Then they gather the data they need to make more informed estimates. Students determine the number of decimal places in a simple decimal multiplication product, not by mechanically adding the number of places in the factors, but by estimating a reasonable range for the product and placing the decimal point so that their computed product falls within that range. Students read Counting on Frank and estimate how many dogs would fill their classroom. Students use estimates to compare fractions. Expand the sense of magnitudes of different number types to include integers, rational numbers, and roots.
Students challenge each other to find target numbers on a number line.
First one student asks another to find 3.2. The second target number then must be between 0 and 3.2, say 1.74. The third must then be between 0 and 1.74 and so on. Students use their calculators to explore the types of decimal expansions for common fractions. They discover that some such decimals terminate, some repeat, and some appear to do neither.