**6th Grade Mathematics Standards**

**In April of 2014, the Indiana State Board of Education approved the adoption of new standards for Mathematics.**

*The 2014 Indiana Academic Standards for Mathematics are the result of a process designed to identify, evaluate, synthesize, and create the most high-quality, rigorous standards for Indiana students. The standards are designed to ensure that Indiana students are prepared to enter and successfully complete postsecondary education, and that they are prepared for long-term, economically-viable career opportunities.*

The Indiana Academic Standards for Mathematics demonstrate what students should know and be able to do in the areas of K-8 Mathematics; Algebra I, II, and Geometry; and higher-level high school Mathematics courses. Instruction in Mathematics provides vital content and skills for lifelong learning and problem solving in our increasingly complex technological world and engages students in the essential thinking skills and processes used across subject areas.

These new standards have been validated as college and career ready by the Indiana Education Roundtable, the Indiana Commission for Higher Education, the Indiana Department of Education, the Indiana Center for Education and Career Innovation, and the Indiana State Board of Education. This means that students who successfully master these objectives for what they should know and be able to do in Mathematics disciplines by the time they graduate from high school will be ready to go directly into the workplace or a postsecondary educational opportunity without the need for remediation.

The Indiana Academic Standards for Mathematics demonstrate what students should know and be able to do in the areas of K-8 Mathematics; Algebra I, II, and Geometry; and higher-level high school Mathematics courses. Instruction in Mathematics provides vital content and skills for lifelong learning and problem solving in our increasingly complex technological world and engages students in the essential thinking skills and processes used across subject areas.

These new standards have been validated as college and career ready by the Indiana Education Roundtable, the Indiana Commission for Higher Education, the Indiana Department of Education, the Indiana Center for Education and Career Innovation, and the Indiana State Board of Education. This means that students who successfully master these objectives for what they should know and be able to do in Mathematics disciplines by the time they graduate from high school will be ready to go directly into the workplace or a postsecondary educational opportunity without the need for remediation.

**NUMBER SENSE**

GRADE 6

GRADE 6

6.NS.1: Understand that positive and negative numbers are used to describe quantities having opposite directions or values (e.g.,

temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation.

**6.NS.2:**Understand the integer number system. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3), and that 0 is its own opposite.

**6.NS.3:**Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

**6.NS.4:**Understand that the absolute value of a number is the distance from zero on a number line. Find the absolute value of real numbers and know that the distance between two numbers on the number line is the absolute value of their difference. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

**6.NS.5:**Know commonly used fractions (halves, thirds, fourths, fifths, eighths, tenths) and their decimal and percent equivalents. Convert

between any two representations (fractions, decimals, percents) of positive rational numbers without the use of a calculator.

**6.NS.6:**Identify and explain prime and composite numbers.

**6.NS.7:**Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole

numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.

**6.NS.8:**Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between

two quantities. Use the following notations: a/b, a to b, a:b.

**6.NS.9:**Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.

**6.NS.10:**Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

**COMPUTATION**

GRADE 6

GRADE 6

**6.C.1:**Divide multi-digit whole numbers fluently using a standard algorithmic approach.

**6.C.2:**Compute with positive fractions and positive decimals fluently using a standard algorithmic approach.

**6.C.3:**Solve real-world problems with positive fractions and decimals by using one or two operations.

**6.C.4:**Compute quotients of positive fractions and solve real-world problems involving division of fractions by fractions. Use a visual fraction model and/or equation to represent these calculations.

**6.C.5:**Evaluate positive rational numbers with whole number exponents.

**6.C.6:**Apply the order of operations and properties of operations (identity, inverse, commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property) to evaluate numerical expressions with nonnegative rational numbers,

**ALGEBRA AND FUNCTIONS**

GRADE 6

GRADE 6

**6.AF.1:**Evaluate expressions for specific values of their variables, including expressions with whole-number exponents and those that arise from formulas used in real-world problems.

**6.AF.2:**Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent

linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless

of which value is substituted into them.

**6.AF.3:**Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values.

**6.AF.4:**Understand that solving an equation or inequality is the process of answering the following question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

**6.AF.5:**Solve equations of the form x + p = q, x - p = q, px = q, and x/p = q fluently for cases in which p, q and x are all nonnegative rational

numbers. Represent real world problems using equations of these forms and solve such problems.

**6.AF.6:**Write an inequality of the form x > c, x ≥ c, x < c, or x ≤ c, where c is a rational number, to represent a constraint or condition in a realworld or other mathematical problem. Recognize inequalities have infinitely many solutions and represent solutions on a number line

diagram.

**6.AF.7:**Understand that signs of numbers in ordered pairs indicate the quadrant containing the point; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Graph points with rational number

coordinates on a coordinate plane.

**6.AF.8:**Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane.

Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second

coordinate.

**6.AF.9:**Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane.

**6.AF.10:**Use variables to represent two quantities in a proportional relationship in a real-world problem; write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

**GEOMETRY AND MEASUREMENT**

GRADE 6

GRADE 6

**6.GM.1:**Convert between measurement systems (English to metric and metric to English) given conversion factors, and use these

conversions in solving real-world problems.

**6.GM.2:**Know that the sum of the interior angles of any triangle is 180º and that the sum of the interior angles of any quadrilateral is 360º. Use this information to solve real-world and mathematical problems.

**6.GM.3:**Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate; apply these techniques to solve real-world and other mathematical problems.

**6.GM.4:**Find the area of complex shapes composed of polygons by composing or decomposing into simple shapes; apply this technique to solve real-world and other mathematical problems.

**6.GM.5:**Find the volume of a right rectangular prism with fractional edge lengths using unit cubes of the appropriate unit fraction edge

lengths (e.g., using technology or concrete materials), and show that the volume is the same as would be found by multiplying the edge

lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths to solvereal-world and other mathematical problems.

**6.GM.6:**Construct right rectangular prisms from

**DATA ANALYSIS AND STATISTICS**

GRADE 6

GRADE 6

**6.DS.1:**Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for the variability in the answers. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

**6.DS.2:**Select, create, and interpret graphical representations of numerical data, including line plots, histograms, and box plots.

**6.DS.3:**Formulate statistical questions; collect and organize the data (e.g., using technology); display and interpret the data with graphical

representations (e.g., using technology).

**6.DS.4:**Summarize numerical data sets in relation to their context in multiple ways, such as: report the number of observations; describe the nature of the attribute under investigation, including how it was measured and its units of measurement; determine quantitative measures of center (mean and/or median) and spread (range and interquartile range), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; and relate the choice of measures of center and spread to the shape of the data distribution and the context in which the data were gathered.

**PROCESS STANDARDS FOR MATHEMATICS**

PS.1: Make sense of problems and persevere in solving them.

PS.1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points

to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and

meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt. They consider

analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution.

They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their

answers to problems using a different method, and they continually ask themselves, “Does this make sense?” and "Is my

answer reasonable?" They understand the approaches of others to solving complex problems and identify correspondences

between different approaches. Mathematically proficient students understand how mathematical ideas interconnect and

build on one another to produce a coherent whole.

**PS.2: Reason abstractly and quantitatively.**

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

**PS.3: Construct viable arguments and critique the reasoning of others.**

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They analyze situations by breaking them into cases and recognize and use counterexamples. They organize their mathematical thinking, justify their conclusions and communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. They justify whether a given statement is true always, sometimes, or never. Mathematically proficient students participate and collaborate in a mathematics community. They listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

**PS.4: Model with mathematics.**

Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and

the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems

and to organize and communicate mathematical ideas. Mathematically proficient students apply what they know and are

comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need

revision later. They are able to identify important quantities in a practical situation and map their relationships using such

tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to

draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether

the results make sense, possibly improving the model if it has not served its purpose.

**PS.5: Use appropriate tools strategically.**

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might

include pencil and paper, models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical

package, or dynamic geometry software. Mathematically proficient students are sufficiently familiar with tools appropriate

for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the

insight to be gained and their limitations. Mathematically proficient students identify relevant external mathematical

resources, such as digital content, and use them to pose or solve problems. They use technological tools to explore and

deepen their understanding of concepts and to support the development of learning mathematics. They use technology to

contribute to concept development, simulation, representation, reasoning, communication and problem solving.

**PS.6: Attend to precision.**

Mathematically proficient students communicate precisely to others. They use clear definitions, including correct

mathematical language, in discussion with others and in their own reasoning. They state the meaning of the symbols they

choose, including using the equal sign consistently and appropriately. They express solutions clearly and logically by using

the appropriate mathematical terms and notation. They specify units of measure and label axes to clarify the

correspondence with quantities in a problem. They calculate accurately and efficiently and check the validity of their results

in the context of the problem. They express numerical answers with a degree of precision appropriate for the problem

context.

**PS.7: Look for and make use of structure.**

Mathematically proficient students look closely to discern a pattern or structure. They step back for an overview and shift

perspective. They recognize and use properties of operations and equality. They organize and classify geometric shapes

based on their attributes. They see expressions, equations, and geometric figures as single objects or as being composed of

several objects.

**PS.8: Look for and express regularity in repeated reasoning.**

Mathematically proficient students notice if calculations are repeated and look for general methods and shortcuts. They

notice regularity in mathematical problems and their work to create a rule or formula. Mathematically proficient students

maintain oversight of the process, while attending to the details as they solve a problem. They continually evaluate the

reasonableness of their intermediate results.