appropriately when multiplying or dividing quantities. M.1.3.15 Add and subtract M.1.4.15 Analyze numbers with like proportional relationships denominators, e.g., by and use them to solve replacing each mixed world and mathematical number with an equivalent problems. Compute unit fraction, and/or by using rates associated with ratios properties of operations and of fractions, including ratios the relationship between of lengths, areas and other addition and subtraction. quantities measured in like or different units. M.1.3.16 Solve word M.1.4.16 Recognize and problems involving addition represent proportional and subtraction of fractions relationships between referring to the same whole quantities. and having like Decide whether two denominators, e.g., by using quantities are in a visual fraction models and proportional relationship, equations to represent the e.g., by testing for problem. equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. Explain what a (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. M.1.4.17 Use proportional M.1.3.17 Apply and extend relationships to solve previous understandings of multistep ratio and percent multiplication to multiply a problems. fraction by a whole number. Understand a fraction / a b as a multiple of 1 / b. Understand a multiple of a / b as a multiple of 1 / b, and use this understanding to multiply a fraction by a whole number. word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
appropriately when multiplying or dividing quantities. M.1.3.15 Add and subtract numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. M.1.4.15 Analyze proportional relationships and use them to solve and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. M.1.3.16 Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. M.1.4.16 Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. Explain what a (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. M.1.3.17 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a / b as a multiple of 1 / b. Understand a multiple of a / b as a multiple of 1 / b, and use this understanding to multiply a fraction by a whole number. word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. M.1.4.17 Use proportional relationships to solve multistep ratio and percent problems. world
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