# Indiana State Standards for Mathematics: Grade 6

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IN.6.1. Number Sense

6.1.1. Compare, order, and represent on a number line positive and negative integers, fractions, decimals (to hundredths), and mixed numbers.

6.1.2. Interpret the absolute value of a number as 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.

6.1.3. Use percents to represent parts of a whole and find the percentage part of a whole.

6.1.4. Recognize commonly used fractions, decimals, and percents and their equivalents and convert between any two representations of any non-negative rational number without the use of a calculator.

6.1.5. Solve problems involving addition, subtraction, multiplication and division of integers and represent computation with integers on a number line. Describe the effect of operations with numbers less than zero.

6.1.6. Solve problems involving addition, subtraction, multiplication and division of positive fractions and decimals and explain why a particular operation was used for a given situation.

6.1.7. Interpret ratios, model ratios, and use ratios to show the relative sizes of two quantities.

6.1.7.a. Use the notations: a/b, a to b and a:b.

6.1.7.b. Write equivalent ratios,

6.1.7.c. Express a ratio in its simplest form.

6.1.7.d. Find the ratio of two given quantities.

6.1.8. Recognize proportional relationships and solve problems involving proportional relationships. Find the missing term in a pair of equivalent ratios and find one quantity given the other quantity and their ratio.

6.1.9. Solve simple percent, ratio and proportion problems, including problems involving discounts at sales, interest earned and tips.

IN.6.2. Computation

6.2.1. Write and solve one-step linear equations and inequalities in one variable.

6.2.2. Write and use formulas with up to three variables to solve problems.

6.2.3. Apply the correct order of operations and the properties of real numbers [identity, inverse, commutative, associative and distributive properties] to evaluate numerical expressions, including those that use grouping symbols such as parentheses. Justify each step in the process.

6.2.4. Identify and graph ordered pairs in all four quadrants of the coordinate plane.

6.2.5. Solve problems involving linear functions with integer values. Create a table and graph the resulting ordered pairs of integers on a grid. Look for patterns in how a change in one variable relates to a change in the second variable and write the equation.

IN.6.3. Algebra and Functions

6.3.1. Identify, draw and use the properties of vertical, adjacent, complementary, and supplementary angles, and properties of triangles and quadrilaterals, to solve problems involving a missing angle.

6.3.2. Recognize that the sum of the interior angles of any triangle is 180 degrees and that the sum of the interior angles of any quadrilateral is 360 degrees. Use this information to solve problems.

6.3.3. Develop and use the formulas for the circumference and area of a circle.

6.3.4. Recognize that real-world measurements are approximations. Identify appropriate instruments and units for a given measurement situation, taking into account the precision of the measurement desired.

6.3.5. Develop and use the formulas for the surface area and volume of a cylinder and find the surface area and volume of three-dimensional objects built from rectangular solids and cylinders.

IN.6.4. Geometry

6.4.1. Construct and analyze circle graphs and stem-and-leaf plots.

6.4.2. Choose the appropriate display for a single variable set of data from bar graphs, line graphs, circle graphs and stem-and-leaf plots. Justify the choice of data display.

6.4.3. Compare the mean, median and mode for a set of data and explain which measure is most appropriate in a given context.

6.4.4. Solve problems involving probability as a measure of chance and verify that the probabilities computed are reasonable.

6.4.5. Recognize and represent probabilities as ratios, measures of relative frequency, decimals between 0 and 1, and percentages between 0 and 100.

IN.PS. Process Standards

PS.1. Problem Solving

PS.1.1. Build new mathematical knowledge through problem solving.

PS.1.2. Solve problems that arise in mathematics and in other contexts.

PS.1.3. Apply and adapt a variety of appropriate strategies to solve problems.

PS.1.4. Monitor and reflect on the process of mathematical problem solving.

PS.2. Reasoning and Proof

PS.2.1. Recognize reasoning and proof as fundamental aspects of mathematics.

PS.2.2. Make and investigate mathematical conjectures.

PS.2.3. Develop and evaluate mathematical arguments and proofs.

PS.2.4. Select and use various types of reasoning and methods of proof.

PS.3. Communication

PS.3.1. Organize and consolidate their mathematical thinking through communication.

PS.3.2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

PS.3.3. Analyze and evaluate the mathematical thinking and strategies of others.

PS.3.4. Use the language of mathematics to express mathematical ideas precisely.

PS.4. Connections

PS.4.1. Recognize and use connections among mathematical ideas.

PS.4.2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

PS.4.3. Recognize and apply mathematics in contexts outside of mathematics.

PS.5. Representation

PS.5.1. Create and use representations to organize, record, and communicate mathematical ideas.

PS.5.2. Select, apply, and translate among mathematical representations to solve problems.

PS.5.3. Use representations to model and interpret physical, social, and mathematical phenomena.

PS.6. Estimation and Mental Computation

PS.6.1. Know and apply appropriate methods for estimating the results of computations.

PS.6.2. Round numbers to a specified place value.

PS.6.3. Use estimation to decide whether answers are reasonable.

PS.6.4. Decide when estimation is an appropriate strategy for solving a problem.

PS.6.5. Determine appropriate accuracy and precision of measurements in problem situations.

PS.6.6. Use properties of numbers and operations to perform mental computation.

PS.6.7. Recognize when the numbers involved in a computation allow for a mental computation strategy.

PS.7. Technology

PS.7.1. Technology should be used as a tool in mathematics education to support and extend the mathematics curriculum.

PS.7.2. Technology can contribute to concept development, simulation, representation, communication, and problem solving.

PS.7.3. The challenge is to ensure that technology supports-but is not a substitute for- the development of skills with basic operations, quantitative reasoning, and problem-solving skills.

PS.7.3.a. Graphing calculators should be used to enhance middle school and high school students' understanding and skills.

PS.7.3.b. The focus must be on learning mathematics, using technology as a tool rather than as an end in itself.