Even though students generally have a good sense of place values for whole numbers by the time they start 4th grade, they may have trouble extending their understanding to decimal places when they encounter decimals for the first time.
The main difference when dealing with decimals is that convention dictates we do not write any trailing zeros in decimals. For example, when asked which of the following is bigger,
0.3 or 0.28,
some students instinctively conclude that 3 is smaller than 28, so the number on the left is smaller.
To use a visual method to let them have a better sense of the comparative values of decimal numbers, we ask students to shade the standard 100 grid as follows.
0.28 means we shade 28 of the (1/100th) squares:
whereas for 0.3, we shade 3 rows or three column:
In this way, students can visualize that 0.3 is actually 0.30, and that
0.3 > 0.28
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