### NC.5.OA: Operations and Algebraic Thinking

#### (Framing Text): Write and interpret numerical expressions.

NC.5.OA.2: Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving:

NC.5.OA.2.a: Parentheses, using the order of operations.

NC.5.OA.2.b: Commutative, associative and distributive properties.

#### (Framing Text): Analyze patterns and relationships.

NC.5.OA.3: Generate two numerical patterns using two given rules.

NC.5.OA.3.a: Identify apparent relationships between corresponding terms.

NC.5.OA.3.b: Form ordered pairs consisting of corresponding terms from the two patterns.

NC.5.OA.3.c: Graph the ordered pairs on a coordinate plane.

### NC.5.NBT: Number and Operations in Base Ten

#### (Framing Text): Understand the place value system.

NC.5.NBT.1: Explain the patterns in the place value system from one million to the thousandths place.

NC.5.NBT.1.a: Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

NC.5.NBT.3: Read, write, and compare decimals to thousandths.

NC.5.NBT.3.a: Write decimals using base-ten numerals, number names, and expanded form.

NC.5.NBT.3.b: Compare two decimals to thousandths based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons.

#### (Framing Text): Perform operations with multi-digit whole numbers.

NC.5.NBT.6: Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm.

#### (Framing Text): Perform operations with decimals.

NC.5.NBT.7: Compute and solve real-world problems with multi-digit whole numbers and decimal numbers.

NC.5.NBT.7.a: Add and subtract decimals to thousandths using models, drawings or strategies based on place value.

NC.5.NBT.7.b: Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value.

NC.5.NBT.7.d: Use estimation strategies to assess reasonableness of answers.

### NC.5.NF: Number and Operations – Fractions

#### (Framing Text): Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

NC.5.NF.3: Use fractions to model and solve division problems.

NC.5.NF.3.a: Interpret a fraction as an equal sharing context, where a quantity is divided into equal parts.

NC.5.NF.3.b: Model and interpret a fraction as the division of the numerator by the denominator.

### NC.5.MD: Measurement and Data

#### (Framing Text): Represent and interpret data.

NC.5.MD.2: Represent and interpret data.

NC.5.MD.2.a: Collect data by asking a question that yields data that changes over time.

NC.5.MD.2.b: Make and interpret a representation of data using a line graph.

NC.5.MD.2.c: Determine whether a survey question will yield categorical or numerical data, or data that changes over time.

#### (Framing Text): Understand concepts of volume.

NC.5.MD.5: Relate volume to the operations of multiplication and addition.

NC.5.MD.5.a: Find the volume of a rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths.

NC.5.MD.5.b: Build understanding of the volume formula for rectangular prisms with whole-number edge lengths in the context of solving problems.

### NC.5.G: Geometry

#### (Framing Text): Understand the coordinate plane.

NC.5.G.1: Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems.