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Bullitt County Public Schools |
| Number Properties and Operations |
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Big Idea: Number Properties and Operations Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop multiplication and division. They move flexibly and fluently through basic number facts, operations and representations. Their understanding of the base-10 number system expands to include decimals. They examine various meanings and models of fractions. They explore data, perform measurements and examine patterns as part of the development process for number and operations, using other mathematics strands to enrich number. Elementary number encompasses computational fluency with whole numbers, relationships between decimals and fractions and techniques for reasonable estimations. 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. Primary Enduring Knowledge – Understandings Students will understand that • numbers, ways of representing numbers, relationships between 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 increases the ability to solve realistic problems encountered in everyday life. Primary Skills and Concepts – Number Sense Students will • read, write, count and model whole numbers 0-10,000, developing an understanding of place value for ones, tens, hundreds, thousands and ten thousands • apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to describe and compare whole numbers and fractions (e.g., halves, thirds, fourths) in mathematical and real-world problems • order groups of objects according to quantity • order, compare and understand the relative magnitude of numbers from 0-10,000, using the symbols <, >, =, including the use of physical and visual models for smaller numbers • develop beginning fractional concepts (e.g., dividing an object into equal parts and naming the equal parts [e.g., halves, thirds, fourths]) • expand fraction concepts (e.g., whole to part and part to whole; one-half is larger than one-fourth) • be introduced to and use decimals to represent money Kentucky Department of Education Program of Studies – Mathematics – Primary 38 Big Idea: Number Properties and Operations – Continued Primary Skills and Concepts – Estimation Students will • explore appropriate estimation procedures for different situations • apply and describe appropriate strategies for estimating quantities of objects and computational results Primary Skills and Concepts – Number Operations Students will • develop an understanding of the concepts of addition and subtraction using physical objects and concrete materials • explore and develop an understanding of the concepts of multiplication and division using physical models • develop part-whole relations using numbers (e.g., 3+2=5, 1+4=5) • explore and solve two-digit addition and subtraction problems through the use of manipulatives • explore and develop factor-factor-product (e.g., 2x3=6) using manipulatives. (e.g., hundreds charts, base-10 blocks, arrays) • multiply whole numbers through 10 x 10 • relate division facts to multiplication facts (e.g., using factor-factor-product) • solve multi-digit addition and subtraction problems that contain numerals and symbols • add common fractions with like denominators using manipulatives • add and subtract decimals using money • use mental math, pencil-and-paper methods, calculators and/or computers to explore mathematical concepts and to assist with computation in problem solving situations Primary Skills and Concepts – Properties of Numbers and Operations Students will • explore, develop and use the concepts of multiples • skip-count forwards and backwards by 2s, 5s, 10s and 100s, using manipulatives, mental math and written and electronic means to communicate understanding • explore, develop and use the concepts of odd and even numbers • explore and use of properties of numbers for written and mental computation (e.g., 4+7+6 could be mentally regrouped as 4+6+7 using the commutative property of addition) |
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MA-EP-1.1.1 Represent Numbers
The learner will be able to "" Apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to describe whole numbers (0 to 9,999): " Apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to describe fractions (halves, thirds, fourths); " Apply these numbers to represent real-world problems; and " Explain how the base 10 number system relates to place value. DOK - 2 .
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MA-EP-1.1.2 Whole Numbers
The learner will be able to read, write, and rename whole numbers (0 to 9,999) and apply to real-world and mathematical situations.
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MA-EP-1.1.3 Whole Numbers / Fractions
The learner will be able to compare (<, >, =) and order whole numbers to whole numbers, decimals to decimals (as money only) and fractions to fractions (limited to pictorial representations). DOK - 1 .
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MA-EP-1.2.1 Estimation
The learner will be able to apply and describe appropriate strategies for estimating quantities of objects and computational results (limited to addition and subtraction). DOK 2.
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MA-EP-1.3.1 Operations
The learner will be able to analyze real-world situations to identify the appropriate mathematical operations, and will apply operations to solve real-world problems with the following constraints: " Add and subtract whole numbers with three digits or less; " Multiply whole numbers of 10 or less; " Add and subtract fractions with like denominators less than or equal to four; and " Add and subtract decimals related to money. DOK - 2 .
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MA-EP-1.3.2 Skip Count
The learner will be able to skip-count forward and backward by 2s, 5s, 10s and 100s.
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MA-EP-1.3.3 Single Digit Divisors
The learner will be able to divide two digit numbers by single digit divisors (with or without remainders) in real-world and mathematical problems.
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MA-EP-1.5.1 Odd/ Even Numbers
The learner will be able to will identify and provide examples of odd numbers, even numbers, and multiples of a number and will apply these numbers to solve real-world problems. DOK - 2 .
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MA-EP-1.5.2 Properties
The learner will be able to use the commutative properties of addition and multiplication, the identity properties of addition and multiplication and the zero property of multiplication in written and mental computation.
