Fifth Grade

Grade 5 students write and interpret numerical expressions using parentheses, brackets, or braces. Students also generate numerical patterns using two given rules and identify relationships between corresponding terms.

Grade 5 students recognize that in a multi-digit number, including decimals, a digit in any place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Students work with powers of 10 to explain the patterns in the number of zeros in the products when multiplying by powers of 10 and the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Fifth graders will read, write, and compare two decimals to the thousandths based on meanings of the digits in each place. Work in grade five includes performing operations with multi-digit whole numbers and with decimals to the hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and multiplication and division.

Fifth graders use equivalent fractions as a strategy to add and subtract fractions with unlike denominators (including mixed numbers) by replacing the given fractions to equivalent fractions with like denominators and solve word problems involving addition and subtraction of fractions. Students also solve word problems involving division of whole numbers that lead to answers in the form of fractions or mixed numbers. Work also includes multiplication of a fraction by a whole number or by a fraction and use multiplication to find the area of rectangles with fractional side lengths. Students use the relationship between multiplication and division to develop strategies to divide unit fractions by a whole number or a whole number by a unit fraction by using visual fractional models and equations to represent real-world problems.

Grade 5 students convert like measurement units within a given measurement system and use these conversions in solving multi-step, real world problems. Students recognize volume as an attribute of solid figures and understand concepts of volume measurement to solve real world problems.

Fifth graders will graph points in the first quadrant of the coordinate plane to solve real-world and mathematical problems and interpret coordinate values of points in the context of a situation. Students work to understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category and will classify two-dimensional figures in a hierarchy based on properties.