Alaska State Standards for Mathematics: Grade 6

AK.A.N. Mathematical facts, concepts, principles, and theories: Numeration: Understand and use numeration.

[6] N-1. Reading, writing, ordering, or [counting L] (M1.2.1)

[6] N-2. Identifying place value positions from thousandths to millions (L) (M1.2.2)

[6] N-3. Converting between whole numbers written in expanded notation and standard form (M1.2.4)

[6] N-4. [Modeling L], identifying, describing, or illustrating equal parts of a whole, a region, or a set (M1.2.4)

[6] N-5. [Modeling L], identifying, describing, or illustrating equivalent fractions or mixed numbers (M1.2.4. & M3.2.5)

[6] N-6. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the relationships among the four basic operations (M1.2.3)

[6] N-7. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the process of adding and subtracting fractions with different denominators (M1.2.5)

[6] N-8. Describing or illustrating commutative, [associative, inverse L] or identity properties of addition or multiplication using models or explanations (M1.2.7)

[6] N-9. Identifying or describing factors and multiples common to a pair or set of numbers (e.g., Least Common Multiple, L.C.M., or Greatest Common Factor, G.C.F.) (M1.2.6)

[6] N-10. Modeling (base 10 blocks) distributive property (L) (M1.3.6)

AK.A.M. Mathematical facts, concepts, principles, and theories: Measurement: Select and use systems, units, and tools of measurement.

[6] MEA-1. Estimating length to the nearest eighth-inch or millimeter (L) (M2.2.1)

[6] MEA-2. Identifying equivalent measures within systems

[6] MEA-3. Using a scaled ruler to an eighth of an inch or millimeter on a map or drawing (M2.2.1. & M2.2.3)

[6] MEA-4. Calculating elapsed time (minutes, hours) (M2.2.5)

[6] MEA-5. Solving real-world problems involving elapsed time between U.S. time zones (including Alaska Standard time) (M2.2.5)

[6] MEA-6. Converting and using equivalent measurements within the same system (M2.2.2)

[6] MEA-7. Measuring length to the nearest 1/8 of an inch or nearest millimeter (M2.2.1)

AK.A.E. Mathematical facts, concepts, principles, and theories: Estimation and Computation: Perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools.

[6] E&C-1. Identifying or using [a variety of L] strategies (e.g., truncating, rounding to compatible numbers) to estimate the results of addition, subtraction or multiplication from thousandths to millions or simple division (M3.2.1)

[6] E&C-2. Recalling basic addition, subtraction, multiplication, and division facts efficiently (L) (M3.2.2)

[6] E&C-3. Adding or subtracting whole numbers, fractions with unlike denominators to 12, or decimals to the hundredths place (M3.2.3)

[6] E&C-4. Multiplying whole numbers by two- or three-digit numbers, dividing three-digit numbers by one or two-digit numbers, or multiplying or dividing decimals that represent money by whole numbers, or multiplying or dividing proper fractions (M3.2.4)

[6] E&C-5. Developing or interpreting scale models (scale factors such as 1 in. = 1 ft.) (L) (M3.2.6)

AK.A.F. Mathematical facts, concepts, principles, and theories: Functions and Relationships: Represent, analyze, and use patterns, relations, and functions.

[6] F&R-1. Extending patterns (found in the number system, formed by multiples, factors, perfect squares up to 100, powers of ten), up to 10 terms, represented in tables, sequences, or in problem situations (M4.2.1)

[6] F&R-2. Using rules to express the generalization of a pattern using words, lists, or tables, with or without variables (M4.2.4)

[6] F&R-3. Identifying or applying multiplication or division patterns to find missing values in a function (M4.2.2)

[6] F&R-4. Using manipulatives, including a calculator, as tools when describing, extending, or representing a number sequence (L) (M4.2.1. & M 4.2.3)

[6] F&R-5. Solving for an unknown represented by a letter, (addition, subtraction, multiplication, or division) (e.g., 3 x n = 15, n - 5 = 12) (M4.2.5)

AK.A.G. Mathematical facts, concepts, principles, and theories: Geometry: Construct, transform, and analyze geometric figures.

[6] G-1. Using the attributes and properties (sides and angles) of regular polygons to identify, classify, or compare regular or irregular polygons (M5.2.1)

[6] G-2. Identifying, comparing or describing attributes and properties of circles (radius, and diameter) (M5.2.2)

[6] G-3. Using the attributes and properties of prisms (vertices, length and alignment of edges, shape and number of bases, shape of faces) to [model L], identify, compare, or describe triangular or rectangular prisms (M5.2.2)

[6] G-4. Identifying a 3-dimensional shape from the 2-dimensional drawing of the shape (M5.2.2)

[6] G-5. Identifying, creating, or drawing geometric figures that are congruent, similar, or symmetrical (M5.2.3)

[6] G-6. [Drawing or describing the results of transformations of polygons such as slides, turns, or flips L] (M5.2.5)