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| Measurement |
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Students translate from measuring using nonstandard units to using standard units of measurement. They identify measurable attributes of objects, estimate and measure weight, length, perimeter, area, angles, temperature, time and money. They convert units within the same measurement system. 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. Primary Enduring Knowledge – 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. • measurements are determined by using appropriate techniques, tools and formulas. • for each situation, there is an appropriate degree of accuracy in measurement. Primary Skills and Concepts – Measuring Physical Attributes Students will • apply standard units to measure length (inches and centimeters), weight (pounds), time (hours, half-hours, quarter-hours, five- and one-minute intervals), money (coins and bills) and temperature (Fahrenheit and Celsius) • use nonstandard units to measure and compare the length, weight, area or volume of familiar objects • use standard units of measurement to identify, describe and compare measurable attributes of objects (e.g., length, weight, volume) and make estimates using appropriate units of measurement • choose and use appropriate tools for specific measurement tasks • sort/classify or compare and order objects by shape, size and color (e.g., attribute blocks) • estimate weight, length, perimeter, area, angle and time using appropriate units of measurement • explore concepts of perimeter and area of rectangles using manipulatives • identify, compare and order amounts of money using coins and bills and use correct symbols for money • combine coins and bills to make a given amount and make change up to a dollar • relate time to daily activities, tell time to the hour, half-hour, quarter-hour, five minutes and one minute and determine elapsed time Primary Skills and Concepts – Systems of Measurement Students will • determine equivalent U.S. customary measurements • describe, define, give examples of and use to solve real-world and/or mathematical problems both nonstandard and standard (U.S. Customary, metric) units of measurement to include length, time, money, temperature (Fahrenheit and Celsius) and weight |
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MA-EP-2.1.1 Standard Units
The learner will be able to apply standard units to measure length (to the nearest half-inch or the nearest centimeter) and to determine: " weight (nearest pound); " time (nearest quarter hour); " money (identify coins and bills by value) and " temperature (Fahrenheit). DOK 1 .
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MA-EP-2.1.2 Measure Temperature
The learner will be able to use standard units to measure temperature in Fahrenheit and Celsius to the nearest degree.
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MA-EP-2.1.3 Measurement / tools
The learner will be able to choose and use appropriate tools (e.g., thermometer, scales, balances, clock, ruler) for specific measurement tasks.
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MA-EP-2.1.4 Nonstandard / Standard
The learner will be able to use nonstandard and standard units of measurement to identify measurable attributes of an object (length - in, cm; weight - oz, lb) and make an estimate using appropriate units of measurement.
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MA-EP-2.1.5 Units / Compare
The learner will be able to will use units of measurement to describe and compare attributes of objects to include length (in, cm), width, height, money (cost), temperature (F), and weight (oz, lb), and sort objects and compare attributes by shape, size and color.
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MA-EP-2.1.6 Estimate Measurement
The learner will be able to estimate weight, length, perimeter, area, angle measures and time using appropriate units of measurement.
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MA-EP-2.2.1 Measurement / Real-world
The learner will be able to describe, define, give examples of and use to solve real-world and mathematical problems nonstandard and standard (U.S. Customary, metric) units of measurement to include length (in., cm.), time, money, temperature (Fahrenheit) and weight (oz., lb.).
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MA-EP-2.2.2 Elapsed Time
The learner will be able to determine elapsed time by half hours.
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MA-EP-2.2.3 Convert Units
The learner will be able to convert units within the same measurement system including money (dollars, cents), time (minutes, hours, days, weeks, months), weight (ounce, pound) and length (inch, foot).
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| Geometry |
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Students explore and find basic geometric elements and terms, two-dimensional shapes and threedimensional objects. They find and use symmetry. They move two-dimensional figures in a plane and explore congruent and similar figures. 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. Primary 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). • visualization, spatial reasoning and geometric relationships model real-world situations. Primary Skills and Concepts – Shapes and Relationships Students will • identify, describe, model, draw, compare and classify two-dimensional figures and threedimensional objects using elements, attributes and properties • explore the relationships among two-dimensional figures and three-dimensional objects (e.g., using virtual manipulatives) • identify and describe congruent figures in real-world and/or mathematical situations • investigate and solve real-world problems using the elements, attributes and properties of basic two-dimensional figures and three-dimensional objects • identify, draw and represent line segments and angles • determine if simple shapes are congruent Primary Skills and Concepts – Transformations of Shapes Students will • determine lines of symmetry in simple shapes and identify and describe symmetrical twodimensional figures • examine examples of line symmetry in real-world situations and apply one line of symmetry to construct simple geometric designs, using graphic, technological or concrete models/manipulatives to communicate understanding • explore flips, slides and turns with physical models • identify images from flips (reflections), slides (translations) and turns (rotations) in a plane Primary Skills and Concepts – Coordinate Geometry Students will • locate points and figures on a grid representing a positive coordinate system |
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MA-EP-3.1.1 Geormetric terms / Basic
The learner will be able to describe and provide examples of basic geometric elements and terms (sides, edges, faces, vertices, angles), and will apply these elements to solve real-world problems. DOK - 2 .
