At the fifth grade level, students begin graphing in the first quadrant of the Cartesian coordinate system, so one of the problems they may solve is to graph the points (1,1), (3,3) and (4,4). Graphing and using ordered pairs are part of the geometry standards for fifth grade students. Other goals are in the areas of measurement and collection of data, fractions, base 10 and order of operations.
As students consider measurements, they learn the importance of making conversions within the particular system they are using. In the metric system, the curriculum asks them to convert liters to milliliters or kilometers to centimeters. Students also work several sessions on volume and the effects of adding volumes.
Students build upon their previous knowledge of fractions. They face problems such as adding fractions with different denominators, such as 3/4 + 1/8. They work with mixed numbers and with multiplying fractions. The curricula challenge students with story problems using fractions, such as how many 1/2-cup servings are in 6 cups of mashed potatoes.
Students learn the order to complete problems that contain parentheses, brackets and braces. They lean when a problem requires them to add before they multiply. In some of the problems, they do not find a final answer, but they develop the ability to describe the order in which the symbols require solving the problem.