Grade 6 Math Alabama standards Standards

Geometry and Measurement

Data Analysis, Statistics, and Probability

Algebra and Functions

Number Systems and Operations

Proportional Reasoning

Student Mathematical Practices

Apply knowledge of arithmetic to read, write, and evaluate algebraic expressions.

Write, evaluate, and compare expressions involving whole number exponents.

Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

Interpret a variable as an unknown value for any number in a specified set, depending on the context.

Write expressions to represent verbal statements and real-world scenarios.

Identify parts of an expression using mathematical terms such as <em>sum, term, product, factor, quotient</em>, and <em>coefficient</em>.

Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

Determine whether two expressions are equivalent and justify the reasoning.

Use equations and inequalities to represent and solve real-world or mathematical problems.

Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Write and solve an equation in the form of <em>x + p = q</em> or <em>px = q</em> for cases in which <em>p, q,</em> and <em>x</em> are all non-negative rational numbers to solve real-world and mathematical problems.

Interpret the solution of an equation in the context of the problem.

Write and solve inequalities in the form of <em>x > c, x < c, x ≥ c,</em> or <em>x ≤ c</em> to represent a constraint or condition in a real-world or mathematical problem.

Interpret the solution of an inequality in the context of a problem.

Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.

Identify and analyze relationships between independent and dependent variables.

Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Use real-world and mathematical problems to analyze data and demonstrate an understanding of statistical variability and measures of center.

Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

Determine which measure of center best represents a real-world data set.

Interpret the measures of center and variability in the context of a problem.

Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.

Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

Use graphical representations of real-world data to describe the context from which they were collected.

Graph polygons in the coordinate plane to solve real-world and mathematical problems.

Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

Determine missing vertices of a rectangle with the same <em>x</em>-coordinate or the same <em>y</em>-coordinate when graphed in the coordinate plane.

Use coordinates to find the length of a side between points having the same <em>x</em>-coordinate or the same <em>y</em>-coordinate.

Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which consecutive vertices have the same <em>x</em>-coordinate or the same <em>y</em>-coordinate).

Solve real-world and mathematical problems to determine area, surface area, and volume.

Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.

Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

Use models (cubes or drawings) and the volume formulas (V = <em>lwh</em> and V = <em>Bh</em>) to find and compare volumes of right rectangular prisms.

Use prior knowledge of multiplication and division to divide fractions.

Interpret and compute quotients of fractions using visual models and equations to represent problems.

Use quotients of fractions to analyze and solve problems.

Compute multi-digit numbers fluently and determine common factors and multiples.

Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

Add, subtract, multiply, and divide decimals using a standard algorithm.

Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

Use factors and multiples to determine prime factorization.

Apply knowledge of the number system to represent and use rational numbers in a variety of forms.

Locate integers and other rational numbers on a horizontal or vertical line diagram.

Define <em>opposites</em> as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Find the position of pairs of integers and other rational numbers on the coordinate plane.

Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the <em>x</em> and <em>y</em> coordinates.

Identify <em>(a,b)</em> and <em>(a,-b)</em> as reflections across the <em>x</em>-axis.

Identify <em>(a,b)</em> and <em>(-a,b)</em> as reflections across the <em>y</em>-axis.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts

Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

Develop an understanding of ratio concepts and use reasoning about ratios to solve problems.

Use appropriate notations [<em>a/b, a to b, a:b</em>] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Use unit rates to represent and describe ratio relationships.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Geometry and Measurement

Data Analysis, Statistics, and Probability

Algebra and Functions

Number Systems and Operations

Proportional Reasoning

Demonstrate a simple ratio relationship using ratio notation given a real-world problem.

Graph or identify ordered pairs in the first quadrant of the coordinate plane between 0 and 5, limited to whole numbers.

Match an algebraic expression with one variable to its real-world situation.

Evaluate algebraic expressions when given specific values for the variables (e.g. x + 2, where x = 4).

Match equations and inequalities to real-world situations.

Identify the independent and dependent variables among two quantities that change in relationship to one another in real-world situations (e.g. purchase total depends on number of items purchased).

Find the range and median (when given an odd number of data points) and mean (involving one- or two digit numbers) in real-world situations.

Interpret graphical representations of a data set (e.g., line plots, dot plots, bar graphs, stem and leaf plots, or line graphs).

Graph squares, rectangles, and triangles in the first quadrant of the coordinate plane.

Calculate problems involving perimeter of squares, triangles, rectangles, and other polygons with sides up to 10 units and calculate problems involving the area of rectangles and squares with sides up to 10 units (whole numbers only).

Solve real-world and mathematical problems involving the volume of cubes and rectangular prisms.

Use models to divide fractions (limit to unit fractions).

Apply the concepts of dividing multidigit numbers without remainders to real-world problems.

Solve two-factor multiplication problems with products up to 100 (whole numbers only).

Describe quantities with positive and negative numbers (e.g., temperature, sea level, etc.).

STEM Technologies III

STEM Technologies II

STEM Technologies I

Describe the development of technology as a human activity that is the result of creatively meeting individual or collective needs.

Identify inventions and innovations that have evolved through slow and methodical processes of testing and refinement.

Utilize the design process to produce products and systems.

Identify the steps of an engineering design process.

Identify criteria and constraints in a design.

Describe how the design process is used to develop solutions for a problem.

Describe the importance of documentation and how it is used to communicate ideas.

Model designs to transform ideas into practical solutions.

Obtain, evaluate, and share information to support the assertion that there is no perfect design.

Practice brainstorming as a group problem-solving design process in which each person in the group presents ideas in an open forum.

Identify two-dimensional and three-dimensional representations of the design solution.

Explain the close link between technology and creativity and how it results in innovation.

Describe the permanence of digital data and the importance of managing one's digital identity and reputation.

Engage in positive, safe, legal, and ethical behaviors when using technology, including during social interactions online and when using networked devices.

Identify research strategies to locate information and other resources for their intellectual and/or creative pursuits.

Identify information from digital resources, using a variety of tools and methods to create a collection of artifacts that demonstrates meaningful connections or conclusions.

Identify real-world issues, develop ideas, and pursue solutions to address the issues.

Describe technological systems, including input, processes, output, and feedback.

Explain how technological systems can be connected to one another.

Identify the difference between open loop and closed loop systems.

Identify positive and negative ways the use of technology affects humans.

Investigate the management of waste produced by technological systems as a societal issue.

Describe how technologies can be used to repair damage caused by natural disasters and to break down waste from various products and systems.

Describe the development of a technology from the demands, values, and interests of employers.

Incorporate safety procedures in handling, operating, and maintaining tools and machinery; handling materials; utilizing personal protective equipment; maintaining a safe work area; and following protocols for fire and electrical safety.

Demonstrate effective workplace and employability skills, including communication, awareness of diversity, positive work ethic, problem-solving, time management, and teamwork.

Explore the range of careers available in the field and investigate their educational requirements, and demonstrate job-seeking skills including resume-writing and interviewing.

Demonstrate digital literacy by using digital and electronic tools appropriately, safely, and ethically.

Participate in a Career and Technical Student Organization (CTSO) to increase knowledge and skills and to enhance leadership and teamwork.

Investigate how technological systems can be connected to one another.

Design a plan to produce products and systems.

Create criteria and constraints in a design.

Use the design process to develop solutions for a problem.

Employ brainstorming in a group problem-solving setting where each person presents design process related ideas in an open forum as part of the design process.

Model two-dimensional and three-dimensional solutions of a design.

Test and modify designs to transform ideas into practical solutions.

Accurately identify different resources used in projects.

Make a product or system to solve a problem and document the solution.

Create and maintain a digital identity and reputation, demonstrating an awareness of the permanence of one's actions in the digital world.