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MA-EP-3.1.2 Two-dimensional Shapes
The learner will be able to describe and provide examples of basic two-dimensional shapes (circles, triangles, squares, rectangles, trapezoids, rhombuses, hexagons), and will apply these shapes to solve real-world problems. DOK - 2 .
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MA-EP-3.1.3 Three-dimensional Shapes
The learner will be able to describe and provide examples of basic three-dimensional objects (spheres, cones, cylinders, pyramids, cubes) and will apply the attributes to solve real-world and mathematical problems. DOK 1 .
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MA-EP-3.1.5 Congruent Figures
The learner will be able to identify and describe congruent figures in real-world and mathematical problems.
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MA-EP-3.2.1 Line Symmetry
The learner will be able to describe and provide examples of line symmetry in real-world and mathematical problems or will apply one line of symmetry to construct a simple geometric design. DOK 2 .
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MA-EP-3.3.1 Coordinate Grid
The learner will be able to locate points on a grid representing a positive coordinate system.
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| Data Analysis and Probability |
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Students pose questions, plan and collect data, organize and display data and interpret displays of data. They generate outcomes for simple probability activities, determine fairness of probability games and explore likely and unlikely events. 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. Primary 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. • probability can be used to make decisions or predictions or to draw conclusions. Primary Skills and Concepts – Data Representations Students will • make a graph using concrete manipulatives and read data displayed on a concrete graph • display, read and compare data on student-invented graphs • read, display, compare and interpret student-collected data • display, read and compare data on a pictograph and bar graph • display data in line plots • analyze and make inferences from data displays (drawings, tables/charts, tally tables, pictographs, bar graphs, circle graphs, line plots, two-circle Venn diagrams) • use technology to organize and display data collected from student investigations Primary Skills and Concepts – Experiments and Samples Students will • pose questions to generate data • use data from student investigations to make predictions or draw simple conclusions • use tools (including technology when appropriate) to organize and display student-collected data Primary Skills and Concepts – Probability Students will • explore chance through games and events • compare likely and unlikely outcomes • explore basic concepts of probability through simple experiments |
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MA-EP-4.1.1 Data Displays
The learner will be able to analyze and make inferences from data displays (drawings, tables/charts, tally tables, pictographs, bar graphs, circle graphs with two or three sectors, line plots, two-circle Venn diagrams). DOK - 3 .
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MA-EP-4.1.2 Data Collection
The learner will be able to collect data.
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MA-EP-4.1.3 Organize and display data
The learner will be able to organize and display data.
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MA-EP-4.2.1 Mode/ Range
The learner will be able to determine the mode (of a set of data with no more than one mode) and the range of a set of data.
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MA-EP-4.3.1 Data / Pose Questions
The learner will be able to pose questions that can be answered by collecting data.
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MA-EP-4.4.3 Probabililty /Event
The learner will be able to describe and give examples of the probability of an unlikely event (near zero) and a likely event (near one).
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| Algebraic Thinking |
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Students explore and examine patterns and develop rules to go with patterns. They generate input-output for functions and create tables to analyze functions. Students use number sentences with missing values. 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. Primary 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 (e.g., finding the missing value in open sentences). • 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. Primary Skills and Concepts – Patterns, Relations and Functions Students will • identify and describe patterns in real life and in numerical and geometric situations • reproduce and extend patterns using manipulatives • use pictures or words to create, reproduce, extend and explain patterns of shapes, objects, movements, sounds and numbers • recognize and extend simple number patterns • explore input-output machines (e.g., function machines) and solve simple function machine tasks • use calculators to explore how constant addition produces a pattern and can be expressed as a rule for a pattern Primary Skills and Concepts – Variables, Expressions and Operations Students will • explore unknowns and open sentences to express relationships • create stories about mathematical sentences with missing values Primary Skills and Concepts – Equations and Inequalities Students will • solve simple equations (e.g., 1 + 1 = [ ]; [ ] - 2 = 7) • solve simple inequalities (e.g., [ ] < 6) • solve for unknowns in simple open sentences • read and create story problems to represent mathematical sentences with missing values • use manipulatives, numbers and/or symbols to model real-world situations with simple number sentences |
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MA-EP-5.1.1 Simple Patterns
The learner will be able to extend simple patterns (e.g., 2,4,6,8, …; ???? …). DOK 2 .
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MA-EP-5.1.2 Functions / Describe
The learner will be able to describe functions (input-output) through pictures and words. DOK 2 .
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MA-EP-5.1.3 Input/ Output
The learner will be able to determine the value of an output given a function rule and an input value.
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MA-EP-5.3.1 Number Sentences
The learner will be able to model real-world and mathematical problems with simple number sentences (equations and inequalities) with a missing value (e.g., 2 + ? = 7, ___< 6) and apply simple number sentences to solve mathematical and real-world problems. DOK 2 .
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