Kentucky State Standards for Mathematics: Grade 7

KY.PS. Program of Studies 2006

MA-7-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-7-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-7-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-7-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-7-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-7-NPO-S-NS1. Program of Studies: Skills and Concepts - Students will extend number sense for percents and integers.

MA-7-NPO-S-NS2. Program of Studies: Skills and Concepts - Students will extend applications of operations (+, -, x, /) to include integers.

MA-7-NPO-S-NS3. Program of Studies: Skills and Concepts - Students will develop number sense for (pi) as one example of an irrational number.

MA-7-NPO-S-NS4. Program of Studies: Skills and Concepts - Students will use whole number exponents to represent/express numbers.

MA-7-NPO-S-NS5. Program of Studies: Skills and Concepts - Students will compare, order and determine equivalent relationships among fractions, decimals and percents.

MA-7-NPO-S-NS6. Program of Studies: Skills and Concepts - Students will provide examples of and use models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) to describe and write equivalent forms of integers, fractions, decimals, percents, square roots and pi.

MA-7-NPO-S-SC1. Program of Studies: Skills and Concepts - Students will develop addition, subtraction, multiplication and division of integers both concretely and symbolically (mental, pencil and paper, calculators).

MA-7-NPO-S-SC2. Program of Studies: Skills and Concepts - Students will extend concepts and application of operations with fractions and decimals to include percents.

MA-7-NPO-S-SC3. Program of Studies: Skills and Concepts - Students will add, subtract, multiply, divide and apply order of operations (including positive whole number exponents) with fractions, decimals and integers to solve real-world problems.

MA-7-NPO-S-SC4. Program of Studies: Skills and Concepts - Students will explain inversely-related operations (addition and subtraction; multiplication and division).

MA-7-NPO-S-PNO1. Program of Studies: Skills and Concepts - Students will identify, explain and apply properties (e.g., commutative, associative, inverse and identity for addition and multiplication; distributive).

MA-7-NPO-S-PNO2. Program of Studies: Skills and Concepts - Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world problems (e.g., use prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]).

MA-7-NPO-S-E1. Program of Studies: Skills and Concepts - Students will estimate and mentally compute to solve real-world and/or mathematical problems with fractions, decimals, percents and integers, checking for reasonable and appropriate computational results.

MA-7-NPO-S-E2. Program of Studies: Skills and Concepts - Students will estimate large and small quantities of objects.

MA-7-NPO-S-RP1. Program of Studies: Skills and Concepts - Students will compute percentages and use percentages in proportional reasoning.

MA-7-NPO-S-RP2. Program of Studies: Skills and Concepts - Students will determine and solve proportions in real-world and mathematical situations.

MA-7-NPO-S-RP3. Program of Studies: Skills and Concepts - Students will develop proportional reasoning and apply to real-world and mathematical problems (e.g., rates, scaling, similarity).

MA-7-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 US Customary and metric units of measurement. (Academic Expectations 2.10, 2.11)

MA-7-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-7-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-7-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-7-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-7-M-S-MPA1. Program of Studies: Skills and Concepts - Students will read and use measurement tools (e.g., rulers, scales, protractors, angle rulers)

MA-7-M-S-MPA2. Program of Studies: Skills and Concepts - Students will estimate and find angle measures and segment measures

MA-7-M-S-MPA3. Program of Studies: Skills and Concepts - Students will estimate and find circle measurements in standard units (radius, diameter, circumference, area) and relationships among them

MA-7-M-S-MPA4. Program of Studies: Skills and Concepts - Students will develop and use the formulas for area of a triangle, a parallelogram and a trapezoid and relate each to the formula for the area of a rectangle (b x h).

MA-7-M-S-MPA5. Program of Studies: Skills and Concepts - Students will determine the length of sides (to the nearest eighth of an inch or nearest centimeter), area and perimeter of triangles, quadrilaterals (rectangles, squares, trapezoids) and other polygons. (Using the Pythagorean theorem will not be required as a strategy).

MA-7-M-S-MPA6. Program of Studies: Skills and Concepts - Students will explain how measurements and measurement formulas are related or different (e.g., perimeter and area of rectangles).

MA-7-M-S-MPA7. Program of Studies: Skills and Concepts - Students will investigate and demonstrate fixed area with changing perimeter and fixed perimeter with changing area.

MA-7-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-7-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-7-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-7-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-7-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-7-G-U-5. Program of Studies: Understandings - Students will understand that visualization, spatial reasoning and geometric relationships model real-world situations.

MA-7-G-S-SR1. Program of Studies: Skills and Concepts - Students will describe, provide examples of and identify (using correct notation, label and name) the basic geometric elements (e.g., points, segments, rays, lines, angles and planes), including both real world and/or mathematical situations.

MA-7-G-S-SR2. Program of Studies: Skills and Concepts - Students will identify characteristics of angles (e.g., adjacent, vertical, corresponding, interior, exterior).

MA-7-G-S-SR3. Program of Studies: Skills and Concepts - Students will identify properties for classifying, describe, provide examples of and identify elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular and irregular polygons); apply properties of these figures to solve real-world problems.

MA-7-G-S-SR4. Program of Studies: Skills and Concepts - 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-7-G-S-SR5. Program of Studies: Skills and Concepts - Students will represent three-dimensional geometric objects with special attention to developing spatial sense (e.g., top view, side view, three-dimensional objects drawn on isometric dot paper).

MA-7-G-S-SR6. Program of Studies: Skills and Concepts - Students will describe and provide examples of congruent and similar figures and apply congruent and similar figures to solve real-world problems.

MA-7-G-S-CG1. Program of Studies: Skills and Concepts - Students will identify and graph ordered pairs on a coordinate system, identifying the origin, axes and ordered pairs.

MA-7-G-S-CG2. Program of Studies: Skills and Concepts - Students will apply graphing in the coordinate system to solve real-world and/or mathematical problems.

MA-7-G-S-TS1. Program of Studies: Skills and Concepts - Students will move shapes in a plane and/or in a coordinate plane (translate [slide], rotate [turn] about the origin or a vertex, reflect [flip] over a horizontal or vertical line).

MA-7-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-7-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-7-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-7-DAP-U-3. Program of Studies: Understandings - Students will understand that the choice of data display can affect the visual message communicated.

MA-7-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-7-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-7-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-7-DAP-S-DR1. Program of Studies: Skills and Concepts - Students will collect, organize, construct, analyze and interpret data and data displays in a variety of graphical methods, including circle graphs, multiple line graphs, double bar graphs and double stem-and-leaf plots.

MA-7-DAP-S-DR2. Program of Studies: Skills and Concepts - Students will select an appropriate graph to represent given data and justify its use.

MA-7-DAP-S-DR3. Program of Studies: Skills and Concepts - Students will compare data from various types of graphs.

MA-7-DAP-S-DR4. Program of Studies: Skills and Concepts - Students will relate different representations of data (e.g., tables, graphs, diagrams, plots).

MA-7-DAP-S-DR5. Program of Studies: Skills and Concepts - Students will read/interpret, analyze and make inferences from a box and whisker plot of data and make predictions and draw conclusions from the data.

MA-7-DAP-S-DR6. Program of Studies: Skills and Concepts - Students will make decisions about how misleading representations affect interpretations and conclusions about data (e.g. changing the scale on a graph).

MA-7-DAP-S-ES1. Program of Studies: Skills and Concepts - Students will pose questions; collect, organize and display data.

MA-7-DAP-S-ES2. Program of Studies: Skills and Concepts - Students will explore how sample size affects the reliability of the outcome.

MA-7-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-7-DAP-S-CD2. Program of Studies: Skills and Concepts - Students will determine, apply and compare measures of mean, median, mode and/or range, as appropriate to the problem situation.

MA-7-DAP-S-CD3. Program of Studies: Skills and Concepts - Students will identify clusters, gaps and outliers within the data.

MA-7-DAP-S-P1. Program of Studies: Skills and Concepts - Students will make predictions, draw conclusions and verify results from statistical data and probability experiments.

MA-7-DAP-S-P2. Program of Studies: Skills and Concepts - Students will determine appropriate techniques to use when investigating possible outcomes of probability problems (using counting techniques, tree diagrams, area models and exhaustive organized lists, charts and tables).

MA-7-DAP-S-P3. Program of Studies: Skills and Concepts - Students will investigate and explain the role of probability in decision making.

MA-7-DAP-S-P4. Program of Studies: Skills and Concepts - Students will design and conduct probability experiments.

MA-7-DAP-S-P5. Program of Studies: Skills and Concepts - Students will determine theoretical (mathematical) probabilities (expressed as a ratio, decimal or percent), compare to experimental results and explain reasons why there might be differences.

MA-7-DAP-S-P6. Program of Studies: Skills and Concepts - Students will explore concepts of randomness and independent events.

MA-7-DAP-S-P7. Program of Studies: Skills and Concepts - Students will apply counting techniques to determine the size of a sample space.

MA-7-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-7-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-7-AT-U-2. Program of Studies: Understandings - Students will understand that numerical patterns can be written as rules that generate the pattern.

MA-7-AT-U-3. Program of Studies: Understandings - Students will understand that algebra represents mathematical situations and structures for analysis and problem solving.

MA-7-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-7-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-7-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-7-AT-S-PRF1. Program of Studies: Skills and Concepts - Students will recognize, create and extend patterns and generalize the pattern by determining the rule for any term.

MA-7-AT-S-PRF2. Program of Studies: Skills and Concepts - Students will represent, analyze and generalize functional relationships (input/output) through tables, graphs and verbal rules.

MA-7-AT-S-PRF3. Program of Studies: Skills and Concepts - Students will organize input-output coordinate pairs into tables and plot points in all four quadrants of a coordinate (Cartesian) system/grid; interpret resulting patterns/trends.

MA-7-AT-S-PRF4. Program of Studies: Skills and Concepts - Students will relate tables, graphs, verbal rules and equations.

MA-7-AT-S-PRF5. Program of Studies: Skills and Concepts - Students will explain how the change in the input affects the change in the output (e.g., in tables or graphs).

MA-7-AT-S-VEO1. Program of Studies: Skills and Concepts - Students will simplify numeric and algebraic expressions.

MA-7-AT-S-VEO2. Program of Studies: Skills and Concepts - Students will substitute values for variables to evaluate algebraic expressions.

MA-7-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-7-AT-S-EI1. Program of Studies: Skills and Concepts - Students will use multiple representations to model and solve single-variable equations and inequalities.

MA-7-AT-S-EI2. Program of Studies: Skills and Concepts - Students will solve problems involving formulas.

MA-7-AT-S-EI3. Program of Studies: Skills and Concepts - Students will model and solve real-world problems with one- or two-step equations or inequalities (e.g., 2x + 1 = 9, 3x + 3 < 9).

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-07-1. 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-07-1.1. Number Sense

MA-07-1.1.1. Students will provide examples of and identify integers, fractions, decimals, percents and pi. DOK 1

MA-07-1.1.2. Students will describe and provide examples of representations of numbers (whole numbers, fractions, decimals, percents, integers, square roots and pi) 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 mathematical problems.

MA-07-1.1.3. Students will convert among whole numbers, fractions, decimals, percents and pi and will compare and order these numbers. DOK 2

MA-07-1.2. Estimation

MA-07-1.2.1. Students will estimate to solve real-world and mathematical problems with fractions, decimals and percents, checking for reasonable and appropriate computational results. DOK 2

MA-07-1.3. Number Operations

MA-07-1.3.1. Students will add, subtract, multiply and divide whole numbers, fractions and decimals to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions. DOK 2

MA-07-1.3.2. Students will explain how operations (addition and subtraction; multiplication and division) are inversely related.

MA-07-1.3.3. Students will add and subtract integers.

MA-07-1.4. Ratios and Proportional Reasoning

MA-07-1.4.1. Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, sales tax, discounts, rate). DOK 3

MA-07-1.5. Properties of Numbers and Operations

MA-07-1.5.1. 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-07-1.5.2. 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 justify a given step in solving problems. DOK 1

MA-07-2. 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-07-2.1. Measuring Physical Attributes

MA-07-2.1.1. 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, trapezoids) (using the Pythagorean theorem will not be required as a strategy); area and circumference of circles and area and perimeter of compound figures composed of triangles, quadrilaterals and circles. DOK 2

MA-07-2.1.2. Students will estimate measurements of regular and irregular polygons and circles in standard units.

MA-07-2.1.3. Students will explain how measurements and measurement formulas are related or different (e.g., perimeter and area of rectangles).

MA-07-2.1.4. Students will find the measures of angles by estimation and determine measurement with a protractor or angle ruler.

MA-07-2.2. Systems of Measurement

MA-07-2.2.1. Students will convert units within the same measurement system and use these units to solve real-world problems.

MA-07-3. 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-07-3.1. Shapes and Relationships

MA-07-3.1.1. Students will describe, provide examples of and identify (using correct notation, label and name) the basic geometric elements (e.g., points, segments, rays, lines, angles and planes) in real-world and mathematical problems.

MA-07-3.1.2. Students will describe and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular polygons) and will apply these elements and figures to solve real-world and mathematical problems. DOK 2

MA-07-3.1.3. 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-07-3.1.4. Students will describe and provide examples of congruent and similar figures and will apply congruent and similar figures to solve real-world and mathematical problems. DOK 2

MA-07-3.2. Transformations of Shapes

MA-07-3.2.2. Students will translate (slide) and reflect (flip) figures in a coordinate plane.

MA-07-3.2.3. Students will identify rotations (clockwise or counterclockwise) of figures about the origin in the plane (90 degrees, 180 degrees, 270 degrees).

MA-07-3.3. Coordinate Geometry

MA-07-3.3.1. Students will identify and graph ordered pairs on a coordinate system, 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-07-4. 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-07-4.1. Data Representations

MA-07-4.1.1. 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, scatter plots). DOK 3

MA-07-4.1.2. Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.

MA-07-4.1.3. Students will read/interpret, analyze and make inferences from box and whisker plots of data and make predictions and draw conclusions from the data.

MA-07-4.1.4. Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs, stem-and-leaf plots) and will explain why the type of display is appropriate for the data. DOK 2

MA-07-4.1.5. Students will make decisions about how misleading representations affect interpretations and conclusions about data (e.g. changing the scale on a graph).

MA-07-4.2. Characteristics of Data Sets

MA-07-4.2.1. Students will determine the mean, median, mode and range of a set of data and will identify clusters, gaps and outliers within the data. DOK 2

MA-07-4.4. Experiments and Samples (not assessed at this level) - Probability

MA-07-4.4.1. Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation. DOK 2

MA-07-4.4.2. Students will determine theoretical probabilities of simple events; determine probabilities based on the results of an experiment and make inferences from probability data. DOK 3

MA-07-4.4.3. Students will tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related.

MA-07-5. 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-07-5.1. Patterns, Relations and Functions

MA-07-5.1.1. Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems. DOK 3

MA-07-5.1.2. Students will represent, analyze and generalize first degree relationships using tables, graphs and words and will apply the relationships to solve real-world and mathematical problems. DOK 2

MA-07-5.1.3. Students will explain how tables, graphs, patterns, verbal rules and equations relate to each other.

MA-07-5.1.5. Students will explain how the change in one quantity affects the change in another quantity (e.g., in tables or graphs). DOK 2

MA-07-5.2. Variables, Expressions and Operations

MA-07-5.2.1. Students will substitute values for variables (up to three different variables) and evaluate algebraic expressions. DOK 2

MA-07-5.2.2. Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.

MA-07-5.3. Equations and Inequalities

MA-07-5.3.1. Students will model and solve real-world and mathematical problems with one- or two-step single variable, first degree equations or inequalities (e.g., 2x+1 = 9, 3x+3 < 9). (Statements and solutions use only non-negative numbers.) DOK 2