Alaska State Standards for Mathematics: Grade 10

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

[10] N-1. Identifying their subsets (natural, whole, integers, rational, irrational) (M1.4.1)

[10] N-2. Simplifying expressions with positive and negative exponents (M1.4.4. & M3.4.4)

[10] N-3. Expressing square roots in simplest radical form (M1.4.4. & M3.4.4)

[10] N-4. Describing or illustrating the effects of arithmetic operations on real numbers (M1.4.3)

[10] N-5. Describing or illustrating the use of inverse operations (cubing/cube root) (M1.4.3. & 1.4.5)

[10] N-6. Describing or illustrating [counting and adding in different bases L] (M1.4.2)

[10] N-7. Identifying or applying commutative, identity, associative, inverse, or distributive properties to real numbers and variables (M1.4.5)

[10] N-8. Identifying or writing the prime factorization of a variable expression using exponents (M1.4.4)

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

[10] MEA-1. Converting square and cubic units within the same system, English or metric, in real-world applications (M2.4.2)

[10] MEA-2. [Applying right triangle trigonometry (sine, cosine, and tangent) to find missing dimensions in real-world applications L] (M2.4.4)

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.

[10] E&C-1. Explaining why one strategy is more appropriate than another and determining why the estimation result is greater or less than the exact answer (L) (M3.4.1)

[10] E&C-2. Applying basic operations with real numbers using powers [and scientific notation L] (M3.4.2. & M3.4.3)

[10] E&C-3. Solving problems involving percent increase or decrease (M3.4.5)

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

[10] F&R-1. Describing or extending patterns (families of functions: linear, quadratic, absolute value), up to the nth term, represented in tables, sequences, graphs, or in problem situations (M4.4.1)

[10] F&R-2. Generalizing equations and inequalities (linear, quadratic, absolute value) using a table of ordered pairs or a graph (M4.4.4)

[10] F&R-3. Describing in words how a change in one variable or constant in an equation affects the outcome of the equation (M4.3.2)

[10] F&R-4. [Using a calculator as a tool when describing, extending, representing, or graphing patterns, linear or quadratic equations L] (M4.4.2)

[10] F&R-5. Modeling (graphically or algebraically) or solving situations using systems of linear equations or inequalities (including real-world applications) (M4.4.3)

[10] F&R-6. Selecting and using the quadratic formula to solve problems (M4.4.2)

[10] F&R-7. Solving or identifying solutions to literal equations or formulas for a variable involving multi-steps (e.g., solve for h when A = 1/2h(b1 + b2)) (M4.4.2)

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

[10] G-1. Identifying, analyzing, comparing, or using properties of plane figures:

[10] G-2. Using isometric drawings to create two-dimensional drawings of three-dimensional objects (shapes that are composites of rectangular right prisms) (L) (M5.4.2)

[10] G-3. Identifying congruent and similar figures using Euclidean geometry (e.g., [constructions L], coordinate geometry) (M5.4.3)

[10] G-4. Using transformations to show congruence or similarity of figures on a coordinate plane (M5.4.4)

[10] G-5. Determining the volume or surface area of spheres or compound solids (M5.3.4)

[10] G-6. Graphing a line segment on a coordinate grid and/or identifying its length or midpoint by using formulas (M5.4.5)

[10] G-7. Graphing a system of equations on a coordinate grid, identifying a solution, or determining their relationship (intersecting, parallel, perpendicular) (M5.4.5)

[10] G-8. Drawing, measuring, or constructing geometric models of plane figures (containing parallel and/or perpendicular lines, angles, perpendicular bisectors, congruent angles, regular polygons) (L) (M5.4.6)

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

[10] S&P-1. [Designing, collecting L], organizing, displaying, or explaining the classification of data in real-world problems (e.g., science or humanities, peers, community, or careers), using information from tables or graphs that display two or more sets of data [or with technology L] (M6.4.1)

[10] S&P-2. Using information from a display to solve a problem or analyzing the validity of statistical conclusions (M6.4.1. & M6.4.4)

[10] S&P-3. Using and justifying range and measures of central tendency to determine the best representation of the data for a practical situation (M6.4.3)

[10] S&P-4. Using a best fit line to describe trends and make predictions about data (M6.4.2)

[10] S&P-5. Explaining in words or identifying the difference between experimental and theoretical probability of independent or dependent events (M6.4.5)

[10] S&P-6. Analyzing data to make predictions about the probability of independent or dependent events as a basis for solving real-world problems (M6.4.5)

[10] S&P-7. Designing, conducting, analyzing, and communicating the results of a multi-stage probability experiment (L) (M6.4.6)

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

[10] PS-1. Applying multi-step, integrated, mathematical problem-solving strategies (M7.4.2)

[10] PS-2. Verifying the answer by using an alternative strategy (M7.4.3)

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

[10] PS-3. Representing mathematical problems numerically, graphically, and/or symbolically communicating math ideas in writing; or using appropriate vocabulary, symbols, or technology to explain, justify, and defend strategies and solutions (M8.4.1, M8.4.2, & M8.4.3)

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

[10] PS-4. Using methods of proof including direct, indirect, and counter examples to validate conjectures (M9.4.3)

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

[10] PS-5. Using real-world contexts such as global issues and careers (M10.4.1. & 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.

