American Samoa College and Career Ready Standards: Grade 3
Skills available for American Samoa third-grade math standards
Strand
Print skill plan
1-2
Number Sense, Properties, and Operations
3.1 Students investigate numbers, ways of representing numbers, relationships among numbers, and number systems.
3.1.1 Round whole numbers to the nearest 10 or 100 using place value understanding
3.1.1 Round whole numbers to the nearest 10 or 100 using place value understanding
3.1.1.a: Identify place value of numbers (digits) using a place-value chart
3.1.1.a: Identify place value of numbers (digits) using a place-value chart
3.1.1.b: Determine the place values of whole numbers to 10,000 using amounts of thousands, hundreds, tens, and ones (e.g., 38,006 equals 38 thousands, 0 hundreds, 0 tens, and 6 ones)
3.1.1.b: Determine the place values of whole numbers to 10,000 using amounts of thousands, hundreds, tens, and ones (e.g., 38,006 equals 38 thousands, 0 hundreds, 0 tens, and 6 ones)
3.1.1.c: Explain and apply rules of rounding numbers
3.1.1.c: Explain and apply rules of rounding numbers
3.1.1.d: Apply understanding of place value in order to round whole numbers to the nearest 10 or 100
3.1.1.d: Apply understanding of place value in order to round whole numbers to the nearest 10 or 100
3.1.2 Develop understanding of fractions as numbers, their representations on the number line, the notion of equivalent fractions, and comparing fractions by size
3.1.2 Develop understanding of fractions as numbers, their representations on the number line, the notion of equivalent fractions, and comparing fractions by size
3.1.2.a: Identify a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (e.g., 1/2 is one part of two parts; 1/4 is one part of four parts; 1/10 is one part of ten parts)
3.1.2.a: Identify a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (e.g., 1/2 is one part of two parts; 1/4 is one part of four parts; 1/10 is one part of ten parts)
3.1.2.b: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts, and recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line
3.1.2.b: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts, and recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line
3.1.2.c: Identify a fraction a/b as the quantity formed by the parts of size 1/b
Understand fractions
Show fractions
Match fractions and models
Word problems
3.1.2.c: Identify a fraction a/b as the quantity formed by the parts of size 1/b
Understand fractions
Show fractions
Match fractions and models
Word problems
3.1.2.d: Represent a fraction a/b on a number line diagram by marking off a length 1/b from 0, and recognize
3.1.2.d: Represent a fraction a/b on a number line diagram by marking off a length 1/b from 0, and recognize
3.1.2.e: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size:
3.1.2.e: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size:
3.1.2.e.i: Describe two fractions as "equivalent" (equal) if they are of the same size or the same point on a number line
3.1.2.e.i: Describe two fractions as "equivalent" (equal) if they are of the same size or the same point on a number line
3.1.2.e.ii: Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4; 4/6 = 2/3), and explain why the fractions are equivalent (e.g., by using a visual fraction model)
Model equivalent fractions
Find equivalent fractions
3.1.2.e.ii: Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4; 4/6 = 2/3), and explain why the fractions are equivalent (e.g., by using a visual fraction model)
Model equivalent fractions
Find equivalent fractions
3.1.2.e.iii: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers (e.g., express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram)
3.1.2.e.iii: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers (e.g., express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram)
3.1.2.e.iv: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that the comparison above is valid only when the two fractions refer to the same whole, and record the result of the comparison with either the symbol >, =, or <, and justify the conclusion (e.g., by using a visual fraction model)
Compare using models
Compare using number lines
Compare fractions
3.1.2.e.iv: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that the comparison above is valid only when the two fractions refer to the same whole, and record the result of the comparison with either the symbol >, =, or <, and justify the conclusion (e.g., by using a visual fraction model)
