Kentucky State Standards for Mathematics: Grade 6

KY.PS. Program of Studies 2006

MA-6-NPO. Big Idea: Number Properties and Operations - Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers. (Academic Expectations 2.7, 2.8)

MA-6-NPO-U-1. Program of Studies: Understandings - Students will understand that numbers, ways of representing numbers, relationships among numbers and number systems are means of representing real-world quantities.

MA-6-NPO-U-2. Program of Studies: Understandings - Students will understand that meanings of and relationships among operations provide tools necessary to solve realistic problems encountered in everyday life.

MA-6-NPO-U-3. Program of Studies: Understandings - Students will understand that computing fluently and making reasonable estimates with fractions, decimals and whole numbers increases the ability to solve realistic problems encountered in everyday life.

MA-6-NPO-U-4. Program of Studies: Understandings - Students will understand that proportional reasoning is a tool for modeling and solving problems encountered in everyday situations.

MA-6-NPO-S-NS1. Program of Studies: Skills and Concepts - Students will continue to develop number sense using fractions, decimals and percents, including percents greater than 100% and improper fractions.

MA-6-NPO-S-NS2. Program of Studies: Skills and Concepts - Students will extend applications of operations (+, -, x, /) to include fractions and decimals.

MA-6-NPO-S-NS3. Program of Studies: Skills and Concepts - Students will develop place value of large and small numbers, including decimals.

MA-6-NPO-S-NS4. Program of Studies: Skills and Concepts - Students will explore positive integral exponents (e.g. squares, cubes).

MA-6-NPO-S-NS5. Program of Studies: Skills and Concepts - Students will compare, order and convert between whole numbers, fractions, decimals and percents using concrete materials, drawings or pictures and mathematical symbols (e.g., <, less than or equal to, >, greater than or equal to, =, not equal to, order on a number line).

MA-6-NPO-S-E1. Program of Studies: Skills and Concepts - Students will estimate and mentally compute to solve real-world and/or mathematical problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results.

MA-6-NPO-S-E2. Program of Studies: Skills and Concepts - Students will estimate large and small quantities of objects.

MA-6-NPO-S-NO1. Program of Studies: Skills and Concepts - Students will develop addition, subtraction, multiplication and division of common fractions and decimals with manipulatives and symbols (e.g., mental computation, paper and pencil, calculators)

MA-6-NPO-S-NO2. Program of Studies: Skills and Concepts - Students will add, subtract, multiply, divide and apply order of operations with whole numbers, fractions and decimals to solve real-world problems

MA-6-NPO-S-NO3. Program of Studies: Skills and Concepts - Students will explain and/or demonstrate inversely-related operations (addition and subtraction; multiplication and division).

MA-6-NPO-S-PNO1. Program of Studies: Skills and Concepts - Students will determine prime numbers, composite numbers, prime factorization, factors, multiples, greatest common factor and least common multiple.

MA-6-NPO-S-PNO2. Program of Studies: Skills and Concepts - Students will simplify fractions and determine equivalent fractions.

MA-6-NPO-S-PNO3. Program of Studies: Skills and Concepts - Students will use prime numbers, composite numbers, factors, multiples and divisibility to solve problems.

MA-6-NPO-S-PNO4. Program of Studies: Skills and Concepts - Students will explore and/or demonstrate how applications of properties (e.g., commutative, associative, inverse and identity for addition and multiplication) show relationships among numbers and operations.

MA-6-NPO-S-RP1. Program of Studies: Skills and Concepts - Students will develop meaning of percent and how to determine a percentage.

MA-6-NPO-S-RP2. Program of Studies: Skills and Concepts - Students will develop meaning of ratio (e.g., describe and compare two sets of data using ratios and appropriate notations: 3:5, 3/5, 3 to 5).

MA-6-NPO-S-RP3. Program of Studies: Skills and Concepts - Students will define and apply ratios to solve real-world problems.

MA-6-M. Big Idea: Measurement - Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use U.S. Customary and metric units of measurement. (Academic Expectations 2.10, 2.11)

MA-6-M-U-1. Program of Studies: Understandings - Students will understand that there are two major measurement systems (U.S. Customary and metric) and either may be used to solve problems.

MA-6-M-U-2. Program of Studies: Understandings - Students will understand that measurable attributes of objects and the units, systems and processes of measurement are powerful tools for making sense of the world around them.

