American Samoa College and Career Ready Standards: Grade 6
Skills available for American Samoa sixth-grade math standards
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1-2
Number Sense, Properties, and Operations
6.1 Students investigate numbers, ways of representing numbers, relationships among numbers, and number systems.
6.1.1 Determine the ratio between two quantities, the unit rate a/b associated with a ratio a:b with b ? 0, and use rate language (with appropriate units) in the context of a ratio relationship
6.1.1 Determine the ratio between two quantities, the unit rate a/b associated with a ratio a:b with b ? 0, and use rate language (with appropriate units) in the context of a ratio relationship
6.1.1.a: Write ratios in their simplest form
6.1.1.a: Write ratios in their simplest form
6.1.1.b: Write ratios and rates, and find unit rates (e.g., "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar."; "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.")
Ratios
Rates
6.1.1.b: Write ratios and rates, and find unit rates (e.g., "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar."; "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.")
Ratios
Rates
6.1.1.c: Compare and order ratios (e.g., "The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every 2 wings there was 1 beak."; "For every vote candidate A received, candidate C received nearly three votes.")
6.1.1.c: Compare and order ratios (e.g., "The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every 2 wings there was 1 beak."; "For every vote candidate A received, candidate C received nearly three votes.")
6.1.2 Apply and extend previous understandings of numbers to the system of rational numbers
6.1.2 Apply and extend previous understandings of numbers to the system of rational numbers
6.1.2.a: Show examples where positive and negative numbers are used together to describe quantities having opposite directions or values
6.1.2.a: Show examples where positive and negative numbers are used together to describe quantities having opposite directions or values
6.1.2.b: Identify a rational number as a point on the number line, and then extend number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates
Rational numbers
Number lines
Coordinate plane
6.1.2.b: Identify a rational number as a point on the number line, and then extend number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates
Rational numbers
Number lines
Coordinate plane
6.2 Students perform mathematical operations and determine how they relate to one another.
6.2.1 Compute fluently with multidigit numbers, and find common factors and multiples
6.2.1 Compute fluently with multidigit numbers, and find common factors and multiples
6.2.1.a: Divide multidigit numbers fluently using the standard algorithm
6.2.1.a: Divide multidigit numbers fluently using the standard algorithm
6.2.1.b: Add, subtract, multiply, and divide multidigit decimals fluently using the standard algorithm for each operation
Addition and subtraction
Multiplication and division
Mixed operations
6.2.1.b: Add, subtract, multiply, and divide multidigit decimals fluently using the standard algorithm for each operation
Addition and subtraction
Multiplication and division
Mixed operations
6.2.1.c: Find the greatest common factor of two whole numbers less than or equal to 100, and the least common multiple of two whole numbers less than or equal to 12
6.2.1.c: Find the greatest common factor of two whole numbers less than or equal to 100, and the least common multiple of two whole numbers less than or equal to 12
6.2.1.d: Express (using the distributive property) a sum of two whole numbers 1?100 with a common factor as a multiple of a sum of two whole numbers with no common factor [e.g., express 36 + 8 as 4 (9 + 2)]
6.2.1.d: Express (using the distributive property) a sum of two whole numbers 1?100 with a common factor as a multiple of a sum of two whole numbers with no common factor [e.g., express 36 + 8 as 4 (9 + 2)]
6.2.2 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions
6.2.2 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions
6.2.2.a: Interpret and compute quotients of fractions (e.g., by using visual fraction models)
6.2.2.a: Interpret and compute quotients of fractions (e.g., by using visual fraction models)
6.2.2.b: Solve word problems involving division of fractions by fractions, using equations to represent the problems (e.g., create a story context for [2/3] ÷ [3/4] and use a visual fraction model to show the quotient)
6.2.2.b: Solve word problems involving division of fractions by fractions, using equations to represent the problems (e.g., create a story context for [2/3] ÷ [3/4] and use a visual fraction model to show the quotient)
6.2.2.c: Discuss the relation between multiplication and division of the general form (a/b) ÷ (c/d) = ad/bc (e.g., explain that [2/3] ÷ [3/4] = 8/9 because 3/4 of 8/9 is 2/3 such as, "How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?"; and "How many 3/4 cup servings are in 2/3 of a cup of yogurt?"; and "How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mile?")
6.2.2.c: Discuss the relation between multiplication and division of the general form (a/b) ÷ (c/d) = ad/bc (e.g., explain that [2/3] ÷ [3/4] = 8/9 because 3/4 of 8/9 is 2/3 such as, "How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?"; and "How many 3/4 cup servings are in 2/3 of a cup of yogurt?"; and "How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mile?")
