Mathematics Curriculum

The mathematics standards prepare Alaska students to be competitive on the national and world stage. These standards are a set of specific, rigorous expectations that build students’ conceptual understanding, mathematical language, and application of processes and procedures coherently from one grade level to the next so all students will be prepared for postsecondary experiences. The focus areas for each grade level and each conceptual category narrative establish a depth of knowledge as opposed to a breadth of knowledge across multiple standards in each grade level or content area. The standards stress both conceptual understanding and procedural skills to ensure students learn and can apply the critical information needed to succeed at each level.
Grade Level Overview

Kindergarten  Grade 5
Kindergarten
Counting and Cardinality
 Know number names and the count sequence.
 Count to tell the number of objects.
 Compare numbers.
Operations and Algebraic Thinking
 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
 Identify and continue patterns.
Number and Operations in Base Ten
 Work with numbers 1119 to gain foundations for place value.
Measurement and Data
 Describe and compare measurable attributes.
 Classify objects and count the number of objects in categories.
 Work with time and money.
Geometry
 Identify and describe shapes.
 Analyze, compare, create, and compose shapes.
Grade 1
Counting and Cardinality
 Know ordinal names and counting flexibility.
 Count to tell the number of objects.
 Compare numbers.
Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction.
 Understand and apply properties of operations and the relationship between addition and subtraction.
 Add and subtract up to 20.
 Work with addition and subtraction equations.
 Identify and continue patterns
Number and Operations in Base Ten Extend the counting sequence.
 Understand place value.
 Use place value understanding and properties of operations to add and subtract.
Measurement and Data Measure lengths indirectly and by iterating length units.
 Work with time and money.
 Represent and interpret data.
Geometry
 Reason with shapes and their attributes.
Grade 2
Operations and Algebraic Thinking
 Represent and solve problems involving addition and subtraction.
 Add and subtract up to 20.
 Work with equal groups of objects to gain foundations for multiplication.
 Identify and continue patterns.
Number and Operations in Base Ten Understand place value.
 Use place value understanding and properties of operations to add and subtract.
Measurement and Data
 Measure and estimate lengths in standard units.
 Relate addition and subtraction to length.
 Work with time and money.
 Represent and interpret data.
Geometry
 Reason with shapes and their attributes.
Grade 3
Operations and Algebraic Thinking
 Represent and solve problems involving multiplication and division.
 Understand properties of multiplication and the relationship between multiplication and division.
 Multiply and divide up to 100.
 Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Number and Operations in Base Ten Use place value understanding and properties of operations to perform multidigit arithmetic.
Number and Operations  Fractions
 Develop understanding of fractions as numbers.
Measurement and Data
 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
 Represent and interpret data.
 Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Geometry
 Reason with shapes and their attributes.
Grade 4
Operations and Algebraic Thinking
 Use the four operations with whole numbers to solve problems.
 Gain familiarity with factors and multiples.
 Generate and analyze patterns.
Number and Operations in Base Ten
 Generalize place value understanding for multidigit whole numbers.
 Use place value understanding and properties of operation to perform multidigit arithmetic.
Number and OperationsFractions
 Extending of fraction equivalence and ordering.
 Build fractions from unit fractions by applying and extending previous understands of operation on whole numbers.
 Understand decimal notation for fractions, and compare decimal fractions.
Measurement and Data
 Solve problems involving measurement and conversions of measurements from larger unit to a smaller unit and involving time.
 Represent and interpret data.
 Geometric measurement: understand concepts of angle and measure angles.
Geometry
 Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Grade 5
Operations and Algebraic Thinking
 Write and interpret numerical expressions.
 Analyze patterns and relationships.
Number and Operations in Base Ten
 Understand the place value system.
 Perform operations with multidigit whole numbers and with decimals to hundredths.
Number and OperationsFractions
 Use equivalent fractions as a strategy to add and subtract fractions.
 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
 Convert like measurement units within a given measurement system and solve problems involving time.
 Represent and interpret data.
 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Geometry
 Graph points on the coordinate plane to solve realworld and mathematical problems.
 Classify twodimensional figures into categories based on their properties.