[6] G-7. Estimating or determining area or perimeter of polygons (parallelograms, trapezoids, triangles) using a key, ruler, or given measures (M5.2.4)

[6] G-8. [Estimating the area and circumference of a circle using a grid or manipulatives and comparing the relationship of the diameter to the circumference L] (M5.2.4. & M5.3.4)

[6] G-9. [Estimating or determining the volume of a right rectangular prism using manipulatives and formulas (e.g., cereal box, sand box, planter) L] (M5.3.4)

[6] G-10. Graphing a vertical or horizontal line segment (given whole number coordinates for its end points) on a coordinate grid and/or identifying its length or midpoint (e.g., using a map to trace a route and calculate distance) (M5.2.6. & M5.2.7)

[6] G-11. Drawing or measuring quadrilaterals with given dimensions or angles (L) (M5.3.7)

AK.A.S. Mathematical facts, concepts, principles, and theories: Statistics and Probability: Formulate questions, gather and interpret data, and make predictions.

[6] S&P-1. [Designing an investigation and collecting L], organizing, or displaying, using appropriate scale for data displays (tables, bar graphs, line graphs, or circle graphs), data in real-world problems (e.g., social studies, friends, or school), with whole numbers up to 100 (M6.2.1. & M6.2.2)

[6] S&P-2. Using information from a variety of displays (tables, bar graphs, line graphs, circle graphs, or Venn diagrams) (M6.2.2)

[6] S&P-3. Using mean, median, mode, or range (M6.2.3)

[6] S&P-4. [Analyzing whether a game is mathematically fair or unfair by explaining the probability of all possible outcomes L] (M6.2.4)

[6] S&P-5. Solving or identifying solutions to problems involving possible combinations (e.g., if ice cream sundaes come in 3 flavors with 2 possible toppings, how many different sundaes can be made using only one flavor of ice cream with one topping?) (M6.2.5)

AK.B.PS. Problem Solving: Problem Solving: Understand and be able to select and use a variety of problem-solving strategies.

[6] PS-1. Selecting, modifying, and applying appropriate problem solving strategies (e.g., graphing, Venn diagrams, tables, lists, working backwards, guess and check, or extend a pattern) and verifying results (M7.3.2)

[6] PS-2. Evaluating and interpreting solutions to problems (M7.3.3)

AK.C.PS. Communication: Form and use appropriate methods to define and explain mathematical relationships.

[6] PS-3. Representing problems using mathematical language including concrete, pictorial, and/or symbolic representation; or using appropriate vocabulary, symbols, and technology to explain mathematical solutions (M8.2.1, M8.2.2, & M8.2.3)

AK.D.PS. Reasoning: Use logic and reason to solve mathematical problems.

[6] PS-4. Using informal deductive reasoning in concrete contexts; or justifying answers and mathematical strategies using examples (M9.3.1. & M9.3.3)

AK.E.PS. Connections: Apply mathematical concepts and processes to situations within and outside of school (M10.2.1, M10.2.2)

[6] PS-5. Using real-world contexts such as social studies, friends, school and community (M10.2.1, M10.2.2, & M10.3.2)

AK.M1. Numeration: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should understand and use numeration, including numbers, number systems, counting numbers, whole numbers, integers, fractions, decimals, and percents; and irrationals and complex numbers.

M1.3.1. Read, write, model, and order real numbers, explaining scientific notation, exponents, and percents.

M1.3.2. Model counting in a different base system.

M1.3.3. Translate between equivalent representations of the same number. Select a representation that is appropriate for the situation.

M1.3.4. Describe and model the relationship of fractions to decimals, percents, ratios, and proportions.

M1.3.5. Use, explain, and define the rules of divisibility, prime and composite numbers, multiples, and order of operations.

M1.3.6. Use commutative, identity, associative, and distributive properties with variables.

AK.M2. Measurement: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should select and use appropriate systems, units, and tools of measurement, including estimation.

M2.3.1. Estimate and measure various dimensions to a specified degree of accuracy.

M2.3.2. Estimate and convert measurements within the same system.

M2.3.3. Use a variety of methods and tools to construct and compare plane figures.

M2.3.4. Describe and apply the relationships between dimensions of geometric figures to solve problems using indirect measurement; describe and apply the concepts of rate and scale.

M2.3.5. Apply information about time zones and elapsed time to solve problems.

AK.M3. Estimation and Computation: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, a calculator, and a computer.

M3.3.1. Apply, explain, and assess the appropriateness of a variety of estimation strategies including truncating and rounding to compatible numbers.

M3.3.2. Apply basic operations efficiently and accurately, using estimation to check the reasonableness of results.

M3.3.3. Add and subtract fractions, decimals, and percents.

M3.3.4. Multiply and divide rational numbers in various forms including fractions, decimals, and percents.

M3.3.5. Convert between equivalent fractions, decimals, percents, and proportions. Convert from exact to decimal representations of irrational numbers.

