Comparing and Ordering Fractions, Mixed Numbers, and Decimals

• Any decimal number can be written in fraction form. However, it is not possible to write every fraction as a terminating decimal (one that has a finite number of digits). Students in Grade 4 should not encounter very many repeating or otherwise nonterminating decimals, so be careful when you choose denominators for exercises in which students write fractions as decimals or compare fractions and decimals.

• When making a number line to use as a teaching tool, use quarter-inch grid paper. Then a number line 10 units long is 2 inches long. If each grid line represents a tenth, one half is at . Now use a ruler to put some more tick marks on the number line: is at ", is at 1".

• Use place-value charts to help students line up the digits, not only when they are comparing and ordering decimal numbers, but also when they are adding and subtracting decimals. Make a sheet of charts with spaces for thousands through hundredths and a special space for decimal points. Use this sheet as a copymaster and allow students to use copies freely.

• Help students establish benchmarks of their own for decimal numbers that compare to their benchmarks of 0, , and 1 for fractions. A good way to practice is to sort (or have students sort) grids colored to represent a wide variety of decimal numbers. Make piles labeled about 0, about 0.5, and about 1 as students practice saying the decimal name of each number.