Compare using models
Compare using number lines
Compare fractions
3.2 Students perform mathematical operations and determine how they relate to one another.
3.2.1 Represent and solve problems involving multiplication and division using grouping
3.2.1 Represent and solve problems involving multiplication and division using grouping
3.2.1.a: Interpret or describe a context in which a total number of objects can be expressed as products of whole numbers (e.g., interpret 8 × 3 as the total number of objects in 8 groups of 3 objects each)
Equal groups
Arrays
Number lines
Relate addition and multiplication
3.2.1.a: Interpret or describe a context in which a total number of objects can be expressed as products of whole numbers (e.g., interpret 8 × 3 as the total number of objects in 8 groups of 3 objects each)
Equal groups
Arrays
Number lines
Relate addition and multiplication
3.2.1.b: Interpret whole-number quotients of whole numbers (e.g., interpret 84 ÷ 3 as the number of objects in each share when 84 objects are partitioned equally into 3 shares)
3.2.1.b: Interpret whole-number quotients of whole numbers (e.g., interpret 84 ÷ 3 as the number of objects in each share when 84 objects are partitioned equally into 3 shares)
3.2.1.c: Describe a context in which a total number of objects, a number of shares, or a number of groups can be expressed mathematically (e.g., 5 × 7; 56 ÷ 8)
3.2.1.c: Describe a context in which a total number of objects, a number of shares, or a number of groups can be expressed mathematically (e.g., 5 × 7; 56 ÷ 8)
3.2.1.d: Draw pictures of "groupings" to illustrate examples of dividing a 2?digit number by a 1-digit number with a remainder (e.g., 15/4 = 3R3)
3.2.1.d: Draw pictures of "groupings" to illustrate examples of dividing a 2?digit number by a 1-digit number with a remainder (e.g., 15/4 = 3R3)
3.2.1.e: Represent and solve problems involving multiplication and division within 100 and situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem)
Multiplication
Division
Mixed operations
3.2.1.e: Represent and solve problems involving multiplication and division within 100 and situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem)
Multiplication
Division
Mixed operations
3.2.1.f: Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48; 5 = _ ÷ 3; 6 × 6 = ?)
3.2.1.f: Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48; 5 = _ ÷ 3; 6 × 6 = ?)
3.2.2 Perform multidigit arithmetic in base 10 using place value understanding and properties of operations
3.2.2 Perform multidigit arithmetic in base 10 using place value understanding and properties of operations
3.2.2.a: Add and subtract within 1,000, using strategies and algorithms based on place value
Addition
Subtraction
3.2.2.a: Add and subtract within 1,000, using strategies and algorithms based on place value
Addition
Subtraction
3.2.2.b: Add and subtract within 1,000, using strategies and algorithms based on properties of operations
3.2.2.b: Add and subtract within 1,000, using strategies and algorithms based on properties of operations
3.2.2.c: Add and subtract within 1,000, using strategies and algorithms based on the relationship between addition and subtraction
3.2.2.c: Add and subtract within 1,000, using strategies and algorithms based on the relationship between addition and subtraction
3.2.2.d: Multiply one-digit whole numbers by multiples of 10 in the range 10?90, using strategies based on place value and properties of operations
3.2.2.d: Multiply one-digit whole numbers by multiples of 10 in the range 10?90, using strategies based on place value and properties of operations
3.2.2.e: Multiply one-digit whole numbers by multiples of 10 in the range 10?90 (e.g., 9 × 80; 5 × 60)
3.2.2.e: Multiply one-digit whole numbers by multiples of 10 in the range 10?90 (e.g., 9 × 80; 5 × 60)
3.2.3 Explain the relationship between multiplication and division, and apply properties of multiplication
3.2.3 Explain the relationship between multiplication and division, and apply properties of multiplication
3.2.3.a: Explain the relationship between multiplication and division: - Apply commutative property of multiplication (e.g., if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known) - Apply associative property of multiplication (e.g., if 3 × 5 × 2 can be found by first 3 × 5 = 15 then 15 × 2 = 30, or, by first 5 × 2 = 10 then 3 × 10 = 30) - Apply distributive property of multiplication [e.g., knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56]
Properties of multiplication
Relationship between multiplication and division
3.2.3.a: Explain the relationship between multiplication and division: - Apply commutative property of multiplication (e.g., if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known) - Apply associative property of multiplication (e.g., if 3 × 5 × 2 can be found by first 3 × 5 = 15 then 15 × 2 = 30, or, by first 5 × 2 = 10 then 3 × 10 = 30) - Apply distributive property of multiplication [e.g., knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56]
Properties of multiplication
Relationship between multiplication and division
3.2.3.b: Relate division to multiplication as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)
3.2.3.b: Relate division to multiplication as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)
3.2.3.c: Multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations (e.g., show that if 8 × 5 = 40, then 40 ÷ 5 = 8)
Multiplication skill builders
Multiplication facts for 2, 3, 4, 5, and 10
Multiplication facts for 6, 7, 8, and 9
Multiplication facts up to 10
Division skill builders
Division facts for 2, 3, 4, 5, and 10
Division facts for 6, 7, 8, and 9
Division facts up to 10
Mixed operations
Properties of operations
3.2.3.c: Multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations (e.g., show that if 8 × 5 = 40, then 40 ÷ 5 = 8)
Multiplication skill builders
Multiplication facts for 2, 3, 4, 5, and 10
Multiplication facts for 6, 7, 8, and 9
Multiplication facts up to 10
Division skill builders
Division facts for 2, 3, 4, 5, and 10
Division facts for 6, 7, 8, and 9
Division facts up to 10
Mixed operations
Properties of operations
3.2.3.d: Recite or recall all products of two one-digit numbers
3.2.3.d: Recite or recall all products of two one-digit numbers
3.2.3.e: Multiply a 2- to 4-digit number by a 1-digit number
3.2.3.e: Multiply a 2- to 4-digit number by a 1-digit number
3-4
Patterns, Algebra, and Functions
3.3 Students investigate patterns, functions and quantitative relationships and apply that knowledge to modeling, analyzing or solving mathematical and real-word problems.
