Read Microsoft Word - Maryland Grade 3 Correlation - FEB 2005.doc text version

Maryland Mathematics Curriculum, Third Grade Correlations of the TEN UNDERSTANDING MATHEMATICS PLUS Programs By Neufeld Learning Systems Inc. February 2005 Note: a. The Understanding Math PLUS series of programs consist of 10 programs written for Kindergarten to 10th Grade. The 10 programs are: Understanding Fractions Understanding Whole Numbers and Integers Understanding Probability Understanding Percent Understanding Exponents Understanding Equations Understanding Algebra Understanding Graphing Understanding Numeration Understanding Measurement and Geometry Note: b. The Understanding Numeration software for K to 3 is set up so that the teacher selects items in the following order: Concept .. from 5 concepts .. Counting, Comparing & Ordering, Place Value, Operations and Problem Solving. Skill .. chosen from the list of specific learning expectations Level .. indicates the levels of development for Kindergarten to 3rd grade. Level A B C D Upper Range of Number 10 20 100 1000

Lesson .. 250 lessons are sequenced to build understanding of concepts. A detailed Lesson Synopsis on the website www.neufeldmath.com to assist the teacher by stating the lesson contents but also by giving lesson suggestions. Worksheet .. off computer worksheets are selected from the CD by a code. Note: c. The remaining 9 Understanding Math programs for 4th to 10th grade are set up so that they can be used in a variety of teaching and learning environments ranging from a teacher centered approach with 1 computer to a student centered lab approach. The lessons can also be used in remediation, tutorial, intervention, resource, fast-tracking. Each topic has: ..an interactive concept introduction, usually with a variety of graphic approaches. ..a number of particular examples ..practice questions with random questions but particular feedback ..a topic test with random questions and tracking ..off computer worksheets selected from the website .. www.neufeldmath.com

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 1

*Curriculum is correlated with Understanding Math programs in the following manner: MAT+ (Understanding Math Plus, 4-10) / Program Title / Topic Number & Title / Lesson Title OR NUM (Understanding Numeration, K-3) / Concept Title / Level (A-D) / Topic Title STANDARD 1.0 KNOWLEDGE OF ALGEBRA, PATTERNS, AND FUNCTIONS Students will algebraically represent, model, analyze, or solve mathematical or realworld problems involving patterns or functional relationships. Patterns and Functions 1. Identify, describe, extend, and create numeric patterns and functions Represent and analyze numeric patterns using skip counting Assessment limit: Use 2, 5, 10, or 100 starting with any whole number (0 ­ 1000) Represent and analyze numeric patterns using skip counting Assessment limit: Use 3 or 4 starting with 0, 1, 2, 3, or 4 (0 ­ 30) NUM / COUNTING / Skip Counting and Patterns / C / Patterns in Rows; Skip Counting to 100; Skip Count by 2s to 100; Next by 5s; Next by 2s Represent and analyze numeric patterns using skip counting backward Assessment limit: Use 10 or 100 starting with any whole number (0 ­ 1000) Complete a function table using a given addition or subtraction rule NUM / OPERATIONS / Fact Families ­ Add & Subtract / C / Check Subtraction by Addition 2. Identify, describe, extend, and create non-numeric growing or repeating patterns Represent and analyze growing patterns using symbols, shapes, designs, or pictures Assessment limit: Start at the beginning, show at least 3 levels but no more than 5 levels, and ask for the next level Represent and analyze repeating patterns using symbols, shapes, designs, or pictures Assessment limit: Use no more than 4 objects in the core of the pattern MAT+ / Understanding Algebra / Topic 3 ­ Patterns, Patterns, Patterns / Introduction: Math is Patterns; Geometric Patterns: Examples 1 through 8; Number Patterns: Examples 1 through 6; Number and Geometric Patterns: Examples 1 & 2 Expressions, Equations, and Inequalities

