For products of whole numbers with two factors up to and including 10:<ul><li>Interpret the factors as representing the number of equal groups and the number of objects in each group.</li><li>Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties.</li></ul>
For whole-number quotients of whole numbers with a one-digit divisor and a one-digit quotient:<ul><li>Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group.</li><li>Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor.</li></ul>
Represent, interpret, and solve one-step problems involving multiplication and division.<ul><li>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.</li><li>Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem.</li></ul>
Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison.
Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem.
Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10.<ul><li>Know from memory all products with factors up to and including 10.</li><li>Illustrate and explain using the relationship between multiplication and division.</li><li>Determine the unknown whole number in a multiplication or division equation relating three whole numbers.</li></ul>
Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number.
Interpret patterns of multiplication on a hundreds board and/or multiplication table.
| Standard | Definition | Code |
|---|---|---|
| For products of whole numbers with two factors up to and including… | For products of whole numbers with two factors up to and including 10:<ul><li>Interpret the factors as representing the number of equal groups and the number of objects in each group.</li><li>Illustrate and explain strategies including arrays, repeated addition, decomposing a factor, and applying the commutative and associative properties.</li></ul> | NC.3.OA.1 |
| For whole-number quotients of whole numbers with a one-digit divisor and a… | For whole-number quotients of whole numbers with a one-digit divisor and a one-digit quotient:<ul><li>Interpret the divisor and quotient in a division equation as representing the number of equal groups and the number of objects in each group.</li><li>Illustrate and explain strategies including arrays, repeated addition or subtraction, and decomposing a factor.</li></ul> | NC.3.OA.2 |
| Represent, interpret | Represent, interpret, and solve one-step problems involving multiplication and division.<ul><li>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.</li><li>Solve division word problems with a divisor and quotient up to and including 10. Represent the problem using arrays, pictures, repeated subtraction and/or equations with a symbol for the unknown number to represent the problem.</li></ul> | NC.3.OA.3 |
| Interpret a multiplication equation as a comparison | Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. | NC.4.OA.1 |
| Solve an unknown-factor problem, by using division strategies and/or changing… | Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. | NC.3.OA.6 |
| Demonstrate fluency with multiplication and division with factors, quotients… | Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10.<ul><li>Know from memory all products with factors up to and including 10.</li><li>Illustrate and explain using the relationship between multiplication and division.</li><li>Determine the unknown whole number in a multiplication or division equation relating three whole numbers.</li></ul> | NC.3.OA.7 |
| Solve two-step word problems using addition, subtraction | Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. | NC.3.OA.8 |
| Interpret patterns of multiplication on a hundreds board and/or multiplication… | Interpret patterns of multiplication on a hundreds board and/or multiplication table. | NC.3.OA.9 |
Add and subtract whole numbers up to and including 1,000.<ul><li>Use estimation strategies to assess reasonableness of answers.</li><li>Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems.</li><li>Use expanded form to decompose numbers and then find sums and differences.</li></ul>
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.
| Standard | Definition | Code |
|---|---|---|
| Add and subtract whole numbers up to and including 1,000.<ul><li>Use estimation… | Add and subtract whole numbers up to and including 1,000.<ul><li>Use estimation strategies to assess reasonableness of answers.</li><li>Model and explain how the relationship between addition and subtraction can be applied to solve addition and subtraction problems.</li><li>Use expanded form to decompose numbers and then find sums and differences.</li></ul> | NC.3.NBT.2 |
| Use concrete and pictorial models, based on place value and the properties of… | 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. | NC.3.NBT.3 |
Represent and interpret scaled picture and bar graphs:<ul><li>Collect data by asking a question that yields data in up to four categories.</li><li>Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided.</li><li>Solve one and two-step "how many more" and "how many less" problems using information from these graphs.</li></ul>
Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour.
Solve problems involving customary measurement.<ul><li>Estimate and measure lengths in customary units to the quarter-inch and half-inch, and feet and yards to the whole unit.</li><li>Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds.</li><li>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.</li></ul>
Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares.
Relate area to the operations of multiplication and addition.<ul><li>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.</li><li>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.</li><li>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.</li></ul>
Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length.
| Standard | Definition | Code |
|---|---|---|
| Represent and interpret scaled picture and bar graphs:<ul><li>Collect data by… | Represent and interpret scaled picture and bar graphs:<ul><li>Collect data by asking a question that yields data in up to four categories.</li><li>Make a representation of data and interpret data in a frequency table, scaled picture graph, and/or scaled bar graph with axes provided.</li><li>Solve one and two-step "how many more" and "how many less" problems using information from these graphs.</li></ul> | NC.3.MD.3 |
| Tell and write time to the nearest minute | 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.1 |
| Solve problems involving customary measurement.<ul><li>Estimate and measure… | Solve problems involving customary measurement.<ul><li>Estimate and measure lengths in customary units to the quarter-inch and half-inch, and feet and yards to the whole unit.</li><li>Estimate and measure capacity and weight in customary units to a whole number: cups, pints, quarts, gallons, ounces, and pounds.</li><li>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.</li></ul> | NC.3.MD.2 |
| Find the area of a rectangle with whole-number side lengths by tiling without… | Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares. | NC.3.MD.5 |
| Relate area to the operations of multiplication and addition.<ul><li>Find the… | Relate area to the operations of multiplication and addition.<ul><li>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.</li><li>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.</li><li>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.</li></ul> | NC.3.MD.7 |
| Solve problems involving perimeters of polygons, including finding the… | Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. | NC.3.MD.8 |
Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts;<ul><li>Explain that a unit fraction is one of those parts.</li><li>Represent and identify unit fractions using area and length models.</li></ul>
Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models.<ul><li>Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction.</li><li>Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0.</li></ul>
Represent equivalent fractions with area and length models by:<ul><li>Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths.</li><li>Explaining that a fraction with the same numerator and denominator equals one whole.</li><li>Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.</li></ul>
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.
| Standard | Definition | Code |
|---|---|---|
| Interpret unit fractions with denominators of 2, 3, 4, 6 | Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts;<ul><li>Explain that a unit fraction is one of those parts.</li><li>Represent and identify unit fractions using area and length models.</li></ul> | NC.3.NF.1 |
| Interpret fractions with denominators of 2, 3, 4, 6 | Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models.<ul><li>Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction.</li><li>Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0.</li></ul> | NC.3.NF.2 |
| Represent equivalent fractions with area and length models by:<ul><li>Composing… | Represent equivalent fractions with area and length models by:<ul><li>Composing and decomposing fractions into equivalent fractions using related fractions: halves, fourths and eighths; thirds and sixths.</li><li>Explaining that a fraction with the same numerator and denominator equals one whole.</li><li>Expressing whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.</li></ul> | NC.3.NF.3 |
| Compare two fractions with the same numerator or the same denominator by… | 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. | NC.3.NF.4 |
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.
| Standard | Definition | Code |
|---|---|---|
| Reason with two-dimensional shapes and their attributes | 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. | NC.3.G.1 |