6.2.3 Use ratio and rate reasoning to solve real-world and mathematical problems
6.2.3 Use ratio and rate reasoning to solve real-world and mathematical problems
6.2.3.a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, compare ratios using tables, and plot the pairs of values on the coordinate plane
Equivalent ratios
Ratio tables
Plot on the coordinate plane
Compare ratios
6.2.3.a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, compare ratios using tables, and plot the pairs of values on the coordinate plane
Equivalent ratios
Ratio tables
Plot on the coordinate plane
Compare ratios
6.2.3.b: Solve unit rate problems including those involving unit pricing and constant speed (e.g., if it takes 7 hours to mow 4 lawns, then, at that rate, "How many lawns can be mowed in 35 hours?"; and "At what rate are lawns being mowed?")
6.2.3.b: Solve unit rate problems including those involving unit pricing and constant speed (e.g., if it takes 7 hours to mow 4 lawns, then, at that rate, "How many lawns can be mowed in 35 hours?"; and "At what rate are lawns being mowed?")
6.2.3.c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity), and solve problems involving finding the whole, given a part and the percent
Represent percentages
Convert between percents, fractions, and decimals
Solve percent problems with models
Find a percent of a number
Find what percent one number is of another
Find the whole
Solve percent problems
6.2.3.c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity), and solve problems involving finding the whole, given a part and the percent
Represent percentages
Convert between percents, fractions, and decimals
Solve percent problems with models
Find a percent of a number
Find what percent one number is of another
Find the whole
Solve percent problems
6.2.3.d: Convert measurement units using ratio reasoning, and manipulate and transform units appropriately when multiplying or dividing quantities
6.2.3.d: Convert measurement units using ratio reasoning, and manipulate and transform units appropriately when multiplying or dividing quantities
3-4
Patterns, Algebra, and Functions
6.3 Students investigate patterns, functions and quantitative relationships and apply that knowledge to modeling, analyzing or solving mathematical and real-word problems.
6.3.1 Write, read, and evaluate expressions in which letters stand for numbers, and analyze tables, graphs, and rules to determine functional relationships
6.3.1 Write, read, and evaluate expressions in which letters stand for numbers, and analyze tables, graphs, and rules to determine functional relationships
6.3.1.a: Write and evaluate numerical expressions involving whole-number exponents
Write expressions
Evaluate expressions
6.3.1.a: Write and evaluate numerical expressions involving whole-number exponents
Write expressions
Evaluate expressions
6.3.1.b: Write expressions that record operations with numbers and with letters standing for numbers (e.g., express the calculation "Subtract y from 5" as 5 − y)
6.3.1.b: Write expressions that record operations with numbers and with letters standing for numbers (e.g., express the calculation "Subtract y from 5" as 5 − y)
6.3.1.c: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient), and view one or more parts of an expression as a single entity (e.g., describe the expression 2 [8 + 7] as a product of two factors and view [8 + 7] as both a single entity and a sum of two terms)
6.3.1.c: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient), and view one or more parts of an expression as a single entity (e.g., describe the expression 2 [8 + 7] as a product of two factors and view [8 + 7] as both a single entity and a sum of two terms)
6.3.1.d: Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems
Evaluate variable expressions
Real-world formulas
6.3.1.d: Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems
Evaluate variable expressions
Real-world formulas
6.3.1.e: Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order or order of operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2 unit)
6.3.1.e: Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order or order of operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2 unit)
6.3.1.f: (+) Analyze tables, graphs, and rules to determine functional relationships, and explain process
6.3.1.f: (+) Analyze tables, graphs, and rules to determine functional relationships, and explain process
6.3.1.g: Interpret data to write an equation for a function, and solve the equation to find missing values
Find values
Write equations
6.3.1.g: Interpret data to write an equation for a function, and solve the equation to find missing values
Find values
Write equations
6.3.1.h: Represent linear functions using ordered pairs and graphs
6.3.1.h: Represent linear functions using ordered pairs and graphs
6.4 Students use symbolic forms, operations, and properties to represent, model, solve, and analyze mathematical situations and structures.
6.4.1 Generate equivalent expressions using properties of operations, use variables to represent numbers, and write expressions when solving a real-world or mathematical problem
6.4.1 Generate equivalent expressions using properties of operations, use variables to represent numbers, and write expressions when solving a real-world or mathematical problem
6.4.1.a: Show or explain how a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set
6.4.1.a: Show or explain how a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set
6.4.1.b: Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 [2 + x] to produce the equivalent expression [6 + 3x])
6.4.1.b: Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 [2 + x] to produce the equivalent expression [6 + 3x])
6.4.1.c: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them)
6.4.1.c: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them)
6.4.2 Investigate reasoning behind solving an equation or inequality, and explain how inequality relates to familiar constraints and conditions in a real-world or mathematical problem
6.4.2 Investigate reasoning behind solving an equation or inequality, and explain how inequality relates to familiar constraints and conditions in a real-world or mathematical problem
6.4.2.a: Explore solving an equation or inequality as a process of answering a question, "Which values from a specified set, if any, make the equation or inequality true?"