MA-6-M-U-3. Program of Studies: Understandings - Students will understand that measurements are determined by using appropriate techniques, tools, formulas and degree of accuracy needed for the situation.

MA-6-M-S-SM1. Program of Studies: Skills and Concepts - Students will describe and provide examples of U.S. Customary and metric units of measurement; use these units to solve real-world and/or mathematical problems.

MA-6-M-S-SM2. Program of Studies: Skills and Concepts - Students will estimate, compare and convert (meaning to make ballpark comparisons/not memorize conversion factors between U.S. and metric) units of measurement for length, weight/mass and volume/capacity within the U.S. customary system and within the metric system: length (e.g., parts of an inch, inches, feet, yards, miles, millimeters, centimeters, meters, kilometers); weight/mass (e.g., pounds, tons, grams, kilograms); volume/capacity (e.g., cups, pints, quarts, gallons, milliliters, liters).

MA-6-M-S-MPS1. Program of Studies: Skills and Concepts - Students will find perimeter of regular and irregular polygons in metric and U.S. customary units.

MA-6-M-S-MPA2. Program of Studies: Skills and Concepts - Students will read and use measurement tools (e.g., rulers, scales, protractors, angle rulers).

MA-6-M-S-MPA3. Program of Studies: Skills and Concepts - Students will find area of plane figures composed of triangles, squares and rectangles by subdividing and measuring; use square units appropriately.

MA-6-M-S-MPA4. Program of Studies: Skills and Concepts - Students will estimate and find angle measures and segment measures.

MA-6-M-S-MPA5. Program of Studies: Skills and Concepts - Students will estimate measurements in standard units, including fractions and decimals.

MA-6-M-S-MPA6. Program of Studies: Skills and Concepts - Students will explain how measurements and measurement formulas are related or different (e.g., compare the perimeter with the area of a rectangle).

MA-6-G. Big Idea: Geometry - Middle grade students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. (Academic Expectation 2.8, 2.9)

MA-6-G-U-1. Program of Studies: Understandings - Students will understand that characteristics and properties of two-dimensional figures and three-dimensional objects describe the world and are used to develop mathematical arguments about geometric relationships and to evaluate the arguments of others.

MA-6-G-U-2. Program of Studies: Understandings - Students will understand that representational systems, including coordinate geometry, are means for specifying locations and describing spatial relationships and are organizers for making sense of the world around them.

MA-6-G-U-3. Program of Studies: Understandings - Students will understand that transformations and symmetry are used to analyze real-world situations (e.g., art, nature, construction and scientific exploration).

MA-6-G-U-4. Program of Studies: Understandings - Students will understand that shape and area are conserved during mathematical transformations (flips, slides and turns). Scale conserves shape, but changes size.

MA-6-G-U-5. Program of Studies: Understandings - Students will understand that visualization, spatial reasoning and geometric relationships model real-world situations.

MA-6-G-S-SR1. Program of Studies: Skills and Concepts - Students will formulate and use the rules for the sum of angle measures in a triangle (180 degrees) and in a quadrilateral (360 degrees).

MA-6-G-S-SR2. Program of Studies: Skills and Concepts - Students will identify and use relationships among lines (e.g., parallel, perpendicular).

MA-6-G-S-SR3. Program of Studies: Skills and Concepts - Students will identify, describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference).

MA-6-G-S-SR4. Program of Studies: Skills and Concepts - Students will identify, describe and provide examples and properties of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals, regular polygons); apply these properties and figures to solve real-world problems.

MA-6-G-S-SR5. Program of Studies: Skills and Concepts - Students will describe, provide examples of and identify properties (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms and pyramids).

MA-6-G-S-SR6. Program of Studies: Skills and Concepts - Students will describe and provide examples of congruent and similar plane figures; apply congruent and similar plane figures to solve real-world problems.

MA-6-G-S-CG1. Program of Studies: Skills and Concepts - Students will identify and graph ordered pairs on a positive coordinate system, identifying the origin, axes and ordered pairs.

MA-6-G-S-CG2. Program of Studies: Skills and Concepts - Students will apply graphing in the positive coordinate system to solve real-world and mathematical problems.

MA-6-G-S-TS1. Program of Studies: Skills and Concepts - Students will determine lines of symmetry for a plane figure, sketch plane figures with multiple lines of symmetry and apply line symmetry to real-world and/or mathematical situations.

MA-6-G-S-TS2. Program of Studies: Skills and Concepts - Students will transform (translate and reflect across a horizontal or vertical line) figures in the first quadrant of the coordinate plane and determine new coordinates of the shape after transformation.

MA-6-G-S-TS3. Program of Studies: Skills and Concepts - Students will explore the rotation of a figure in a plane in the first quadrant, with and without manipulatives.

MA-6-DAP. Big Idea: Data Analysis and Probability - Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities. (Academic Expectations 2.7, 2.8, 2.13)

MA-6-DAP-U-1. Program of Studies: Understandings - Students will understand that quantitative literacy is a necessary tool to be an intelligent consumer and citizen.

MA-6-DAP-U-2. Program of Studies: Understandings - Students will understand that the collection, organization, interpretation and display of data can be used to answer questions.

MA-6-DAP-U-3. Program of Studies: Understandings - Students will understand that the choice of data display can affect the visual message communicated.

MA-6-DAP-U-4. Program of Studies: Understandings - Students will understand that inferences and predictions from data are used to make critical and informed decisions.

MA-6-DAP-U-5. Program of Studies: Understandings - Students will understand that for a given set of data or a graph, statistical measures (mean, median, mode, range) can be used to describe the distribution of the data.

MA-6-DAP-U-6. Program of Studies: Understandings - Students will understand that probability can be used to make decisions or predictions or to draw conclusions.

MA-6-DAP-S-DR1. Program of Studies: Skills and Concepts - Students will select an appropriate graph to represent given data and justify the selection.

MA-6-DAP-S-DR2. Program of Studies: Skills and Concepts - Students will collect, organize, construct, analyze and interpret data in a variety of graphical methods, including line plots, line graphs, circle graphs, bar graphs and stem-and-leaf plots.

MA-6-DAP-S-DR3. Program of Studies: Skills and Concepts - Students will compare data from various types of graphs.

MA-6-DAP-S-DR4. Program of Studies: Skills and Concepts - Students will relate different representations of data (e.g., tables, graphs, diagrams, plots).

MA-6-DAP-S-ES1. Program of Studies: Skills and Concepts - Students will pose questions; collect, organize and display data.

MA-6-DAP-S-ES2. Program of Studies: Skills and Concepts - Students will explore how sample size affects the reliability of the outcome.

MA-6-DAP-S-CD1. Program of Studies: Skills and Concepts - Students will make predictions, draw conclusions and verify results from statistical data and probability experiments.

MA-6-DAP-S-CD2. Program of Studies: Skills and Concepts - Students will determine and apply measures of distribution (mean, median, mode, range).

MA-6-DAP-S-P1. Program of Studies: Skills and Concepts - Students will describe or determine (e.g., tables, tree diagrams) the sample space of an event.

MA-6-DAP-S-P2. Program of Studies: Skills and Concepts - Students will investigate solutions to probability problems using counting techniques, tree diagrams, charts and tables.

MA-6-DAP-S-P3. Program of Studies: Skills and Concepts - Students will make predictions, draw conclusions and verify results from statistical data and probability experiments.

MA-6-DAP-S-P4. Program of Studies: Skills and Concepts - Students will determine simple probabilities based on the results of an experiment and make inferences based on the data.

MA-6-DAP-S-P5. Program of Studies: Skills and Concepts - Students will explore the role of probability in decision making.

MA-6-AT. Big Idea: Algebraic Thinking - Middle grade students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities. (Academic Expectations 2.8, 2.11, 2.12)

MA-6-AT-U-1. Program of Studies: Understandings - Students will understand that patterns, relations and functions are tools that help explain or predict real-world phenomena.

MA-6-AT-U-2. Program of Studies: Understandings - Students will understand that numerical patterns can be written as rules that generate the pattern.

MA-6-AT-U-3. Program of Studies: Understandings - Students will understand that algebra represents mathematical situations and structures for analysis and problem solving.

MA-6-AT-U-4. Program of Studies: Understandings - Students will understand that real-world situations can be represented using mathematical models to analyze quantitative relationships.

MA-6-AT-U-5. Program of Studies: Understandings - Students will understand that functions are used to analyze change in various contexts and model real-world phenomena.

MA-6-AT-U-6. Program of Studies: Understandings - Students will understand that functions can be written in words, in a symbolic sentence or in a table.

MA-6-AT-S-PRF1. Program of Studies: Skills and Concepts - Students will recognize, create and extend patterns (give an informal description of the continuation of a pattern and/or generalize a pattern through a verbal rule).

MA-6-AT-S-PRF2. Program of Studies: Skills and Concepts - Students will represent, interpret and describe function relationships through tables, graphs and verbal rules.

MA-6-AT-S-PRF3. Program of Studies: Skills and Concepts - Students will organize input-output coordinate pairs into tables and plot points in the first quadrant of a coordinate (Cartesian) system/grid.

MA-6-AT-S-PRF4. Program of Studies: Skills and Concepts - Students will explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables).

MA-6-AT-S-VEO1. Program of Studies: Skills and Concepts - Students will explore the use of variables in expressions and equations.

MA-6-AT-S-VEO2. Program of Studies: Skills and Concepts - Students will substitute numerical values for variables and evaluate algebraic expressions.

MA-6-AT-S-VEO3. Program of Studies: Skills and Concepts - Students will describe, define and provide examples of algebraic expressions based on real-world and/or mathematical situations.

MA-6-AT-S-EI1. Program of Studies: Skills and Concepts - Students will use concrete and/or informal methods to solve equations with one variable that model real-world situations.

MA-6-AT-S-EI2. Program of Studies: Skills and Concepts - Students will solve problems involving simple formulas (e.g., A=lw, D=rt).

MA-6-AT-S-EI3. Program of Studies: Skills and Concepts - Students will model and solve real-world problems with one variable equations and inequalities (e.g., 8x=4, x + 2>5).

KY.AE. Academic Expectation

AE.1. Students are able to use basic communication and mathematics skills for purposes and situations they will encounter throughout their lives.

1.1. Students use reference tools such as dictionaries, almanacs, encyclopedias, and computer reference programs and research tools such as interviews and surveys to find the information they need to meet specific demands, explore interests, or solve specific problems.

1.2. Students make sense of the variety of materials they read.

1.3. Students make sense of the various things they observe.

1.4. Students make sense of the various messages to which they listen.

1.5-1.9. Students use mathematical ideas and procedures to communicate, reason, and solve problems.

1.10. Students organize information through development and use of classification rules and systems.

1.11. Students write using appropriate forms, conventions, and styles to communicate ideas and information to different audiences for different purposes.

1.12. Students speak using appropriate forms, conventions, and styles to communicate ideas and information to different audiences for different purposes.

1.13. Students make sense of ideas and communicate ideas with the visual arts.

1.14. Students make sense of ideas and communicate ideas with music.

1.15. Students make sense of and communicate ideas with movement.

1.16. Students use computers and other kinds of technology to collect, organize, and communicate information and ideas.

AE.2. Students shall develop their abilities to apply core concepts and principles from mathematics, the sciences, the arts, the humanities, social studies, practical living studies, and vocational studies to what they will encounter throughout their lives.

2.7. Mathematics: Students understand number concepts and use numbers appropriately and accurately.

2.8. Mathematics: Students understand various mathematical procedures and use them appropriately and accurately.

2.9. Mathematics: Students understand space and dimensionality concepts and use them appropriately and accurately.

2.10. Mathematics: Students understand measurement concepts and use measurements appropriately and accurately.

2.11. Mathematics: Students understand mathematical change concepts and use them appropriately and accurately.

2.12. Mathematics: Students understand mathematical structure concepts including the properties and logic of various mathematical systems.

2.13. Mathematics: Students understand and appropriately use statistics and probability.

KY.CC. Core Content for Assessment v.4.1

MA-06-1. Number Properties and Operations: Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers.

MA-06-1.1. Number Sense

MA-06-1.1.1. Students will provide examples of and identify fractions, decimals and percents. DOK 1

MA-06-1.1.2. Students will describe and provide examples of representations of numbers (whole numbers, fractions in simplest form, mixed numbers, decimals, percents) and operations in a variety of equivalent forms using models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences), based on real-world and/or mathematical situations.

MA-06-1.1.3. Students will convert between any two of the following numbers: fractions, decimals and percents (less than or equal to100%); and will compare and order these numbers. DOK 2

MA-06-1.2. Estimation

MA-06-1.2.1. Students will estimate to solve real-world and mathematical problems with whole numbers, fractions, decimals, and percents, checking for reasonable and appropriate computational results. DOK 2

MA-06-1.3. Number Operations

MA-06-1.3.1. Students will add, subtract, multiply and divide, whole numbers, fractions and decimals to solve real-world problems and apply order of operations to simplify numerical expressions. DOK 2

MA-06-1.3.2. Students will explain how operations (addition and subtraction; multiplication and division) are inversely related.

