### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### Mathematical Processes

Standard 1 — Mathematical Processes

Conceptual StrandThe Mathematical Process Standards are embedded in the content standards to reap the learning benefits gained from attention to them. These standards exemplify best teaching practices in mathematical instruction and mirror the NCTM Process Standards as well as the Common Core Mathematical Practices.Guiding QuestionWhat is the role of the mathematical processes standards in formative instruction?

Use mathematical language, symbols, and definitions while developing mathematical reasoning.
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and
State Performance Indicator
Solve problems using a calendar.

Solve problems involving elapsed time.
Determine the correct change from a transaction less than a dollar.

Match the spoken, written, concrete, and pictorial representations of fractions with denominators up to ten.
Represent problems mathematically using diagrams, numbers, and symbolic expressions.
Identify and use vocabulary to describe attributes of two- and three-dimensional shapes.

Select appropriate units and tools to solve problems involving measures.

Express answers clearly in verbal, numerical, or graphical (bar and picture) form, using units when appropriate.

### Number and Operations

Standard 2 — Number and Operations

Conceptual StrandThe Number and Operations Standard describes deep and fundamental understanding of, and proficiency with, counting, numbers, and arithmetic, as well as an understanding of number systems and their structures.Guiding QuestionHow do students develop number sense that allows them to naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results?

Understand the place value of whole numbers to ten-thousands place including expanded notation for all arithmetic operations.
Develop understanding of multiplication and related division facts through multiple strategies and representations.
Relate multiplication and division as inverse operations.
Solve multiplication and division problems using various representations.
Understand the meaning and uses of fractions.
Use various strategies and models to compare and order fractions and identify equivalent fractions.
Add and subtract fractions with like denominators using various models.
State Performance Indicator
Read and write numbers up to 10,000 in numerals and up to 1,000 in words.

Identify the place value of numbers in the ten-thousands, thousands, hundreds, tens, and ones positions.
Convert between expanded and standard form with whole numbers to 10,000.

Compare and order numbers up to 10,000 using the words less than, greater than, and equal to, and the symbols , =.

Identify various representations of multiplication and division.
Recall basic multiplication facts through 10 times10 and the related division facts.
Compute multiplication problems that involve multiples of ten using basic number facts.
Solve problems that involve the inverse relationship between multiplication and division.
Solve contextual problems involving the addition (with and without regrouping) and subtraction (with and without regrouping) of two- and three digit whole numbers.
Identify equivalent fractions given by various representations.
Recognize and use different interpretations of fractions.
Name fractions in various contexts that are less than, equal to, or greater than one.
Recognize, compare, and order fractions (benchmark fractions, common numerators, or common denominators).
Add and subtract fractions with like denominators.

### Algebra

Standard 3 — Algebra

Conceptual StrandThe Algebra Standard emphasizes relationships among quantities, including functions, patterns, ways of representing mathematical relationships, and the analysis of change.Guiding QuestionHow does algebra encompass the relationships among quantities, the use of symbols, the modeling of phenomena, and the mathematical study of change?

Develop meaning for and apply the commutative, associative, and distributive properties using various representations.
Develop understanding that a letter or a symbol can represent an unknown quantity in a simple mathematical expression/equation.
Describe and analyze patterns and relationships in contexts.
Create and represent patterns using words, tables, graphs, and symbols.

State Performance Indicator
Verify a conclusion using algebraic properties.

Express mathematical relationships using number sentences/equations.
Find the missing values in simple multiplication and division equations.
Describe or extend (including finding missing terms) geometric and numeric patterns.

### Geometry and Measurement

Standard 4 — Geometry and Measurement

Conceptual StrandGeometry studies geometric shapes and structures and their characteristics and relationships. Understanding what a measurable attribute is and becoming familiar with the units and processes that are used in measuring attributes are the major emphasis of this standard.Guiding QuestionHow can students make and explore conjectures about geometry and reason carefully about geometric ideas while expanding their understanding of precision in measurement?

Describe, compare, and analyze properties of polygons.
Understand and apply the concepts of congruence and symmetry.
Understand and use attributes of 2- and 3-dimensional figures to solve problems.
Use appropriate units, strategies and tools to solve problems involving perimeter.
Solve measurement problems involving fractional parts of linear units and capacity units.
State Performance Indicator
Recognize polygons and be able to identify examples based on geometric definitions.
Determine if two figures are congruent based on size and shape.

Identify the line of symmetry in a two-dimensional design or shape.

Calculate the perimeter of shapes made from polygons.
Choose reasonable units of measure, estimate common measurements using benchmarks, and use appropriate tools to make measurements.
Measure length to the nearest centimeter or half inch.
Solve problems requiring the addition and subtraction of lengths.

### Data, Probability and Statistics

Standard 5 — Data, Probability and Statistics

Conceptual StrandThe Data Analysis and Probability Standard recommends that students formulate questions that can be answered using data and addresses what is involved in gathering and using the data wisely. The basic concepts and applications of probability are also addressed, with an emphasis on the way that probability and statistics are related.Guiding QuestionHow do students experiences with the collection and analysis of data enable them to reason statistically and understand the various purposes of surveys, observational studies, and experiments?