Academic standards list

Mathematics - Grade 5 — 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
Given a series of geometric statements, draw a conclusion about the figure described.
Estimate fraction and decimal sums or differences.
Recognize the unit associated with the remainder in a division problem or the meaning of the fractional part of a whole given in either decimal or fraction form.
Identify missing information and/or too much information in contextual problems.

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
Extend the understanding of place value through millions and millionths in various contexts and representations.
Write natural numbers (to 50) as a product of prime factors and understand that this is unique (apart from order).
Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division.
Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm.
Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals.
State Performance Indicator
Read and write numbers from millions to millionths in various contexts.
Write the prime factorization of numbers through 50 using both exponential and standard notation.
Select a reasonable solution to a real-world division problem in which the remainder must be considered.
Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers.
Solve addition and subtraction problems involving both fractions and decimals.
Add and subtract proper and improper fractions as well as mixed numbers.
Recognize equivalent representations for the same number.
Write terminating decimals in the form of fractions or mixed numbers.
Compare whole numbers, decimals and fractions using the symbols , and =.


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
Understand and use order of operations.
Develop and apply the concept of variable.
Understand and apply the substitution property.
Solve single-step linear equations and inequalities.
State Performance Indicator
Evaluate algebraic expressions involving decimals and fractions using order of operations.
Use variables appropriately to represent numbers whose values are not yet known.
Find the unknown in single-step equations involving fractions and mixed numbers.
Given a set of values, identify those that make an inequality a true statement.

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
Use basic formulas and visualization to find the area of geometric figures.
Describe polyhedral solids and analyze their properties, including volume and surface area.
Describe length/distance relationships using the first quadrant of the coordinate system.
Solve problems that require attention to both approximation and precision of measurement.
State Performance Indicator
Solve contextual problems that require calculating the area of triangles and parallelograms.
Decompose irregular shapes to find perimeter and area.
Identify a three-dimensional object from two-dimensional representations of that object and vice versa.
Solve problems involving surface area and volume of rectangular prisms and polyhedral solids.
Find the length of vertical or horizontal line segments in the first quadrant of the coordinate system, including problems that require the use of fractions and
Record measurements in context to reasonable degree of accuracy using decimals and/or fractions.

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
Make, record, display and interpret data and graphs that include whole numbers, decimals, and fractions.
Describe the shape and important features of a set of data using the measures of central tendency.
State Performance Indicator
Depict data using various representations, including decimal and/or fractional data.
Make predictions based on various data representations, including double bar and line graphs.
Calculate measures of central tendency to analyze data.
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