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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 6 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 and whole numbers 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 6 Skills and Concepts – Number Sense Students will • continue to develop number sense using fractions, decimals and percents, including percents greater than 100% and improper fractions • extend applications of operations (+,-,×,÷ ) to include fractions and decimals • develop place value of large and small numbers, including decimals • explore positive integral exponents (e.g. squares, cubes) • compare, order and convert between whole numbers, fractions, decimals and percents using concrete materials, drawings or pictures and mathematical symbols (e.g., <,=,>,=,=,. , order on a number line) Grade 6 Skills and Concepts – Estimation 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 • estimate large and small quantities of objects |
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MA-06-1.1.1 Fractions/Decimals/Percent
The learner will be able to provide examples of and describe fractions, decimals, and percents. DOK - 1 .
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MA-06-1.1.2 Number Representations
The learner will be able to 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.
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MA-06-1.1.3 Number Sense
The learner will be able to convert between any two of the following numbers: fractions, decimals, and percents (less than or equal to 100%; and will compare these numbers. DOK - 2 .
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MA-06-1.2.1 Estimation
The learner will be able to estimate to solve real-world and/or mathematical problems with whole numbers, fractions, decimals, and percents, checking for reasonable and appropriate computational results. DOK - 2 .
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MA-06-1.3.1 Number Operations
The learner will be able to add, subtract, multiply, divide, and apply order of operations with whole numbers, fractions, and decimals to solve real-world problems. DOK - 2 .
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MA-06-1.3.2 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-06-1.4.1 Ratios / Real-world Problem
The learner will be able to describe and apply ratios to solve real-world problems. DOK - 2 .
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MA-06-1.5.1 Prime Factorizaton
The learner will be able to identify and apply prime numbers, composite numbers, prime factorization, factors, multiples, and divisibility to solve real-world problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK - 2 .
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MA-06-1.5.2 Properties /Adddition / Mul
The learner will be able to identify how the commutative properties, the associative properties, and the identity properties for addition and multiplication are used to simplify numerical expressions. DOK - 1 .
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| Measurement |
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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 U.S. Customary and metric units of measurement. 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 6 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 6 Skills and Concepts – Measuring Physical Attributes Students will • find perimeter of regular and irregular polygons in metric and U.S. customary units • read and use measurement tools (e.g., rulers, scales, protractors, angle rulers) • find area of plane figures composed of triangles, squares and rectangles by subdividing and measuring; use square units appropriately • estimate and find angle measures and segment measures • estimate measurements in standard units, including fractions and decimals • explain how measurements and measurement formulas are related or different (e.g., compare the perimeter with the area of a rectangle) Grade 6 Skills and Concepts – Systems of Measurement 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 • 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: o length (e.g., parts of an inch, inches, feet, yards, miles, millimeters, centimeters, meters, kilometers); o weight/mass (e.g., pounds, tons, grams, kilograms); o volume/capacity (e.g., cups, pints, quarts, gallons, milliliters, liters) |
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MA-06-2.1.1 Measuring Phy Attributes
The learner will be able to determine: " Measures of rectangles and figures that can be divided into rectangular shapes, including lengths to the nearest eighth of an inch or nearest centimeter; and " The area and perimeter of triangles and quadrilaterals (rectangles, squares). (Using the Pythagorean theorem will not be required as a strategy.) DOK - 2 .
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MA-06.2.1.2 Measurements Estimates
The learner will be able to estimate measurements in standard units including fractions and decimals.
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MA-06-2.1.3 Measurement Formulas
The learner will be able to explain how measurements and measurement formulas are related or different (perimeter and area of rectangles).
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MA-06-2.2.4 U.S. and Metric Units
The learner will be able to describe and provide examples of U.S. Customary and metric units of measurement and use these units to solve real-world and/or mathematical problems.
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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 6 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 6 Skills and Concepts – Shapes and Relationships Students will • formulate and use the rules for the sum of angle measures in a triangle (180°) and in a quadrilateral (360°) • identify and use relationships among lines (e.g., parallel, perpendicular) • identify, describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference) • 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 • 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) • describe and provide examples of congruent and similar plane figures; apply congruent and similar plane figures to solve real-world problems Grade 6 Skills and Concepts – Transformations of Shapes 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 • 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 • explore the rotation of a figure in a plane in the first quadrant, with and without manipulatives Grade 6 Skills and Concepts – Coordinate Geometry Students will • identify and graph ordered pairs on a positive coordinate system, identifying the origin, axes and ordered pairs • apply graphing in the positive coordinate system to solve real-world and mathematical problems |
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MA-06-3.1.1 Geometric Elements -Basic
The learner will be able to describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference). DOK - 2 .