M1.4.1. Read, write, model, order, and define real numbers and subsets.

M1.4.2. Add in a different base system.

M1.4.3. Compare and contrast the relationship between various applications of the same operation.

M1.4.4. Translate between equivalent representations of the same exponential expression.

M1.4.5. Recognize, describe, and use properties of the real number system.

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.

M2.4.1. Evaluate measurements for accuracy, precision, and error with respect to the measuring tools, methods, and the computational process.

M2.4.2. Estimate and convert measurements between different systems.

M2.4.3. Apply various measurement systems to describe situations and solve problems.

M2.4.4. Use indirect methods, including the Pythagorean Theorem and right triangle trigonometry, to find missing dimensions.

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.

M3.4.1. Use estimation to solve problems and to check the accuracy of solutions; state whether the estimation is greater or less than the exact answer.

M3.4.2. Add and subtract real numbers using scientific notation, powers, and roots.

M3.4.3. Multiply and divide real numbers in various forms including scientific notation, powers, and roots.

M3.4.4. Select, convert, and apply an equivalent representation of a number for a specified situation.

M3.4.5. Use ratios and proportions to model and solve fraction and percent problems with variables.

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.

M4.4.1. Identify, graph, and describe the graphs of basic families of functions including linear, absolute value, quadratic, and exponential using a graphing calculator.

M4.4.2. Create and solve linear and quadratic equations and inequalities.

M4.4.3. Create and solve simple systems of equations, algebraically and graphically, using a graphing calculator.

M4.4.4. Use discrete structures, such as networks, matrices, sequences, and iterations, as tools to analyze patterns, expressions, and equations.

M4.4.5. Add, subtract, multiply, divide, and simplify rational expressions; add, subtract, and multiply polynomials.

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.

M5.4.1. Identify and use the properties of polygons, including interior and exterior angles, and circles (including angles, arcs, chord, secants, and tangents) to solve problems.

M5.4.2. Create 2-dimensional representations of 3-dimensional objects.

M5.4.3. Identify congruent and similar figures using Euclidean and coordinate geometries; apply this information to solve problems.

M5.4.4. Use transformations to demonstrate geometric properties.

M5.4.5. Use coordinate geometry to graph linear equations, determine slopes of lines, identify parallel and perpendicular lines, and to find possible solutions to sets of equations.

M5.4.6. Construct geometric models, transformations, and scale drawings using a variety of methods including paper folding, compass, straight edge, protractor, and technology.

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.

M6.4.1. Analyze and draw inferences from a wide variety of data sources that summarize data; construct graphical displays with and without technology.

M6.4.2. Determine the line of best fit and use it to predict unknown data values.

M6.4.3. Describe data, selecting measures of central tendencies and distribution, to convey information in the data.

M6.4.4. Analyze the validity of statistical conclusions and the use, misuse, and abuse of data caused by a wide variety of factors including choices of scale, inappropriate choices of measures of center, incorrect curve fitting, and inappropriate uses of controls or sample groups.

M6.4.5. Analyze data from multiple events and predict theoretical probability; find and compare experimental and theoretical probability for a simple situation, discussing possible differences between two results.

M6.4.6. Design, conduct, analyze, and communicate the results of multi-stage probability experiments.

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.

M7.4.1. Recognize and formulate mathematical problems from within and outside the field of mathematics.

M7.4.2. Apply multi-step, integrated, mathematical problem-solving strategies, persisting until a solution is found or it is clear no solution exits.

M7.4.3. Verify the answer by using an alternative strategy.

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.

M8.4.1. Use appropriate technology to represent the information and ideas in a problem.

M8.4.2. Use numerical, graphic, and symbolic representations to support oral and written communication about math ideas.

M8.4.3. Explain, justify, and defend mathematical ideas, solutions, and methods to various audiences.

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.

M9.4.1. Follow and evaluate an argument, judging its validity using inductive or deductive reasoning and logic.

M9.4.2. Make and test conjectures.

M9.4.3. Use methods of proofs including direct, indirect, and counterexamples, to validate conjectures.

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.

M10.4.1. Apply mathematical skills and processes to global issues.

M10.4.2. Describe how mathematics can be used in knowing how to prepare for careers.