# Academic standards list

### Mathematics - Grade 4 — Mathematics

### 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

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

Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument.

### 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.

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.

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.

Add and subtract proper fractions with like and unlike denominators and simplify the answer.

Solve problems using whole number division with one- or two-digit divisors.

### 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

### 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.

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.

Identify attributes of simple and compound figures composed of 2- and 3- dimensional shapes.

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,…

### 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.

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.

**This website provides a reference tool for browsing academic standards and locating associated resources. We are not the originator of these academic standards. Although we strive to maintain accuracy, there may be revisions, updates, or errors within the text and structure of the information displayed. In case of any discrepancy, please respect the originator's published version (http://www.tn.gov/education/article/mathematics-standards) as the definitive record.**

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