Fifth-grade students will be asked to master fractions. They add and subtract fractions with unlike denominators by turning them into equivalent fractions. For example, they would add 2/3 + 1/4 by changing it to 8/12 + 3/12 = 11/12. They also learn to multiply a fraction by a whole number or another fraction, and they divide fractions by a whole numbers and vice versa. It's important at this level for children to use models and draw visual representations to demonstrate an understanding of the process. They should solve real-life problems. A parent can give a child two candy bars and ask him how he would divide them among three people.
Place-value knowledge is expanded in fifth grade to decimal numbers. Children learn to read, write and compare numbers to the thousandths place. They can explain why .116 is less than .161. A number line helps students realize that 1.56 is between the whole numbers 1 and 2. They practice rounding decimal numbers to the nearest tenth, hundredth and thousandth. Manipulative objects, such as money or plastic flats, rods and squares help kids grasp the concept of decimal numbers. Fifth-graders add, subtract, multiply and divide decimals through hundredths. They make reasonable estimations and can explain why their answers make sense.
Students in fifth grade stretch their knowledge of geometric concepts. They classify two-dimensional figures and put them into categories. For example, they recognize that squares are rectangles and all rectangles have four right angles. Fifth-grade students also graph points on a coordinate plane. They understand that there is an X and Y axis and that the two intersect at the origin. They can form ordered pairs and plot points in a quadrant of a coordinate grid.
Students learn two measurement systems: customary and metric. Fifth-graders convert measures within a given system. For example, they might change 5 meters into centimeters or 8 quarts into gallons. They create line plots and bar graphs and interpret data. Volume of a rectangular prism is emphasized at this grade level. Children determine the number of cubic units that will fill a prism without gaps or overlaps. Once they understand the concept, they use formulas such as "volume = length x width x height" to determine solutions. They use their knowledge to solve real-world problems.
Fifth-graders study patterns, number relationships and expressions. They analyze how one pattern is the same or different than another pattern. They work with the order of operations and symbols such as parentheses and brackets. They use this understanding of grouping symbols to write and interpret expressions. For example, when given the words, “5 plus 18 doubled,” they would write the expression 2 x (5 + 18). If they are given the expression, (7 x 8) – 2/3, they can write the words, “the product of 7 and 8, less two-thirds.” They learn that 0.5 x (20 – 14) is the same as 1/2 of (20 – 14).