Mathematics Standards for Colorado — Grade 3

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G31.1a

Use place value and properties of operations to perform multi-digit arithmetic. (CCSS: 3.NBT) i. Use place value to round whole numbers to the nearest 10 or 100. (CCSS: 3.NBT.1) ii. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 3.NBT.2) iii. Multiply one-digit whole numbers by multiples of 10 in the range 1090 using strategies based on place value and properties of operations. 1 (CCSS: 3.NBT.3)

G31.1a.i

Use place value to round whole numbers to the nearest 10 or 100. (CCSS: 3.NBT.1)

G31.1a.ii

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 3.NBT.2)

G31.1a.iii

Multiply one-digit whole numbers by multiples of 10 in the range 1090 using strategies based on place value and properties of operations. 1 (CCSS: 3.NBT.3)

G31.2a

Develop understanding of fractions as numbers. (CCSS: 3.NF) i. Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; describe a fraction a/b as the quantity formed by a parts of size 1/b. (CCSS: 3.NF.1) ii. Describe a fraction as a number on the number line; represent fractions on a number line diagram.2 (CCSS: 3.NF.2) iii. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (CCSS: 3.NF.3) 1. Identify two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (CCSS: 3.NF.3a) 2. Identify and generate simple equivalent fractions. Explain3 why the fractions are equivalent.4 (CCSS: 3.NF.3b) 3. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.5 (CCSS: 3.NF.3c) 4. Compare two fractions with the same numerator or the same denominator by reasoning about their size. (CCSS: 3.NF.3d) 5. Explain why comparisons are valid only when the two fractions refer to the same whole. (CCSS: 3.NF.3d) 6. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.6 (CCSS: 3.NF.3d)

G31.2a.i

Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; describe a fraction a/b as the quantity formed by a parts of size 1/b. (CCSS: 3.NF.1)

G31.2a.ii

Describe a fraction as a number on the number line; represent fractions on a number line diagram.2 (CCSS: 3.NF.2)

G31.2a.iii

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (CCSS: 3.NF.3) 1. Identify two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (CCSS: 3.NF.3a) 2. Identify and generate simple equivalent fractions. Explain3 why the fractions are equivalent.4 (CCSS: 3.NF.3b) 3. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.5 (CCSS: 3.NF.3c) 4. Compare two fractions with the same numerator or the same denominator by reasoning about their size. (CCSS: 3.NF.3d) 5. Explain why comparisons are valid only when the two fractions refer to the same whole. (CCSS: 3.NF.3d) 6. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.6 (CCSS: 3.NF.3d)

G31.3a

Represent and solve problems involving multiplication and division. (CCSS: 3.OA) i. Interpret products of whole numbers.7 (CCSS: 3.OA.1) ii. Interpret whole-number quotients of whole numbers.8 (CCSS: 3.OA.2) iii. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.9 (CCSS: 3.OA.3) iv. Determine the unknown whole number in a multiplication or division equation relating three whole numbers.10 (CCSS: 3.OA.4) v. Model strategies to achieve a personal financial goal using arithmetic operations (PFL)

G31.3a.i

Interpret products of whole numbers.7 (CCSS: 3.OA.1)

G31.3a.ii

Interpret whole-number quotients of whole numbers.8 (CCSS: 3.OA.2)

G31.3a.iii

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.9 (CCSS: 3.OA.3)

G31.3a.iv

Determine the unknown whole number in a multiplication or division equation relating three whole numbers.10 (CCSS: 3.OA.4)

G31.3a.v

Model strategies to achieve a personal financial goal using arithmetic operations (PFL)

G31.3b

Apply properties of multiplication and the relationship between multiplication and division. (CCSS: 3.OA) i. Apply properties of operations as strategies to multiply and divide.11 (CCSS: 3.OA.5) ii. Interpret division as an unknown-factor problem.12 (CCSS: 3.OA.6)

G31.3b.i

Apply properties of operations as strategies to multiply and divide.11 (CCSS: 3.OA.5)

G31.3b.ii

Interpret division as an unknown-factor problem.12 (CCSS: 3.OA.6)

G31.3c

Multiply and divide within 100. (CCSS: 3.OA) i. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division13 or properties of operations. (CCSS: 3.OA.7) ii. Recall from memory all products of two one-digit numbers. (CCSS: 3.OA.7)

G31.3c.i

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division13 or properties of operations. (CCSS: 3.OA.7)

