Operations and Algebraic Thinking

• Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
• Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
• Generate two numerical patterns using two given rules; Identify apparent relationships between corresponding terms; form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Number and Operations in Base Ten

• Explain patterns in the number of zeros of the product when multiplying by powers of 10, and explain patterns in the placement of the decimal point when multiplying or dividing by powers of 10; use whole-number exponents to denote powers of 10.
• Read, write, and compare decimals to thousandths.
• Use place value understanding to round decimals to any place.
• Fluently multiply multi-digit whole numbers using the standard algorithm.
• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using various strategies; illustrate and explain the calculation with equations, arrays, and/or area models.
• Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and various strategies.

Number and Operations Fractions

• Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
• Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by 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.
• Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
• Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Measurement and Data

• Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real world problems.
• Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
• Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
• Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Geometry

• Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
• Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
• Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
• Classify two-dimensional figures in a hierarchy based on properties.