Academic standards list

Mathematics - Grade 6 — 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

 
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
Make conjectures and predictions based on data.
 
Judge the reasonableness of the results of rational number estimates and/or computations.
 
Use concrete, pictorial, and symbolic representation for integers.
 
Select the representation that models one of the arithmetic properties (commutative, associative, or distributive).
 
Model algebraic expressions using algebra tiles.
 

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 and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals.
Solve multi-step mathematical, contextual and verbal problems using fractions, mixed numbers, and decimals.
Understand and use ratios, rates and percents.
Understand and convert between fraction, decimal, and percent forms of rational numbers.
Develop meaning for integers; represent and compare quantities with integers.
State Performance Indicator
Solve problems involving the multiplication and division of fractions.
 
Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.
 
Solve problems involving the addition, subtraction, multiplication, and division of decimals.
 
Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals.
 
Transform numbers from one form to another (fractions, decimals, percents, and mixed numbers).
 
Solve problems involving ratios, rates and percents.
 
Locate positive rational numbers on the number line.
 
Locate integers on the number line.
 

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?
 
Grade Level Expectation
Write and solve two-step equations and inequalities.
Interpret and represent algebraic relationships with variables in expressions, simple equations and inequalities.
Extend order of operations to include grouping symbols and exponents.
Use expressions, equations and formulas to solve problems.
Use multiple representations including symbolic algebra to model and/or solve contextual problems that involve linear relationships.
Understand and use the Cartesian coordinate system.
State Performance Indicator
Represent on a number line the solution of a linear inequality.
 
Use order of operations and parentheses to simplify expressions and solve problems.
 
Write equations that correspond to given situations or represent a given mathematical relationship.
 
Rewrite expressions to represent quantities in different ways.
 
Translate between verbal expressions/sentences and algebraic expressions/equations.
 
Solve two-step linear equations using number sense, properties, and inverse operations.
 
Use algebraic expressions and properties to analyze numeric and geometric patterns.
 
Select the qualitative graph that models a contextual situation (e.g., water filling then draining from a bathtub).
 
Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
 

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 basic properties of triangles, quadrilaterals, and other polygons.
Use the concepts of translation, rotation, reflection, and symmetry to understand congruence in the plane.
Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes.
Develop and use formulas for surface area and volume of 3-dimensional figures.
State Performance Indicator
Identify, define or describe geometric shapes given a visual representation or a written description of its properties.
 
Find a missing angle measure in problems involving interior/exterior angles and/or their sums.
 
Solve problems using the Triangle Inequality Theorem.
 
Calculate with circumferences and areas of circles.
 
Determine the surface area and volume of prisms, pyramids and cylinders.
 
Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.
 

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
Understand the meaning of probability and how it is expressed.
Interpret representations of data from surveys and polls, and describe sample bias and how data representations can be misleading.
State Performance Indicator
Determine the theoretical probability of simple and compound events in familiar contexts.
 
Identify features of graphs that may be misleading.
 
Determine whether or not a sample is biased.
 
 
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