6.4.2.a: Explore solving an equation or inequality as a process of answering a question, "Which values from a specified set, if any, make the equation or inequality true?"
6.4.2.b: Determine (using the substitution method ) whether a given number in a specified set makes an equation or inequality true
6.4.2.b: Determine (using the substitution method ) whether a given number in a specified set makes an equation or inequality true
6.4.2.c: Solve linear equations and inequalities in one variable with whole-number coefficients and constants with rational number solutions
6.4.2.c: Solve linear equations and inequalities in one variable with whole-number coefficients and constants with rational number solutions
6.4.2.d: Write and solve equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers
Models and diagrams
Real-world problems
6.4.2.d: Write and solve equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers
Models and diagrams
Real-world problems
6.4.2.e: Solve simple algebraic equations expressed in real-world and mathematical problems
6.4.2.e: Solve simple algebraic equations expressed in real-world and mathematical problems
6.4.2.f: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem; recognize that inequalities of the form x > c or x < c have infinitely many solutions; and represent solutions of such inequalities on number line diagrams
6.4.2.f: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem; recognize that inequalities of the form x > c or x < c have infinitely many solutions; and represent solutions of such inequalities on number line diagrams
5-6
Measurement, Geometry, and Spatial Sense
6.5 Students explore properties, relationships, and transformations of shapes and space using coordinate geometry and other representational systems.
6.5.1 Describe and compare regular or nonregular polygons, and find the angle measures of regular polygons
6.5.1 Describe and compare regular or nonregular polygons, and find the angle measures of regular polygons
6.5.1.a: Describe and compare the sides and angles of regular or irregular polygons
6.5.1.a: Describe and compare the sides and angles of regular or irregular polygons
6.5.1.b: Calculate the sum of interior angles in polygons (e.g., 180° in a triangle, and 360° in a quadrilateral)
6.5.1.b: Calculate the sum of interior angles in polygons (e.g., 180° in a triangle, and 360° in a quadrilateral)
6.5.2 Define properties of points, lines, parallel lines, and perpendicular lines, and introduce the basic concept of the Pythagorean theorem
6.5.2 Define properties of points, lines, parallel lines, and perpendicular lines, and introduce the basic concept of the Pythagorean theorem
6.5.2.a: Identify and classify properties of points, lines, segments, parallel lines, and perpendicular lines
6.5.2.a: Identify and classify properties of points, lines, segments, parallel lines, and perpendicular lines
6.5.2.b: Evaluate sums of square roots
6.5.2.b: Evaluate sums of square roots
6.5.2.c: Describe what a right triangle is
6.5.2.c: Describe what a right triangle is
6.5.2.d: (+) Illustrate relationship of the side-lengths of right triangles using sum of square areas
6.5.2.d: (+) Illustrate relationship of the side-lengths of right triangles using sum of square areas
6.5.2.e: (+) Infer the basic concept of the Pythagorean theorem
6.5.2.e: (+) Infer the basic concept of the Pythagorean theorem
6.5.3 Identify and analyze properties of, and relationships among, acute, right, and obtuse triangles
6.5.3 Identify and analyze properties of, and relationships among, acute, right, and obtuse triangles
6.5.3.a: Construct and compare triangles in different orientations, including scalene, isosceles, equilateral, right, obtuse, and acute triangles
6.5.3.a: Construct and compare triangles in different orientations, including scalene, isosceles, equilateral, right, obtuse, and acute triangles
6.5.3.b: Classify triangles by side lengths and angle measures
6.5.3.b: Classify triangles by side lengths and angle measures
6.5.3.c: Describe properties of and relationships among acute, right, and obtuse triangles
6.5.3.c: Describe properties of and relationships among acute, right, and obtuse triangles
6.5.3.d: Solve problems involving angles and side measures of triangles
6.5.3.d: Solve problems involving angles and side measures of triangles
6.6 Students explore concepts and practical applications of units, geometrical constructions, and measurements of plane and geometric shapes and space.