MA-06-1.4. Ratios and Proportional Reasoning

MA-06-1.4.1. Students will describe and apply ratios to solve real-world problems. DOK 2

MA-06-1.5. Properties of Numbers and Operations

MA-06-1.5.1. Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK 2

MA-06-1.5.2. Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to simplify numerical expressions. DOK 1

MA-06-2. Measurement: Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use US Customary and metric units of measurement.

MA-06-2.1. Measuring Physical Attributes

MA-06-2.1.1. Students will measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and mathematical problems: area and perimeter of triangles; area and perimeter of quadrilaterals (rectangles, squares); (using the Pythagorean theorem will not be required as a strategy) and area and perimeter of compound figures composed of triangles and quadrilaterals. DOK 2

MA-06-2.1.2. Students will estimate measurements in standard units including fractions and decimals.

MA-06-2.1.3. Students will explain how measurements and measurement formulas are related or different (perimeter and area of rectangles).

MA-06-2.2. Systems of Measurement

MA-06-2.2.1. Students will convert units within the same measurement system and use these units to solve real-world problems.

MA-06-3. Geometry: Middle grades students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. They use the Pythagorean theorem.

MA-06-3.1. Shapes and Relationships

MA-6-3.1.1. Students will describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference). DOK 1

MA-06-3.1.2. Students will describe and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles, quadrilaterals, regular polygons) and will apply these elements and figures to solve real-world and mathematical problems. DOK 2

MA-06-3.1.3. Students will describe, provide examples of and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms, and pyramids).

MA-06-3.1.4. Students will identify and describe congruent figures and will apply congruent figures to solve real-world and mathematical problems. DOK 2

MA-06-3.1.5. Students will identify similar figures and apply similar figures to solve real-world and mathematical problems.

MA-06-3.2. Transformations of Shapes

MA-06-3.2.1. Students will describe, provide examples of and apply line symmetry to real-world and mathematical problems.

MA-06-3.2.2. Students will reflect figures across a horizontal or vertical line in the first quadrant; translate figures in a plane in the first quadrant and determine the coordinates of the image after transformation in the first quadrant. DOK 2

MA-06-3.2.3. Students will identify rotations of figures in the plane (90 degrees and 180 degrees).

MA-06-3.3. Coordinate Geometry

MA-06-3.3.1. Students will identify and graph ordered pairs on a positive coordinate system (Quadrant I), correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems. DOK 2

MA-06-4. Data Analysis and Probability: Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities.

MA-06-4.1. Data Representations

MA-06-4.1.1. Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots). DOK 3

MA-06-4.1.2. Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.

MA-06-4.1.4. Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs) and will explain why the type of display is appropriate for the data. DOK 2

MA-06-4.2. Characteristics of Data Sets

MA-06-4.2.1. Students will determine and apply the mean, median, mode and range of a set of data. DOK 2

MA-06-4.4. Experiments and Samples (not assessed at this level) - Probability

MA-06-4.4.1. Students will describe or determine (e.g., tables, tree diagrams) the sample space of an event for a real-world or mathematical situation. DOK 2

MA-06-4.4.2. Students will determine single event probabilities based on the results of an experiment and will make inferences based on the data. DOK 3

MA-06-4.4.3. Students will explore the theoretical probability of simple events.

MA-06-5. Algebraic Thinking: Middle grades students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities.

MA-06-5.1. Patterns, Relations and Functions

MA-06-5.1.1. Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems. DOK 3

MA-06-5.1.2. Students will create tables for functions and will apply the tables to solve real-world problems. DOK 2

MA-06-5.1.3. Students will describe, define, provide examples of and apply to real-world and mathematical problems functions using tables, graphs and verbal rules.

MA-06-5.1.4. Students will explain how tables, graphs and patterns relate to each other.

MA-06-5.1.5. Students will explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables).

MA-06-5.3. Variables, Expressions and Operations

MA-06-5.2.1. Students will substitute values for variables (up to two different variables) and evaluate algebraic expressions. DOK 2

MA-06-5.2.2. Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.

MA-06-5.3.1. Students will model and solve real-world and mathematical problems with simple equations and inequalities (e.g., 8x = 4, x+2 > 5). DOK 2