Academic standards list

Mathematics - Grade 4 — Mathematics


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?
Grade Level Expectation
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
Verify a conclusion using the commutative, associative and distributive properties.
Compare decimals using concrete and pictorial representations.
Determine the correct change from a transaction.
Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument.

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?
Grade Level Expectation
Understand place value of numbers from hundredths to the hundred-thousands place.
Develop fluency with multiplication and single-digit division.
Identify prime and composite numbers.
Understand and use the connections between fractions and decimals.
Add and subtract fractions with like and unlike denominators.
Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations.
State Performance Indicator
Read and write numbers from hundredths to hundred-thousands in numerals and in words.
Locate and place mixed numbers on the number line.
Identify the place value of a specified digit in a number and the quantity it represents.
Find factors, common factors, multiples, and common multiples of two numbers.
Generate equivalent forms of common fractions and decimals and use them to compare size.
Use the symbols and = to compare common fractions and decimals in both increasing and decreasing order.
Convert improper fractions into mixed numbers and/or decimals.
Add and subtract proper fractions with like and unlike denominators and simplify the answer.
Add and subtract decimals through hundredths.
Solve contextual problems using whole numbers, fractions, and decimals.
Solve problems using whole number multi-digit multiplication.
Solve problems using whole number division with one- or two-digit divisors.


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?
Grade Level Expectation
Extend understanding of a variable to equations involving whole numbers, fractions, decimals, and/or mixed numbers.
Use mathematical language and modeling to develop descriptions, rules and extensions of patterns.
Translate between different forms of representations of whole number relationships.
State Performance Indicator
Use letters and symbols to represent an unknown quantity and write a simple mathematical expression
Make generalizations about geometric and numeric patterns.
Represent and analyze patterns using words, function tables, and graphs.

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?
Grade Level Expectation
Understand and use the properties of lines, segments, angles, polygons, and circles.
Understand and use measures of length, area, capacity, and weight.
Solve problems that involve estimating and measuring length, area, capacity and weight.
Understand the representation of location and movement within the first quadrant of a coordinate system.
State Performance Indicator
Classify lines and line segments as parallel, perpendicular, or intersecting.
Graph and interpret points with whole number or letter coordinates on grids or in the first quadrant of the coordinate plane.
Construct geometric figures with vertices at points on a coordinate grid.
Identify acute, obtuse, and right angles in 2-dimensional shapes.
Identify attributes of simple and compound figures composed of 2- and 3- dimensional shapes.
Determine situations in which a highly accurate measurement is important.
Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight.
Convert measurements within a single system that are common in daily life (e.g., hours and minutes, inches and feet, centimeters and meters, quarts and gallons,
Solve problems involving area and/or perimeter of rectangular figures.
Identify images resulting from reflections, translations, or rotations.

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?
Grade Level Expectation
Collect, record, arrange, present, and interpret data using tables and various representations.
Use probability to describe chance events.
State Performance Indicator
Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs).
Solve problems using estimation and comparison within a single set of data.
Given a set of data or a graph, describe the distribution of the data using median, range, or mode.
List all possible outcomes of a given situation or event.
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