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MA-06-3.1.2 Two-dimensional Figures
The learner will be able to describe, and provide examples and properties of two-dimensional figures (circles, triangles, quadrilaterals, regular polygons), and will apply these properties and figures to solve real-world problems. DOK - 2 .
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MA-06-3.1.4 Three-dimensional Figures
The learner will be able to 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).
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MA-06-3.1.5 Congruent and Simular Fig
The learner will be able to describe and provide examples of congruent and similar figures, and will apply congruent and similar figures to solve real-world problems. DOK - 2 .
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MA-06-3.2.1 Line symmetry
The learner will be able to describe, provide examples of, and apply line symmetry to real world and/or mathematical situations.
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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-06-3.2.3 Move Shapes
The learner will be able to move shapes in Quadrant I of the coordinate plane: rotate (turn).
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MA-06-3.3.1 Ordered Pairs
The learner will be able to identify and graph ordered pairs on a positive 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 6 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. Grade 6 Skills and Concepts – Data Representations Students will • select an appropriate graph to represent given data and justify the selection • 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 • compare data from various types of graphs • relate different representations of data (e.g., tables, graphs, diagrams, plots) Grade 6 Skills and Concepts – Characteristics of Data Students will • make predictions, draw conclusions and verify results from statistical data and probability experiments • determine and apply measures of distribution (mean, median, mode, range) Grade 6 Skills and Concepts – Experiments and Samples • pose questions; collect, organize and display data • explore how sample size affects the reliability of the outcome Grade 6 Skills and Concepts – Probability Students will • describe or determine (e.g., tables, tree diagrams) the sample space of an event • investigate solutions to probability problems using counting techniques, tree diagrams, charts and tables • make predictions, draw conclusions and verify results from statistical data and probability experiments • determine simple probabilities based on the results of an experiment and make inferences based on the data • explore the role of probability in decision making |
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MA-06-4.1.1 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). DOK - 3 .
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MA-06-4.1.2 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-06-4.1.3 Data Displays / Construct
The learner will be able to construct 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 .
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MA--6-4.2.1 Mean/Median/Mode/Range
The learner will be able to determine and apply the mean, median, mode, and range of a set of data. DOK - 2 .
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MA-06-4.4.1 Tables / tree diagrams
The learner will be able to describe or determine (e.g., tables, tree diagrams) the sample space of an event. DOK - 2 .
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MA-06-4.4.2 Simple Probabilities
The learner will be able to determine simple probabilities based on the results of an experiment and will make inferences based on the data. DOK - 3 .
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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 6 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 6 Skills and Concepts – Patterns, Relations and Functions 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) • represent, interpret and describe function relationships through tables, graphs and verbal rules • organize input-output coordinate pairs into tables and plot points in the first quadrant of a coordinate (Cartesian) system/grid • explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables) Grade 6 Skills and Concepts – Variables, Expressions and Operations Students will • explore the use of variables in expressions and equations • substitute numerical values for variables and evaluate algebraic expressions • describe, define and provide examples of algebraic expressions based on real-world and/or mathematical situations Grade 6 Skills and Concepts – Equations and Inequalities Students will • use concrete and/or informal methods to solve equations with one variable that model real-world situations • solve problems involving simple formulas (e.g., A=lw, D=rt) • model and solve real-world problems with one variable equations and inequalities (e.g., 8x=4, x+2>5) |
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MA-06-5.1.1 Rules for patterns / Extend
The learner will be able to extend and describe rules for patterns from real-world and/or mathematical problems DOK - 3 .
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MA-06-5.1.2 Tables/Create
The learner will be able to will create tables for functions and will apply the tables to solve real-world problems. DOK - 2 .
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MA-06-5.1.3 Functions / Using Tables
The learner will be able to describe, define, provide examples of, and apply to real world and/or mathematical situations functions using tables, graphs and verbal rules.
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MA-06-5.1.4 Tables, Graphs / Relate
The learner will be able to explain how tables and graphs and patterns relate to each other.
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MA-06-5.1.5 Change in one Quanity
The learner will be able to explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables).
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MA-06-5.2.1 Substitute values for varia
The learner will be able to substitute values for variables (up to two different variables) and evaluate algebraic expressions. DOK - 2.
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MA-06-5.2.2 Expressions w Missing Varia
The learner will be able to describe, define, and provide examples of variables and expressions with a missing value based on real-world and/or mathematical situations.
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MA-06-5.3.1 Simple equations / inequal
The learner will be able to model and solve real-world problems with simple equations and inequalities (e.g., 8x=4, x+2>5). DOK - 2 .
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