Students relate repeated addition, equal groups, and arrays to multiplication and division. With a focus on units of 2, 3, 4, 5, and 10, students use the commutative and distributive properties as strategies to multiply, and they write expressions with three factors as a foundation of the associative property. Students express division as both unknown factor problems and division equations and break apart and distribute the total to divide. They use their understanding of multiplication and division concepts to reason about and solve one- and two-step word problems.

Students compose and decompose metric measurement units and relate them to place value units up to 1 thousand . They use place value understanding and the vertical number line to round two- and three-digit numbers. Students also add and subtract two- and three-digit numbers within 1,000 by using a variety of strategies, including the standard algorithm.

Students extend their learning of multiplication and division to units of 6, 7, 8, 9, 0, and 1 by applying conceptual understanding and by using the commutative, distributive, and associative properties, as applicable. They multiply with two-digit multiples of 10 and solve one- and two-step word problems involving the four operations.

Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-sized square units required to cover the shape without gaps or overlaps. Students understand that rectangular arrays can be decomposed into identical rows or identical columns. They connect the number of rows and columns to the side lengths and then connect area to multiplication. Students use multiplication to determine the area of a rectangle and apply area concepts and strategies to mathematical and real-world problems.

Students develop an understanding of fractions as numbers. They partition a whole into equal parts and recognize 1 of a fractional unit as a unit fraction. Students compose non-unit fractions from unit fractions and use visual fraction models and written fractions to represent parts of a whole. Students use fractions to represent numbers equal to, less than, and greater than 1. They compare fractions by using visual fraction models and by reasoning about the size of fractions that have the same numerator or denominator. Students identify equivalent fractions, and they apply fraction concepts by using rulers to measure to the nearest quarter inch and by plotting fractional length data on line plots.

Students tell time to the nearest minute and use linear models to solve and represent elapsed time word problems. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by the number of sides and angles and make connections to the attributes of shapes. Students recognize perimeter as an attribute of plane figures and solve real-world and mathematical problems involving perimeter. Students also represent and interpret data by using scaled picture graphs, scaled bar graphs, and line plots.