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. Understand and apply ratios, proportions, and percents in a variety of situations. Students begin to see a ratio as both the comparison of two quantities and as a number in its own right. In a social studies unit, students use population and area data for countries in South America to compute population densities, and then compare their results to those for other areas of the world. Students use two different sizes of grid paper to copy a simple drawing of a house from the smaller grid to the larger grid, investigating and discussing the change from one to the other and exploring ways to represent it numerically.