Math

Introduction to the North Carolina Standard Course of Study for Math

As students progress through the grade levels, their strategies for finding solutions to questions improve as they gain experience conducting simple investigations and working in small groups.  Science is taught using inquiry methods, so students may base findings on past experience from previous grades and information around them.  The curriculum is divided into the following strands:

• Cluster 1: Understanding Equal Groups
• Cluster 2: Using Data to Solve Problems
• Cluster 3: Stories with Addition and Subtraction
• Cluster 4: Making Sense of Multiplication and Division
• Cluster 5: Reasoning with Shapes and Their Attributes
• Cluster 6: Applying the Operations to Area and Perimeter
• Cluster 7: Understanding Fractions as Parts of a Whole
• Cluster 8: Using Tools to Measure Length, Weight and Capacity
• Cluster 9: Time

1st Quarter

Cluster 1: Understanding Equal Groups

• NC.3.OA.1 For products of whole numbers with two factors up to and including 10:
• Interpret the factors as representing the number of equal groups and the number of objects in each group.
• Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and apply the commutative and associative properties.
• NC.3.OA.3 Represent, interpret, and solve one-step problems involving multiplication and division.
• Solve multiplication word problems with factors up to and including 10.  Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem.
• Solve division word problems with a divisor and quotient up to and including 10.  Represent the problem using arrays, pictures, and repeated subtraction.

Cluster 2: Using Data to Solve Problems

• 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 axis provided.
• Solve one and two-step “how many more” and “how many less” problems using information from these graphs

Cluster 3: Stories with Addition and Subtraction

• NC.3.NBT.2 Add and subtract whole number up to and including 1000.
• 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.
• NC.3.OA.8 Solve two-step word problems involving addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number.

2nd Quarter

Cluster 3: Stories with Addition and Subtraction (con't)

• NC.3.NBT.2 Add and subtract whole number up to and including 1000.
• 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.
• NC.3.OA.8 Solve two-step word problems involving addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number.

Cluster 4: Stories with Addition and Subtraction

• NC.3.OA.1 For products of whole numbers with two factors up to and including 10:
• Interpret the factors as representing the number of equal groups and the number of objects in each group.
• Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and apply the commutative and associative properties.
• NC.3.OA.2 For whole-number quotients of whole numbers with a one-digit divisor and a one-digit quotient:
• Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group.
• Illustrate and explain strategies including arrays, repeated addition and decomposing a factor.
• NC.3.OA.3 Represent, interpret, and solve one-step problems involving multiplication and division.
• Solve multiplication word problems with factors up to and including 10.  Represent the problem using arrays, pictures, and/or equations with a symbol for the unknown number to represent the problem.
• Solve division word problems with a divisor and quotient up to and including 10.  Represent the problem using arrays, pictures, and repeated subtraction.
• NC.3.OA.6 Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem.
• 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.
• 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.
• NC.3.OA.9 Interpret patterns of multiplication on a hundreds board and/or multiplication table.
• 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.

Cluster 5: Reasoning with Shapes and their Attributes

• NC.3.G.1 Reason with two-dimensional shapes and their attributes.
• Recognize and draw examples and non-examples of types of quadrilaterals including rhombuses, rectangles, squares, parallelograms, and trapezoids.

3rd Quarter

Cluster 6: Applying the Operations to Area and Perimeter

• 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 area of rectangles with whole-number side lengths in the context of problem solving, 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 larger rectangle is the sum of the two smaller rectangles.
• NC.3.MD.8 Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length.

Cluster 7: Understanding Fractions as Part of A Whole

• 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.

4th Quarter

Cluster 8: Using Tools to Measure Length, Weight and Capacity

• 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.

Cluster 9: Time

• 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.