Alaska State Standards for Mathematics: Grade 8

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

[8] N-1. Ordering real numbers (M1.3.1)

[8] N-2. Distinguishing between a whole number in scientific notation and real numbers in standard form (M1.3.1)

[8] N-3. Converting between expanded notation (multiples of ten with exponents ) and standard form (M1.3.3)

[8] N-4. Identifying, describing, or illustrating equivalent representations (M1.3.4. & M3.3.5)

[8] N-5. Expressing products of numbers using exponents (M1.3.1. & M1.3.3)

[8] N-6. [Using models, explanations, number lines, real-life situations, L] describing or illustrating the effects of arithmetic operations on rational numbers (percents) (M1.2.3)

[8] N-7. Using models, explanations, number lines, real-life situations, describing or illustrating the use of inverse operations (addition/subtraction or multiplication/division) (M1.2.3)

[8] N-8. Applying the rules for order of operations to rational numbers (M1.3.5)

[8] N-9. Identifying or writing the prime factorization of a number using exponents (M1.3.5)

[8] N-10. [Using distributive property with real numbers L] (M1.3.6)

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

[8] MEA-1. Converting measurements within the same system (English or metric) (M2.3.2)

[8] MEA-2. Using scale drawings involving indirect measurement (determining the scale factor and applying it to find missing dimension) (M2.3.4)

[8] MEA-3. [Modeling the conversion within the same system L] (M2.3.2)

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.

[8] E&C-1. Applying and assessing the appropriateness of a variety of estimation strategies (L) (M3.3.1)

[8] E&C-2. Adding, subtracting, multiplying or dividing integers or positive rational numbers (M3.3.3. & M3.3.4)

[8] E&C-3. Using percents and percentages (e.g., tax, discount) (M3.3.3. & M3.3.4)

[8] E&C-4. Converting between equivalent fractions, decimals, or percents (M3.3.5)

[8] E&C-5. Using ratio and proportion (M3.3.6)

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

[8] F&R-1. Describing or extending patterns (linear), up to the nth term, represented in, tables, sequences, graphs, or in problem situations (M4.3.1)

[8] F&R-2. Generalizing relationships (linear) using a table of ordered pairs, a graph, or an equation (M4.3.4)

[8] F&R-3. Describing in words how a change in one variable in a formula affects the remaining variables (how changing the length affects the area of quadrilaterals or volume of a rectangular prism ) (M4.3.2)

[8] F&R-4. Using a calculator as a tool when describing, extending, or representing patterns (L) (M4.3.3)

[8] F&R-5. Translating a written phrase to an algebraic expression (M4.3.5)

[8] F&R-6. Solving or identifying solutions to two-step linear equations of the form ax +/- b = c, where a, b and c are rational numbers, and a does not equal 0, translating a story problem into an equation of similar form, or translating a story problem into an equation of similar form and solving it (M4.3.5)

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

[8] G-1. Using the attributes and properties of regular polygons to sketch regular or irregular polygons (L) (M5.3.1)

[8] G-2. Using the attributes and properties of solid figures (vertices, length and alignment of edges, shape and number of bases) to identify and describe cylinders and cones (M5.3.2)

[8] G-3. Using two-dimensional nets to create three-dimensional objects (prisms and cylinders) (M5.3.2)

[8] G-4. Using proportionality to solve real-world problems involving similar shapes (e.g., two real-world objects casting shadows ) (M5.3.3)

[8] G-5. Identifying the results of applying transformations (translations, rotations, reflections, dilations) to figures on a coordinate plane (M5.3.5)

[8] G-6. Determining the volume of right triangular prisms or cylinders (M5.3.4)

[8] G-7. Determining the surface area of cylinders or triangular prisms (M5.3.4)

[8] G-8. Determining the circumference and area of a circle (M5.3.4)

[8] G-9. Graphing or identifying relationships of variables on a coordinate plane (e.g., length/width, area/diameter, cost/pound ) (M5.3.6)

[8] G-10. Drawing, measuring, or constructing geometric figures (polygons, perpendicular bisectors, or perpendicular or parallel lines) (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.

[8] S&P-1. [Designing, collecting L], organizing, displaying, or explaining the classification of data in real-world problems (e.g., science or humanities, peers or community), using histograms, scatter plots, or box and whisker plots with appropriate scale [or with technology L ] (M6.3.1)

[8] S&P-2. Using information from a variety of displays or analyzing the validity of statistical conclusions found in the media (M6.3.2)

[8] S&P-3. Determining or justifying a choice of range, mean, median, or mode as the best representation of data for a practical situation (M6.3.3)

[8] S&P-4. Determining or comparing the experimental and/or theoretical probability of simple events (M6.3.5)

[8] S&P-5. Using a systematic approach to finding sample spaces or to making predictions about the probability of independent events and using the information to solve real-world problems (M6.3.5)

[8] S&P-6. Designing and conducting a simulation to study a problem and communicate the results (L) (M6.3.6)

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

[8] PS-1. Selecting, modifying, and applying a variety of problem-solving strategies (e.g., inductive and deductive reasoning, Venn diagrams, making a simpler problem) and verifying the results (M7.3.2)

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

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

[8] PS-3. Representing mathematical problems numerically, graphically, and/or symbolically, translating among these alternative representations; or using appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions (M8.3.1, M8.3.2, & M8.3.3)

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

[8] PS-4. Generalizing from patterns of observations (inductive reasoning) about mathematical problems and testing using a logical verification (deductive reasoning); or justifying and defending the validity of mathematical strategies and solutions using examples and counterexamples (M9.3.1, M9.3.2, & M9.3.3)

AK.E.PS. Connections: Apply mathematical concepts and processes to situations within and outside of school.

[8] PS-5. Using real-world contexts such as science, humanities, peers, community, and careers (M10.3.1. & M10.4.2)

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.