Operations and Algebraic Thinking

• Interpret a multiplication equation as a comparison; represent verbal statements of multiplicative comparisons as multiplication statements.
• Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number, distinguishing multiplicative comparison from additive comparison.
• Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
• Find all factor pairs for a whole number in the range of 1-100; recognize that a whole number is a multiple of each of its factors; determine whether a given whole number 1-100 is a multiple of a given one-digit number.
• Generate a number of shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Number and Operations in Base Ten

• Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
• Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results.
• Use place value understanding to round multi-digit whole numbers to any place.
• Fluently add and subtract multi-digit whole numbers using the standard algorithm.
• Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations Fractions

• Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions are the same size; use this principle to recognize and generate equivalent fractions.
• Compare two fractions with different numerators and denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or < and justify the conclusions.
• Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
• Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
• Use decimal notation for fractions with denominators 10 or 100.

Measurement and Data

• Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit.
• Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.
• Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
• Make a line plot to display a data set of measurements in fractions of a unit; solve problems involving addition and subtraction of fractions by using information presented in line plots.
• Recognize angles as geometric shapes formed when two rays share a common endpoint, and understand angle measurement.
• Measure angles in whole-number degrees using a protractor; sketch angles of specified measure.
• Recognize angle measure as additive; solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.