G31.3c.ii

Recall from memory all products of two one-digit numbers. (CCSS: 3.OA.7)

G31.3d

Solve problems involving the four operations, and identify and explain patterns in arithmetic. (CCSS: 3.OA) i. Solve two-step word problems using the four operations. (CCSS: 3.OA.8) ii. Represent two-step word problems using equations with a letter standing for the unknown quantity. (CCSS: 3.OA.8) iii. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (CCSS: 3.OA.8) iv. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.14 (CCSS: 3.OA.9)

G31.3d.i

Solve two-step word problems using the four operations. (CCSS: 3.OA.8)

G31.3d.ii

Represent two-step word problems using equations with a letter standing for the unknown quantity. (CCSS: 3.OA.8)

G31.3d.iii

Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (CCSS: 3.OA.8)

G31.3d.iv

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.14 (CCSS: 3.OA.9)

G33.1a

Represent and interpret data. (CCSS: 3.MD) i. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. (CCSS: 3.MD.3) ii. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs.1 (CCSS: 3.MD.3) iii. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. (CCSS: 3.MD.4)

G33.1a.i

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. (CCSS: 3.MD.3)

G33.1a.ii

Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs.1 (CCSS: 3.MD.3)

G33.1a.iii

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. (CCSS: 3.MD.4)

G34.1a

Reason with shapes and their attributes. (CCSS: 3.G) i. Explain that shapes in different categories1 may share attributes2 and that the shared attributes can define a larger category.3 (CCSS: 3.G.1) 1. Identify rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. (CCSS: 3.G.1) ii. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.4 (CCSS: 3.G.2)

G34.1a.i

reason with shapes and their attributes. (CCSS: 3.G) i. Explain that shapes in different categories1 may share attributes2 and that the shared attributes can define a larger category.3 (CCSS: 3.G.1) 1. Identify rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. (CCSS: 3.G.1)

G34.1a.ii

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.4 (CCSS: 3.G.2)

G34.2a

Use concepts of area and relate area to multiplication and to addition. (CCSS: 3.MD) i. Recognize area as an attribute of plane figures and apply concepts of area measurement.5 (CCSS: 3.MD.5) ii. Find area of rectangles with whole number side lengths using a variety of methods6 (CCSS: 3.MD.7a) iii. Relate area to the operations of multiplication and addition and recognize area as additive.7 (CSSS: 3.MD.7)

G34.2a.i

Recognize area as an attribute of plane figures and apply concepts of area measurement.5 (CCSS: 3.MD.5)

G34.2a.ii

Find area of rectangles with whole number side lengths using a variety of methods6 (CCSS: 3.MD.7a)

G34.2a.iii

Relate area to the operations of multiplication and addition and recognize area as additive.7 (CSSS: 3.MD.7)

G34.2b

Describe perimeter as an attribute of plane figures and distinguish between linear and area measures. (CCSS: 3.MD)

G34.2c

Solve real world and mathematical problems involving perimeters of polygons. (CCSS: 3.MD.8) i. Find the perimeter given the side lengths. (CCSS: 3.MD.8) ii. Find an unknown side length given the perimeter. (CCSS: 3.MD.8) iii. Find rectangles with the same perimeter and different areas or with the same area and different perimeters. (CCSS: 3.MD.8)

G34.2c.i

Find the perimeter given the side lengths. (CCSS: 3.MD.8)

G34.2c.ii

Find an unknown side length given the perimeter. (CCSS: 3.MD.8)

G34.2c.iii

Find rectangles with the same perimeter and different areas or with the same area and different perimeters. (CCSS: 3.MD.8)

G34.3a

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. (CCSS: 3.MD) i. Tell and write time to the nearest minute. (CCSS: 3.MD.1) ii. Measure time intervals in minutes. (CCSS: 3.MD.1) iii. Solve word problems involving addition and subtraction of time intervals in minutes8 using a number line diagram. (CCSS: 3.MD.1) iv. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (CCSS: 3.MD.2) v. Use models to add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units.9 (CCSS: 3.MD.2)

G34.3a.i

Tell and write time to the nearest minute. (CCSS: 3.MD.1)

G34.3a.ii

Measure time intervals in minutes. (CCSS: 3.MD.1)

G34.3a.iii

Solve word problems involving addition and subtraction of time intervals in minutes8 using a number line diagram. (CCSS: 3.MD.1)

G34.3a.iv

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (CCSS: 3.MD.2)

G34.3a.v

Use models to add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units.9 (CCSS: 3.MD.2)