3.3.1 Identify and explain arithmetic patterns using properties of operations
3.3.1 Identify and explain arithmetic patterns using properties of operations
3.3.1.a: Identify and explain arithmetic patterns using properties of operations (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends)
3.3.1.a: Identify and explain arithmetic patterns using properties of operations (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends)
3.3.1.b: Describe and extend patterns to determine the next term in a linear or geometric pattern
3.3.1.b: Describe and extend patterns to determine the next term in a linear or geometric pattern
3.4 Students use symbolic forms, operations, and properties to represent, model, solve, and analyze mathematical situations and structures.
3.4.1 Describe and represent relationships of quantities using mathematical expressions, equations, and inequalities, and solve two-step word problems using the four operations
3.4.1 Describe and represent relationships of quantities using mathematical expressions, equations, and inequalities, and solve two-step word problems using the four operations
3.4.1.a: Represent relationships of quantities using equations or inequalities, with letters standing for the unknown quantities
3.4.1.a: Represent relationships of quantities using equations or inequalities, with letters standing for the unknown quantities
3.4.1.b: Solve two-step word problems using the four operations
One-step problems
Two-step word problems
3.4.1.b: Solve two-step word problems using the four operations
One-step problems
Two-step word problems
3.4.1.c: Assess the reasonableness of the answers by mentally computing answers and comparing with the solutions
3.4.1.c: Assess the reasonableness of the answers by mentally computing answers and comparing with the solutions
3.4.1.d: Assess and explain the reasonableness of the answers by estimating answers to whole numbers, including rounding
3.4.1.d: Assess and explain the reasonableness of the answers by estimating answers to whole numbers, including rounding
5-6
Measurement, Geometry, and Spatial Sense
3.5 Students explore properties, relationships, and transformations of shapes and space using coordinate geometry and other representational systems.
3.5.1 Draw and identify lines and angles
3.5.1 Draw and identify lines and angles
3.5.1.a: Draw and label points, lines, and line segments
3.5.1.a: Draw and label points, lines, and line segments
3.5.1.b: Identify angles using objects in the classroom (e.g., clock, scissors, chairs, desks)
3.5.1.b: Identify angles using objects in the classroom (e.g., clock, scissors, chairs, desks)
3.5.1.c: Draw angles and describe their differences
3.5.1.c: Draw angles and describe their differences
3.5.2 Identify and classify relationships among geometric shapes or objects with shared attributes
3.5.2 Identify and classify relationships among geometric shapes or objects with shared attributes
3.5.2.a: Describe how shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals)
Categories
Attributes
3.5.2.a: Describe how shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals)
Categories
Attributes
3.5.2.b: Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories
3.5.2.b: Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories
3.6 Students explore concepts and practical applications of units, geometrical constructions, and measurements of plane and geometric shapes and space.
