Mathematics Standards

Operations and Algebraic Thunking

Represent and solve problems involving multiplication and division.

NC.3.OA.1 Solve problems with multiplication and division up to 10.

• Students build on their work with repeated addition and rectangular arrays from Second Grade.
• Students apply the commutative property (order property), which states the order of numbers does not matter when you are adding or multiplying numbers.
• Students are introduced to the distributive property of multiplication, through decomposing a number, as a strategy for solving multiplication problems.

NC.3.OA.2 Solve problems involving whole number quotients of whole numbers with one-digit divisor and one-digit quotient.

• Students use partition models (fair share) provide students with a total number and the number of groups.
• Students use measurement (repeated subtraction) models provide students with a total number and the number of objects in each group.

NC.3.OA.3 Solve one step problems involving multiplication and division.

• Students apply strategies to various multiplication and division situations to solve word problems.
• Students should use a variety of representations for creating and solving one-step word problems.
• Students in third grade should use a variety of pictures, such as stars, boxes, etc. to represent unknown numbers. Letters are also introduced to represent unknowns in third grade.

Understand properties of multiplication and the relationship between multiplication and division.

NC.3.OA.6 Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem.

Multiply and divide within 100.

NC.3.OA.7 Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10.

• Know from memory all products with factors up to and including 10.
• Illustrate and explain using the relationship between multiplication and division.
• Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Solve two-step problems.

NC.3.OA.8 Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number.

Explore patterns of numbers.

NC.3.OA.9 Interpret patterns of multiplication on a hundreds board and/or multiplication table.

Number and Operations in Base Ten

Use place value to add and subtract.

NC.3.NBT.2 Add and subtract whole numbers up to and including 1,000.

• Use estimation strategies to assess reasonableness of answers.
• Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems.
• Use expanded form to decompose numbers and then find sums and differences.

Generalize place value understanding for multi-digit numbers.

NC.3.NBT.3 Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90.

Number and Operations – Fractions

Understand fractions as numbers.

NC.3.NF.1 Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts;

• Explain that a unit fraction is one of those parts.
• Represent and identify unit fractions using area and length models.

NC.3.NF.2 Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models.

• Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction.
• Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0.

NC.3.NF.3 Represent equivalent fractions with area and length models by:

• Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths.
• Explaining that a fraction with the same numerator and denominator equals one whole.
• Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

NC.3.NF.4 Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths.

Measurement and Data

Solve problems involving measurement.

NC.3.MD.1 Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour.

NC.3.MD.2 Solve problems involving customary measurement.

• Estimate and measure lengths in customary units to the quarter-inch and half-inch, and feet and yards to the whole unit.
• Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds.
• Add, subtract, multiply, or divide to solve one-step word problems involving whole number measurements of length, weight, and capacity in the same customary units.

Represent and interpret data.

NC.3.MD.3 Represent and interpret scaled picture and bar graphs: • Collect data by asking a question that yields data in up to four categories.

• Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided.
• Solve one and two-step “how many more” and “how many less” problems using information from these graphs.

Understand the concept of area.

NC.3.MD.5 Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares.

NC.3.MD.7 Relate area to the operations of multiplication and addition. • Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

• Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning.
• Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles, and that the area of the large rectangle is the sum of the two smaller rectangles.

Understand the concept of perimeter.

NC.3.MD.8 Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length.

Geometry

Reason with shapes and their attributes.

NC.3.G.1 Reason with two-dimensional shapes and their attributes.

• Investigate, describe, and reason about composing triangles and quadrilaterals and decomposing quadrilaterals.
• Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids.