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Bullitt County Public Schools |
| Number Properties and Operations |
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Program of Studies 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 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. Grade 8 Enduring Knowledge – Understandings Students will understand that • numbers, ways of representing numbers, relationships among numbers and number systems are means of representing real-world quantities. • meanings of and relationships among operations provide tools necessary to solve realistic problems encountered in everyday life. • computing fluently and making reasonable estimates with fractions, decimals, percents and integers increases the ability to solve realistic problems encountered in everyday life. • proportional reasoning is a tool for modeling and solving problems encountered in everyday situations. Grade 8 Skills and Concepts – Number Sense Students will • continue to develop number sense to include irrational numbers (e.g., square roots, cube roots, ð) • provide examples of, describe and compare irrational and rational numbers (e.g., magnitude, order on a number line, scientific notation, very large and very small integers, numbers close to zero) • describe and provide multiple representations of numbers (rational, square roots, cube roots and ð) in a variety of equivalent forms using models, diagrams and symbols based on real-world and/or mathematical situations Grade 8 Skills and Concepts – Estimation Students will • estimate to solve real-world and/or mathematical problems with rational numbers and common irrational numbers, checking for reasonable and appropriate computational results • estimate with large and small quantities of objects Grade 8 Skills and Concepts – Number Operations Students will • add, subtract, multiply, divide and apply order of operations (including positive whole number exponents) using rational numbers to solve real-world problems • determine and explain the inverse relationship between addition and subtraction, multiplication and division, or raising to an exponent and taking the root of a number Kentucky Department of Education Program of Studies – Mathematics – Eighth Grade 323 Big Idea: Number Properties and Operations – Continued Grade 8 Skills and Concepts – Ratios and Proportional Reasoning Students will • use percentages and proportions in problem solving, including consumer applications (e.g., simple interest, percentages of increase and decrease, discounts, unit pricing, sale prices) • derive and use formulas for various rates (e.g., distance/time, miles per hour) Grade 8 Skills and Concepts – Properties of Numbers and Operations Students will • identify and use the commutative properties, the associative properties, the identity properties and the inverse properties for addition and multiplication, the distributive property and inverse relationships to justify a given step in solving problems |
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MA-08-1.1.1 Rational / Irrational
The learner will be able to provide examples of and describe rational numbers and irrational numbers (square roots and p only). DOK - 1 .
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MA-08-1.1.2 Number Representations
The learner will be able to describe and provide examples of representations of numbers (rational, square roots, and p) 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.
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MA-08-1.1.3 Number Rep/ convert, compar
The learner will be able to convert, compare and order multiple numerical representations (e.g., fractions, decimals, percentages) of rational numbers and irrational numbers (square roots and p only). DOK 2 .
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MA-08-1.2.1 Estimation / Solve Problems
The learner will be able to estimate to solve real-world and/or mathematical problems with rational numbers, checking for reasonable and appropriate computational results DOK - 2 .
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MA-08-1.3.1 Operations / Order of
The learner will be able to add, subtract, multiply, divide, and apply order of operations (including positive whole number exponents) with rational numbers to solve real-world problems. DOK - 2 .
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MA-08-1.3.2 Operations Inversly Relate
The learner will be able to explain how operations (addition and subtraction; multiplication and division) are inversely related.
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MA-08-1.4.1 Ratios / Real-world Problem
The learner will be able to apply ratios and proportional reasoning to solve real-world problems (e.g., percents, constant rate of change, unit pricing, percent of increase or decrease). DOK - 3 .
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MA-08-1.5.2 Properties /Adddition / Mul
The learner will be able to will identify how the commutative properties, the associative properties, the distributive property, the identity properties for addition and multiplication, and inverse relationships justify a given step in solving problems. DOK - 1 .
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| Measurement |
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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 Program of Studies 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. They use the Pythagorean theorem. Academic Expectations 2.10 Students understand measurement concepts and use measurements appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. Grade 8 Enduring Knowledge – Understandings Students will understand that • there are two major measurement systems (U.S. Customary and metric) and either may be used to solve problems. • measurable attributes of objects and the units, systems and processes of measurement are powerful tools for making sense of the world around them. • measurements are determined by using appropriate techniques, tools, formulas and degree of accuracy needed for the situation. Grade 8 Skills and Concepts – Measuring Physical Attributes Students will • read and use measurement tools (e.g., rulers, scales, protractors, angle rulers, CBL/CBRs) • estimate and find angle measures and segment measures • determine measures of the lengths of sides and the perimeter both regular and irregular shapes, including lengths to the nearest sixteenth of an inch or the nearest millimeter • determine the area of triangles and quadrilaterals • determine the area and circumference of circles • develop and apply the Pythagorean theorem • develop and apply formulas for volume and surface area of cubes, cylinders and right rectangular prisms; investigate relationships between and among them • estimate measurements in standard units in real world and/or mathematical situations • explain how measurements and measurement formulas are related or different (perimeter and area; rate, time and distance; circumference and area of a circle) Grade 8 Skills and Concepts – Systems of Measurement Students will • provide examples of and apply money, time and U.S. Customary and metric units of measurement to solve real-world problems |
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MA-08-2.1.1 Measuring Phy Attributes
The learner will be able to measure lengths (to the nearest sixteenth of an inch or the nearest millimeter) and will determine and use in real-world or mathematical problems: " area and perimeter of triangles and quadrilaterals; " area and circumference of circles; " area and perimeter of compound figures composed of triangles, quadrilaterals and circles; " area from circumference or perimeter and " circumference or perimeter from area. DOK 3 .
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MA-08.2.1.2 Measurements Estimates
The learner will be able to estimate measurements in standard units in real world and/or mathematical situations.
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MA-08-2.1.3 Measurement Angles
The learner will be able to evaluate the measures of angles by estimation, measurement with a protractor or angle ruler and determine angle measures in mathematical and/or real-world situations (e.g., supplementary, external, vertical). DOK 2 .
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MA-08-2.1.4 Right Rectangular Prisims
The learner will be able to apply formulas to determine the volume of right rectangular prisms in real-world problems. DOK - 2 .
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MA-08-2.1.5 Surface Area / Rt Rec Prisi
The learner will be able to will use formulas to find surface area of right rectangular prisms in real world and/or mathematical situations.
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MA-08-2.1.6 Pythagorean Theorem
The learner will be able to apply the Pythagorean theorem to determine the length of a hypotenuse. DOK - 2 .
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MA-08-2.2.1 Convert Units of Measure
The learner will be able to convert units within the same measurement system and use these units to solve real-world problems. DOK 2 .
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| Geometry |
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Program of Studies 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 Students understand various mathematical procedures and use them appropriately and accurately. 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. Grade 8 Enduring Knowledge – 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. • 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. • transformations and symmetry are used to analyze real-world situations (e.g., art, nature, construction and scientific exploration). • shape and area are conserved during mathematical transformations (flips, slides and turns). Scale conserves shape but changes size. • visualization, spatial reasoning and geometric relationships model real-world situations. Grade 8 Skills and Concepts – Shapes and Relationships Students will • describe and provide examples of basic geometric elements that include points, segments, rays, lines, angles and planes; use these elements in real-world and/or mathematical situations • identify and compare properties of two-dimensional figures (circles; triangles: acute, right, obtuse, scalene, isosceles, equilateral; quadrilaterals: square, rectangle, rhombus, parallelogram, trapezoid; regular/irregular polygons); apply these properties and figures to solve real-world problems • compare properties of three-dimensional figures (spheres, cones, cylinders, prisms, pyramids); apply these properties and figures to solve real-world problems • provide examples of and apply congruent and similar two-dimensional figures to solve real-world problems • apply proportional reasoning to solve problems involving scale models and real objects and scale drawings and similar two-dimensional figures Grade 8 Skills and Concepts – Transformations of Shapes Students will • investigate the congruence, proportionality and/or similarity of pre-images and images of dilations (e.g., enlargements, reductions) in a coordinate plane • describe, provide examples of and apply to real-world and/or mathematical situations rotational symmetry (45°, 90º, 180º, 270º, 360º) • rotate (clockwise or counterclockwise) shapes in a coordinate plane about the origin • transform figures in a coordinate plane (translations, reflections and dilations [magnifications and contractions] with the center of dilation at the origin); determine the new coordinates of the image after the transformation |
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MA-08-3.1.1 Geometric Elements -Basic
The learner will be able to 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.
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MA-08-3.1.2 Two-dimensional Figures
The learner will be able to will identify and compare properties of two-dimensional figures (circles, triangles acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular/irregular polygons) and will apply these properties and figures to solve real-world and mathematical problems. DOK 2 .
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MA-08-3.1.3 Three-dimensional Figures
The learner will be able to compare properties of three-dimensional figures (spheres, cones, cylinders, prisms, pyramids) and will apply these properties and figures to solve real-world and mathematical problems. DOK 2 .
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MA-08-3.1.4 Congruent and Simular Fig
The learner will be able to "" provide examples of congruent and similar figures; " apply congruent and similar figures to solve real-world and mathematical problems and " apply proportional reasoning to solve problems involving scale drawings and proportional figures. DOK 3 .
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MA-08-3.2.1 Rotational Symmetry
The learner will be able to describe, provide examples of and apply to real-world and mathematical problems rotational symmetry (90º, 180º, 360º).
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MA-06-3.2.2 Coordinate Plane
The learner will be able to 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. DOK - 2 .
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MA-08-3.2.3 Rotations / Identify
The learner will be able to identify rotations (clockwise or counterclockwise) of figures about the origin in a coordinate plane.
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MA-08-3.3.1 Ordered Pairs
The learner will be able to 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 problems. DOK - 2 .
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| Data Analysis and Probability |
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Program of Studies 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 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.13 Students understand and appropriately use statistics and probability. Grade 8 Enduring Knowledge – Understandings Students will understand that • quantitative literacy is a necessary tool to be an intelligent consumer and citizen. • the collection, organization, interpretation and display of data can be used to answer questions. • the choice of data display can affect the visual message communicated. • inferences and predictions from data are used to make critical and informed decisions. • 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. • probability can be used to make decisions or predictions or to draw conclusions. Skills and Concepts – Data Representations Students will • collect, organize, construct, analyze and make inferences from data in a variety of graphical methods (e.g., drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, scatter plots, histograms, box-and-whiskers plots) • select an appropriate graph to represent data and justify its use • compare similar data from various types of graphs • relate different representations of data (e.g., tables, graphs, diagrams, plots) and explain how misleading representations affect interpretations and conclusions about data Big Idea: Data Analysis and Probability Grade 8 Skills and Concepts – Characteristics of Data Students will • determine and interpret clusters, quartiles, gaps and outliers in data • make predictions, draw conclusions and verify results from statistical data and probability experiments, making use of technology as appropriate • determine and interpret the mean, median, mode and range of a set of data • compare sets of data • explore how statistics can be interpreted in many ways Grade 8 Skills and Concepts – Experiments and Samples Students will • explain how data gathering, bias issues or faulty data analysis can affect the results of data collection, data representation and data interpretation Grade 8 Skills and Concepts – Probability Students will • make predictions, draw conclusions and verify results from probability experiments or simulations, making use of technology as appropriate • analyze situations, such as games of chance, board games or grading scales and make predictions using knowledge of probability • identify and describe the number of possible arrangements of several objects, using a tree diagram or the basic counting principle; make a list, picture, chart or tree diagram to represent a sample space • investigate counting techniques (e.g., networks) • investigate and explain the role of probability in everyday decision making • explore concepts of randomness and independent events • determine theoretical (mathematical) probabilities ( e.g., express probability as a ratio, decimal, percent, area model as appropriate for a given situation) • compare theoretical and experimental results and explain reasons why there might be differences |
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MA-08-4.1.1 Data Displays
The learner will be able to 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 .
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MA-08-4.1.2 Data sets /Related
The learner will be able to explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.
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MA-0-4.1.4 Data Displays / Construct
The learner will be able to "" construct data displays (Venn diagrams, tables, line graphs, stem-and-leaf plots, circle graphs, scatter plots); " explain why the type of display is appropriate for the data and " explain how misleading representations affect interpretations and conclusions about data (e.g., changing the scale on a graph). DOK 2 .
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MA-08-4.1.5 Box/Whisker Plots
The learner will be able to construct box-and-whiskers plots.
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MA--8-4.2.1 Mean/Median/Mode/Range
The learner will be able to "" determine the mean, median, mode and range of a set of data; " identify clusters, gaps and outliers and " apply these concepts to compare sets of data. DOK 2 .
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MA-08-4.3.1 Data / Bias issues
The learner will be able to explain how data gathering, bias issues and faulty data analysis can affect the results of data collection.
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MA-08-4.4.1 Sample Space / Size
The learner will be able to apply counting techniques to determine the size of a sample space. DOK - 2 .
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MA-08-4.4.2 Simple Probabilities
The learner will be able to "" Determine theoretical probabilities of simple events; " Determine probabilities based on the results of an experiment; and " Make inferences from probability data. DOK - 3 .
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MA-08-4.4.3 Results / tabulate
The learner will be able to tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related.
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MA-08-4.4.4 Data Models
The learner will be able to will determine theoretical probabilities and represent them using area models.
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| Algebraic Thinking |
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Program of Studies 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 twostep single variable equations and inequalities. Academic Expectations 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. Grade 8 Enduring Knowledge – Understandings Students will understand that • patterns, relations and functions are tools that help explain or predict real-world phenomena. • numerical patterns can be written as rules that generate the pattern. • algebra represents mathematical situations and structures for analysis and problem solving. • real-world situations can be represented using mathematical models to analyze quantitative relationships. • functions are used to analyze change in various contexts and model real-world phenomena. Functions can be written in words, in a symbolic sentence or in a table. Grade 8 Skills and Concepts – Patterns, Relations and Functions Students will • recognize, create and extend patterns (generalize the pattern by giving the rule for the nth term and explain the generalization) • represent, interpret and describe linear and simple quadratic functional relationships (input/output) through tables, graphs and symbolic rules • organize input-output coordinate pairs into tables, plot points in all four quadrants of a coordinate (Cartesian) system/grid and interpret resulting patterns or trends using technology as appropriate • interpret and explain relationships between tables, graphs, verbal rules and equations, using technology as appropriate • graph linear functions in a four quadrant (Cartesian) system/grid and interpret the results, using technology as appropriate • explain how change in the input affects change in the output (e.g., in d=rt, increasing the time (t) increases the distance (d)) Grade 8 Skills and Concepts – Variables, Expressions and Operations Students will • apply order of operations to evaluate and simplify algebraic expressions • given a formula, substitute appropriate elements from a real-world or mathematical situation • describe, define and provide examples of variables and expressions with a missing value based on real-world and/or mathematical situations Grade 8 Skills and Concepts – Equations and Inequalities Students will • use multiple representations to model and solve one- and two-variable linear equations • solve problems using formulas • investigate linear inequalities using a variety of methods and representations • model and solve real-world problems with one- or two-step equations or inequalities (e.g., 4x+2=22, x-4<-60) |
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MA-08-5.1.1 Numerical Patterns / Variab
The learner will be able to use variables to describe numerical patterns based on arithmetic sequences in real-world and mathematical problems (e.g., ( ) = 2 +3).
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MA-08-5.1.2 Tables/Analyze
The learner will be able to represent, analyze and generalize simple first and second degree functional relationships using tables, graphs, words and algebraic notations and will apply the first degree relationships to solve real-world and mathematical problems. DOK 2 .
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MA-08-5.1.5 Change in one Variable
The learner will be able to will explain how the change in one variable affects the change in another variable (e.g., if rate remains constant, an increase in time results in an increase in distance). DOK 2 .
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MA-08-5.2.1 Algebraic Expressions/Simp
The learner will be able to evaluate and simplify algebraic expressions applying the order of operations. DOK 2 .
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MA-08-5.2.2 Expressions / Missing Value
The learner will be able to describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.
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MA-08-5.3.1 Single Variable Problems
The learner will be able to model and solve single variable, first-degree real-world and mathematical problems (e.g., 5x+2 = x+22, x-4 < -60). DOK 2 .
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