6.6.1 Describe measurable attributes of objects and the units, systems, and processes of measurement
6.6.1 Describe measurable attributes of objects and the units, systems, and processes of measurement
6.6.1.a: Demonstrate understanding of both metric and customary systems of measurement
6.6.1.a: Demonstrate understanding of both metric and customary systems of measurement
6.6.1.b: Convert units between simple metric and customary measurements
Customary units
Metric units
Customary and metric units
6.6.1.b: Convert units between simple metric and customary measurements
Customary units
Metric units
Customary and metric units
6.6.1.c: Select appropriate methods for estimating measurements
6.6.1.c: Select appropriate methods for estimating measurements
6.6.2 Use the coordinate plane to determine transformation and side-length of a polygon
6.6.2 Use the coordinate plane to determine transformation and side-length of a polygon
6.6.2.a: Draw polygons in the coordinate plane given the coordinates for the vertices
6.6.2.a: Draw polygons in the coordinate plane given the coordinates for the vertices
6.6.2.b: Find the length of a side joining the points with the same first or second coordinates in a coordinate plane
6.6.2.b: Find the length of a side joining the points with the same first or second coordinates in a coordinate plane
6.6.2.c: Apply coordinate techniques in the context of solving real-world and mathematical problems
6.6.2.c: Apply coordinate techniques in the context of solving real-world and mathematical problems
6.6.2.d: Perform a combination of translation(s), rotation(s), and/or reflection(s) on a single 2-D shape, with and without technology, and draw and describe the image
6.6.2.d: Perform a combination of translation(s), rotation(s), and/or reflection(s) on a single 2-D shape, with and without technology, and draw and describe the image
6.6.2.e: Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations
6.6.2.e: Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations
6.6.2.f: Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs
6.6.2.f: Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs
6.6.2.g: Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane
6.6.2.g: Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane
6.6.3 Use representations of real-world and mathematical problems to solve area, surface area, and volume problems
6.6.3 Use representations of real-world and mathematical problems to solve area, surface area, and volume problems
6.6.3.a: Develop and apply the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes
6.6.3.a: Develop and apply the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes
6.6.3.b: Apply techniques of composing and decomposing in the context of solving real-world and mathematical problems
Triangles
Quadrilaterals
Compound figures
6.6.3.b: Apply techniques of composing and decomposing in the context of solving real-world and mathematical problems
Triangles
Quadrilaterals
Compound figures
6.6.3.c: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths
6.6.3.c: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths
6.6.3.d: Represent 3-D figures using nets made up of rectangles and triangles, and find the surface area of these figures
6.6.3.d: Represent 3-D figures using nets made up of rectangles and triangles, and find the surface area of these figures
6.6.3.e: Apply the described techniques in the context of solving real-world and mathematical problems
6.6.3.e: Apply the described techniques in the context of solving real-world and mathematical problems
6.6.3.f: (+) Find the perimeter, area, surface area, and volume of a geometric shape using the appropriate formulas (e.g., develop and apply a formula for determining the perimeter of polygons, the area of rectangles, and the volume of right rectangular prisms)
Perimeter
Volume of prisms
Surface area of prisms
Relate volume and surface area
6.6.3.f: (+) Find the perimeter, area, surface area, and volume of a geometric shape using the appropriate formulas (e.g., develop and apply a formula for determining the perimeter of polygons, the area of rectangles, and the volume of right rectangular prisms)
Perimeter
Volume of prisms
Surface area of prisms
Relate volume and surface area
7-8
Data Analysis, Statistics, and Probability
6.7 Students demonstrate statistical thinking and apply statistical methods to collect, organize, analyze, display, and make inferences based on data.
6.7.1 Develop understanding of statistical variability
6.7.1 Develop understanding of statistical variability
6.7.1.a: (+) Identify a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers (e.g., "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages)
6.7.1.a: (+) Identify a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers (e.g., "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages)
6.7.1.b: Explain or show how a set of data collected to answer a statistical question has a distribution that can be described by its center, spread, and overall shape
Line plots
Box-and-whisker plots
6.7.1.b: Explain or show how a set of data collected to answer a statistical question has a distribution that can be described by its center, spread, and overall shape
Line plots
Box-and-whisker plots
6.7.1.c: Recognize that for a numerical data set a measure of center summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number
6.7.1.c: Recognize that for a numerical data set a measure of center summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number
6.7.2 Summarize numerical data sets in relation to their context
6.7.2 Summarize numerical data sets in relation to their context
6.7.2.a: Display numerical data in plots on a number line, including dot plots, histograms, and box plots
6.7.2.a: Display numerical data in plots on a number line, including dot plots, histograms, and box plots
6.7.2.b: Describe or determine quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered
Measures of center and variability
Outliers
6.7.2.b: Describe or determine quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered
Measures of center and variability
Outliers
6.7.2.c: Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered
6.7.2.c: Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered
6.8 Students use concepts of chance and probability to explain outcomes of real-life situations.
6.8.1 Use theoretical or experimental probability to explain the outcome of a situation in real life
6.8.1 Use theoretical or experimental probability to explain the outcome of a situation in real life
6.8.1.a: List, determine, and predict possible outcomes of a simple event or experiment
6.8.1.a: List, determine, and predict possible outcomes of a simple event or experiment
6.8.1.b: Explain the odds of a desired outcome using everyday examples and identify whether the outcome is certain, impossible, likely, or unlikely
6.8.1.b: Explain the odds of a desired outcome using everyday examples and identify whether the outcome is certain, impossible, likely, or unlikely