Grade 5

5.1Write, explain, and evaluate simple numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving parentheses, brackets, or braces, using commutative, associative, and distributive properties.5.10Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.5.11Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.5.12Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.5.13Interpret multiplication as scaling (resizing).5.14Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.5.15Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.5.16Make a line plot to display a data set of measurements in fractions of a unit (12, 14, 18).5.17Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.5.18Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.5.19Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.5.2Generate two numerical patterns using two given rules and complete an input/output table for the data.5.20Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.5.21Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular).5.22Classify quadrilaterals in a hierarchy based on properties.5.23Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.5.3Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.5.4Read, write, and compare decimals to thousandths.5.5Use place value understanding to round decimals to thousandths.5.6Fluently multiply multi-digit whole numbers using the standard algorithm.5.7Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.5.8Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between addition/subtraction and multiplication/division; relate the strategy to a written method, and explain the reasoning used.5.9Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.
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