Demonstrate an understanding of and respect for the rights and obligations of using and sharing intellectual property.

Explore different technologies that involve different sets of processes.

Manage their personal data to maintain digital privacy and security.

Create strategies to locate information and other resources for their intellectual or creative pursuits.

Generate ideas about real-world issues and problems and pursue answers and solutions to them.

Gather and present information about ways corporations may create demand for a product by bringing it onto the market and advertising it.

Differentiate between positive and negative effects of technology usage on human beings, including their safety, comfort, choices, and attitudes about technology's development and use.

Analyze the management of waste produced by technological systems as a societal issue.

Research and communicate how technologies can be used to repair damage caused by natural disasters and to break down waste from the use of various products and systems.

Identify ethical issues associated with the development and use of technology.

Describe how social and cultural priorities and values are reflected in technological devices.

Explain how meeting societal expectations can be a driving force behind the acceptance and use of products and systems.

Incorporate safety procedures in handling, operating, and maintaining tools and machinery; handling materials; utilizing personal protective equipment; maintaining a safe work area; and following protocols for fire and electrical safety.

Demonstrate effective workplace and employability skills, including communication, awareness of diversity, positive work ethic, problem-solving, time management, and teamwork.

Explore the range of careers available in the field and investigate their educational requirements, and demonstrate job-seeking skills including resume-writing and interviewing.

Demonstrate digital literacy by using digital and electronic tools appropriately, safely, and ethically.

Participate in a Career and Technical Student Organization (CTSO) to increase knowledge and skills and to enhance leadership and teamwork.

Design a technological system that can be connected to another system.

Make decisions about the development and use of technologies that put environmental and economic concerns in direct competition with one another.

Develop a plan to produce products and systems.

Critique criteria, constraints, and tradeoffs in a design.

Synthesize elements of the design process to develop solutions for a problem.

Analyze results of solutions to problems using the steps in the design process.

Design two-dimensional and three-dimensional representations of a design solution.

Evaluate designs to transform ideas into practical solutions.

Critique a product or system and document the evaluation.

Apply a design process to solve problems in and beyond the classroom.

Test, evaluate, and modify a design in relation to criteria and constraints.

Design a variety of technologies that involve different sets of processes.

Cultivate a digital identity and reputation, demonstrating an awareness of the permanence of one's actions in the digital world.

Manage their personal data to maintain digital privacy and security, demonstrating awareness of data-collection technology used to track their navigation online.

Employ research strategies to locate information and other resources for their intellectual or creative pursuits.

Evaluate the accuracy, perspective, credibility, and relevance of information, media, data, or other resources.

Curate information from digital resources using a variety of tools and methods to create a collection of artifacts that demonstrate meaningful connections or conclusions.

Develop solutions to real-world issues by analyzing ideas and solutions.

Demonstrate how every part of a system relates to another.

Analyze malfunctions of any part of a system that may affect the system's function and quality.

Compare and contrast trade-offs as a decision process and describe the need for careful compromises among competing factors.

Perform basic maintenance on systems within the program.

Analyze the ways, both positive and negative, that the use of technology affects humans, including their safety, comfort, choices, and attitudes about technology's development and use.

Critique the management of waste produced by technological systems as a societal issue.

Design a solution to alleviate and/or repair the damage caused by various disasters.

Incorporate safety procedures in handling, operating, and maintaining tools and machinery; handling materials; utilizing personal protective equipment; maintaining a safe work area; and following protocols for fire and electrical safety.

Demonstrate effective workplace and employability skills, including communication, awareness of diversity, positive work ethic, problem-solving, time management, and teamwork.

Explore the range of careers available in the field and investigate their educational requirements, and demonstrate job-seeking skills including resume-writing and interviewing.

Demonstrate digital literacy by using digital and electronic tools appropriately, safely, and ethically.

Participate in a Career and Technical Student Organization (CTSO) to increase knowledge and skills and to enhance leadership and teamwork.