of the coins. I might explain that the number of coins is not the same as the value of the coins. If I could ask her a question, I might ask her to explain how she reached the number 8. If she explains that she counted the number of coins, then I could explain the values of the nickels. A future math task that may be beneficial for her is using actual coins while solving the problem. This would help her to see the problem shown visually instead of just stating the names of the coins. She may be able to solve the problem given the coins as a resource.
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