3.6.1 Recognize and describe concept of area as an attribute of plane figures and use it for measurement
3.6.1 Recognize and describe concept of area as an attribute of plane figures and use it for measurement
3.6.1.a: Describe a unit square as a square with side length 1 unit to have one square unit of area
3.6.1.a: Describe a unit square as a square with side length 1 unit to have one square unit of area
3.6.1.b: (E) Define what an area of n square units is (i.e., a plane figure which can be covered without gaps or overlaps by n unit squares)
3.6.1.b: (E) Define what an area of n square units is (i.e., a plane figure which can be covered without gaps or overlaps by n unit squares)
3.6.1.c: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
3.6.1.c: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
3.6.1.d: Express the area of each part as a unit fraction of the whole (e.g., partition a shape into 4 parts with equal areas, and describe the area of each part as 1/4 of the area of the shape)
Show fractions
Identify fractions
3.6.1.d: Express the area of each part as a unit fraction of the whole (e.g., partition a shape into 4 parts with equal areas, and describe the area of each part as 1/4 of the area of the shape)
Show fractions
Identify fractions
3.6.2 Calculate the perimeter of polygons, area of geometric shapes (unit squares), and volume of geometric shapes (unit cubes) by relating area to the operations of multiplication and addition
3.6.2 Calculate the perimeter of polygons, area of geometric shapes (unit squares), and volume of geometric shapes (unit cubes) by relating area to the operations of multiplication and addition
3.6.2.a: Find the perimeter, given the side lengths; or, find an unknown side length and exhibit rectangles with the same perimeter and different areas, or with the same area and different perimeters
Perimeter
Unknown side
Relationship between area and perimeter
3.6.2.a: Find the perimeter, given the side lengths; or, find an unknown side length and exhibit rectangles with the same perimeter and different areas, or with the same area and different perimeters
Perimeter
Unknown side
Relationship between area and perimeter
3.6.2.b: Solve real-world and mathematical problems involving perimeters of polygons
3.6.2.b: Solve real-world and mathematical problems involving perimeters of polygons
3.6.2.c: 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
3.6.2.c: 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
3.6.2.d: Use tiling to show a concrete example that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c
3.6.2.d: Use tiling to show a concrete example that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c
3.6.2.e: Recognize area as additive, and find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, and apply this technique to solve real-world problems (e.g., tiles needed for the classroom floor or a countertop)
3.6.2.e: Recognize area as additive, and find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, and apply this technique to solve real-world problems (e.g., tiles needed for the classroom floor or a countertop)
3.6.3 Solve problems involving measurement and estimation of liquid volumes and masses of objects
3.6.3 Solve problems involving measurement and estimation of liquid volumes and masses of objects
3.6.3.a: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l)
3.6.3.a: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l)
3.6.3.b: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings to represent the problem, such as a beaker with a measurement scale)
3.6.3.b: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings to represent the problem, such as a beaker with a measurement scale)
3.6.4 Solve problems involving measurement and estimation of intervals of time
3.6.4 Solve problems involving measurement and estimation of intervals of time
3.6.4.a: Tell and write time to the nearest minute, in analog or digital
3.6.4.a: Tell and write time to the nearest minute, in analog or digital
3.6.4.b: Measure time intervals in minutes
3.6.4.b: Measure time intervals in minutes
3.6.4.c: Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram)
3.6.4.c: Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram)
7-8
Data Analysis, Statistics, and Probability
3.7 Students demonstrate statistical thinking and apply statistical methods to collect, organize, analyze, display, and make inferences based on data.
3.7.1 Generate, collect, organize, represent, and interpret a simple data set with several categories
3.7.1 Generate, collect, organize, represent, and interpret a simple data set with several categories
3.7.1.a: Create a survey (e.g., in a group or with a partner), and collect data
3.7.1.a: Create a survey (e.g., in a group or with a partner), and collect data
3.7.1.b: Present data using graphs (e.g., bar, pictograph), charts, and/or tables
3.7.1.b: Present data using graphs (e.g., bar, pictograph), charts, and/or tables
3.7.1.c: Generate data by measuring lengths using rulers marked with halves and fourths of an inch
3.7.1.c: Generate data by measuring lengths using rulers marked with halves and fourths of an inch
3.7.1.d: Display measured data by making a line plot, where the horizontal scale is marked off in appropriate units (whole numbers, halves, or quarters)
3.7.1.d: Display measured data by making a line plot, where the horizontal scale is marked off in appropriate units (whole numbers, halves, or quarters)
3.7.1.e: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories
3.7.1.e: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories
3.7.1.f: Solve one- and two-step "how many more" and "how many less" problems, using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent five items)
3.7.1.f: Solve one- and two-step "how many more" and "how many less" problems, using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent five items)
3.8 Students use concepts of chance and probability to explain outcomes of real-life situations.
3.8.1 Determine possible outcomes of simple experiments using charts and tables
3.8.1 Determine possible outcomes of simple experiments using charts and tables
3.8.1.a: Determine possible outcomes of a simple experiment
3.8.1.a: Determine possible outcomes of a simple experiment
3.8.1.b: Collect data through a simple experiment (e.g., tossing a coin), and organize data using tables, charts, and graphs or tree diagrams
3.8.1.b: Collect data through a simple experiment (e.g., tossing a coin), and organize data using tables, charts, and graphs or tree diagrams