Grades 68
Grade 6
Ratios and Proportional Relationships
 Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
 Compute fluently with multidigit numbers and find common factors and multiples.
 Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
 Apply and extend previous understanding of arithmetic to algebraic expressions.
 Reason about and solve onevariable equations and inequalities.
 Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
 Solve realworld and mathematical problems involving area, surface area, and volume.
Statistics and Probability
 Develop understanding of statistical variability.
 Summarize and describe distributions.
Grade 7
Ratios and Proportional Relationships
 Analyze proportional relationships and use them to solve realworld and mathematical problems.
The Number System
 Apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations
 Use properties of operations to generate equivalent expressions.
 Solve reallife and mathematical problems using numerical and algebraic expressions and equations.
Geometry
 Draw, construct and describe geometrical figures and describe the relationships between them.
 Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability
 Use random sampling to draw inferences about a population.
 Draw informal comparative inferences about two populations.
 Investigate chance and develop, use, and evaluate probability models
Grade 8
The Number System
 Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
 Work with radicals and integer exponents.
 Understand the connections between proportional relationships, lines, and linear equations.
Functions
 Define, evaluate, and compare functions.
 Use functions to model relationships between quantities.
Geometry
 Understand congruence and similarity using physical models, transparencies, or geometry software.
 Understand and apply the Pythagorean Theorem.
 Solve realworld and mathematical problems involving volume of cylinders, cones and spheres.
Statistics and Probability
 Investigate patterns of association in bivariate data.

Grades 912
Courses
 Algebra I
 Algebra II
 Geometry
 PreCalculus
 AP Calculus
 AP Statistics
Modeling
Modeling links classroom mathematics and statistics to everyday life, work, and decisionmaking. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions.
Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Specific modeling standards appear throughout the high school standards indicated by an asterisk (*).
If the asterisk appears on the heading for a group of standards, it should be understood to apply to all standards in that group. There are other individual standards under clusters, domains and conceptual categories that have connections to modeling.
Additionally, model with mathematics is a Standard for Mathematical Practice. This practice will be started in kindergarten.
Number and Quantity
The Real Number System
 Extend the properties of exponents to rational exponents.
 Use properties of rational and irrational numbers.
Quantities Reason quantitatively and use units to solve problems.
The Complex Number System
 Perform arithmetic operations with complex numbers.
 Represent complex numbers and their operations on the complex plane. +
 Use complex numbers in polynomial identities and equations.
Vector and Matrix Quantities
 Represent and model with vector quantities.
 Perform operations on vectors.
 Perform operations on matrices and use matrices in applications.
Algebra
Seeing Structure in Expressions
 Interpret the structure of expressions.
 Write expressions in equivalent forms to solve problems.
Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomials.
 Understand the relationship between zeros and factors of polynomials.
 Use polynomial identities to solve problems.
 Rewrite rational expressions.
Creating Equations and Inequalities
 Create equations and inequalities that describe numbers or relationships.
Reasoning with Equations and Inequalities
 Understand solving equations as a process of reasoning and explain the reasoning.
 Solve equations and inequalities in one variable.
 Solve systems of equations.
 Represent and solve equations and inequalities graphically.
Functions
Interpreting Functions
 Understand the concept of a function and use function notation.
 Interpret functions that arise in applications in terms of the context.
 Analyze functions using different representations.
Building Functions Build a function that models a relationship between two quantities.
 Build new functions from existing functions.
Linear, Quadratic, and Exponential Models
 Construct and compare linear, quadratic, and exponential models and solve problems.
 Interpret expressions for functions in terms of the situation they model.
Trigonometric Functions Extend the domain of trigonometric functions using the unit circle.
 Model periodic phenomena with trigonometric functions.
 Prove and apply trigonometric identities.
Geometry
Congruence
 Experiment with transformations in the plane.
 Understand congruence in terms of rigid motions.
 Prove geometric theorems.
 Make geometric constructions.
Similarity, Right Triangles, and Trigonometry
 Understand similarity in terms of similarity transformations.
 Prove theorems involving similarity.
 Define trigonometric ratios and solve problems involving right triangles.
 Apply trigonometry to general triangles.
Circles Understand and apply theorems about circles.
 Find arc lengths and areas of sectors of circles.
Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section.
 Use coordinates to prove simple geometric theorems algebraically.
Geometric Measurement and Dimension Explain volume formulas and use them to solve problems.
 Visualize relationships between twodimensional and threedimensional objects.
Modeling with Geometry
 Apply geometric concepts in modeling situations.
Statistics and Probability
Interpreting Categorical and Quantitative Data
 Summarize, represent, and interpret data on a single count or measurement variable.
 Summarize, represent, and interpret data on two categorical and quantitative variables.
 Interpret linear models.
Making Inferences and Justifying Conclusions
 Understand and evaluate random processes underlying statistical experiments.
 Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data.
 Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Using Probability to Make Decisions Calculate expected values and use them to solve problems.
 Use probability to evaluate outcomes of decisions.