M3.3.6. Solve problems using ratios and proportions.

AK.M4. Functions and Relationships: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should represent, analyze, and use mathematical patterns, relations, and functions using methods such as tables, equations, and graphs.

M4.3.1. Identify numeric and geometric patterns to find the next term and predict the nth term.

M4.3.2. Identify and describe how a change in one variable in a function affects the remaining variables (e.g., how changing the length affects the area and volume of a rectangular prism).

M4.3.3. Use a calculator to find a missing item in an arithmetic and a geometric sequence; predict the graph of each function.

M4.3.4. Translate among and use tables of ordered pairs, graphs on coordinate planes, and linear equations as tools to represent and analyze patterns.

M4.3.5. Find the value of a variable by evaluating formulas and algebraic expressions for given values.

AK.M5. Geometry: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should construct, draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures.

M5.3.1. Identify, classify, compare, and sketch regular and irregular polygons.

M5.3.2. Model, identify, draw, and describe 3-dimensional figures including tetrahedrons, dodecahedrons, triangular prisms, and rectangular prisms.

M5.3.3. Apply the properties of equality and proportionality to solve problems involving congruent or similar shapes.

M5.3.4. Estimate and determine volume and surface areas of solid figures using manipulatives and formulas; estimate and find circumferences and areas of circles.

M5.3.5. Draw and describe the results of transformations including translations (slides), rotations (turns), reflections (flips), and dilations (shrinking or enlarging).

M5.3.6. Use coordinate geometry to represent and interpret relationships defined by equations and formulas including distance and midpoint.

M5.3.7. Draw, measure, and construct geometric figures including perpendicular bisectors, polygons with given dimensions and angles, circles with given dimensions, perpendicular and parallel lines.

AK.M6. Statistics/Probability: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should collect, organize, analyze, interpret, represent, and formulate questions about data and make reasonable and useful predictions about the certainty, uncertainty, or impossibility of an event.

M6.3.1. Collect, analyze, and display data in a variety of visual displays including frequency distributions, circle graphs, box and whisker plots, stem and leaf plots, histograms, and scatter plots with and without technology.

M6.3.2. Interpret and analyze information found in newspapers, magazines, and graphical displays.

M6.3.3. Determine and justify a choice of mean, median, or mode as the best representation of data for a practical situation.

M6.3.4. Make projections based on available data and evaluate whether or not inferences can be made given the parameters of the data.

M6.3.5. Use tree diagrams and sample spaces to make predictions about independent events.

M6.3.6. Design and conduct a simulation to study a problem and communicate the results.

AK.M7. Problem-Solving: A student should understand and be able to select and use a variety of problem-solving strategies. A student who meets the content standard should use computational methods and appropriate technology as problem-solving tools; use problem solving to investigate and understand mathematical content; formulate mathematical problems that arise from everyday situations; develop and apply strategies to solve a variety of problems; check the results against mathematical rules; use common sense to help interpret results; apply what was learned to new situations; and use mathematics with confidence.

M7.3.1. Analyze and summarize a problem using the relationships between the known facts and unknown information.

M7.3.2. Select, modify, and apply a variety of problem-solving strategies including graphing, inductive and deductive reasoning, Venn diagrams, and spreadsheets.

M7.3.3. Evaluate, interpret, and justify solutions to problems.

AK.M8. Communication: A student should understand and be able to form and use appropriate methods to define and explain mathematical relationships. A student who meets the content standard should express and represent mathematical ideas using oral and written presentations, physical materials, pictures, graphs, charts, and algebraic expressions; relate mathematical terms to everyday language; develop, test, and defend mathematical hypotheses; and clarify mathematical ideas through discussion with others.

M8.3.1. Use math vocabulary, symbols, and notation to represent information in the problem.

M8.3.2. Represent a problem numerically, graphically, and symbolically; translate among these alternative representations.

M8.3.3. Use appropriate vocabulary, symbols, and technology to explain, justify, and defend mathematical solutions.

AK.M9. Reasoning: A student should be able to use logic and reason to solve mathematical problems. A student who meets the content standard should analyze situations; draw logical conclusions; use models, known facts, and relationships to explain the student's reasoning; use deductive reasoning to verify conclusions, judge the validity of arguments, and construct valid arguments; and use inductive reasoning to recognize patterns and form mathematical propositions.

M9.3.1. Use informal deductive and inductive reasoning in both concrete and abstract contexts.

M9.3.2. State counterexamples to disprove statements.

M9.3.3. Justify and defend the validity of mathematical strategies and solutions using examples and counterexamples.

AK.M10. Connections: A student should be able to apply mathematical concepts and processes to situations within and outside of school. A student who meets the content standard should explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations; use mathematics in daily life; and use mathematics in other curriculum areas.

M10.3.1. Apply mathematical skills and processes to science and humanities.

M10.3.2. Apply mathematical skills and processes to situations with peers and community.