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 2

3. Write and identify expressions Represent numeric quantities using operational symbols (+, -, x, ÷) Assessment limit: Use operational symbols (+ or -) and whole numbers (0 ­ 50) MAT+ / Understanding Whole Numbers and Integers / Topic 2 ­ Adding and Subtracting Whole Numbers / Add - Partial Sums: Examples 1 through 6; Add ­ Trade First: Examples 1 through 6; Add ­ Right to Left: Examples 1 through 6; Subtract ­ Right to Left: Examples 1 through 6; Subtract ­ Trade First: Examples 1 through 6; Subtract ­ Add Up: Examples 1 through 6; Subtract ­ Add up to Zero: Examples 1 through 4; Whole Numbers Around Us: Examples 1 through 11 MAT+ / Understanding Whole Numbers and Integers / Topic 3 ­ Multiplying and Dividing Whole Numbers / Multiplication Facts: Groups of 6,7,8,9; Commutative Property: 5x1 = 1x5, etc.; The 10x10 Multiplication Table: User Picks, Computer Picks; The 12x12 Multiplication Table: Associative Property, Examples 1,2; Multiples of 10, 100, 1000: Patterns in Multiplication by 10, Patterns in Multiplication by 100, Patterns in Multiplication by 1000, Examples 1,2,3; Multiplying by a Single Digit Number: Repeated Addition: Repeated Addition Examples 1 through 4; Partial Products Examples 1 through 6, Questions 1,2,3; Distributive Property; Lattice Method; The Standard Method; Multiply by a Two Digit Multiplier: Partial Products; The Distributive Method; The Lattice Method; The Standard Method; Divide by a Single Digit Divisor: Fair Sharing Examples 1& 1, Questions 1 through 6; Whole Numbers Around Us: Examples 1 through 11 4. Identify, write, solve, and apply equations and inequalities Represent relationships using appropriate relational symbols (<, >, or =) and operational symbols (+, -, x, ÷) on either side Assessment limit: Use operational symbols (+ or -) and whole numbers (0 ­ 1000) MAT+ / Understanding Equations / Topic 1 ­ Tiles, Balances, and Equations / Definitions: Introduction, Summary Parts 1,2; The Meaning of "Solving and Equations"; Solve by Systematic Trials; Recall Tile Concepts; Balances ­An Introduction; Tiles, Balances, and Equations; Practice Questions; Topic Test MAT+ / Understanding Equations / Topic 2 ­ Solving One-Step Equations / Our Problem; Concepts ­ Examples with Tiles 1 through 4; Concepts ­ Examples without Tiles; Practice Questions; Topic Test Find the missing number (unknown) in a number sentence (equation) using operational symbols (+, -, x, ÷) Assessment limit: Use one operational symbol (+ or -) and whole numbers (0 ­ 100) Find the missing number(s) (unknown) on one or both sides of a number sentence (equation)

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8

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MAT+ / Understanding Equations / Topic 2 ­ Solving One-Step Equations / Our Problem; Concepts ­ Examples with Tiles 1 through 4; Concepts ­ Examples without Tiles; Practice Questions; Topic Test Numeric and Graphic Representations of Relationships 1. Locate points on a number line Represent whole numbers on a number line Assessment limit: Use whole numbers (0 - 500) MAT+ / Understanding Whole Numbers and Integers / Topic 1 ­ The Meaning of Whole Numbers CAN/US / The Number Line Represent proper fractions on a number line Assessment limit: Use fractions that have denominators of 2, 3, or 4 MAT+ / Understanding Fractions / Topic 1 ­ The Meaning of Fractions / Fractions on a Number Line: Halves, Thirds, Quarters, Summary STANDARD 2.0 KNOWLEDGE OF GEOMETRY Students will apply the properties of one, two, or three-dimensional geometric figures to describe, reason, or solve problems about shape, size, position, or motion of objects. Plane Geometric Figures 1. Analyze the properties of plane geometric figures Identify and describe points, lines, line segments, rays, and angles MAT+ / Understanding Graphing / Topic 3 ­ Points on a Grid / In This Topic; Josh's Neighbourhood: Concept, Number Houses; Grids on Maps; Ordered Pairs: Axis, Quadrants, Find a Point, Order in Important, Examples; Shapes, Battleship MAT+ / Understanding Measurement and Geometry / Topic 5 ­ Angles and Their Measure / In This Topic; Lines and Rays; Angles ­ An Introduction; the Degree; Classifying Angles: Classifications, Memory Game; Measuring Angles; Practice Questions; Topic Test MAT+ / Understanding Measurement and Geometry / Topic 6 ­ Angles and Polygons / Parallel Lines; Example with Parallel Lines Identify or describe polygons Assessment limit: Use triangles, quadrilaterals, pentagons, hexagons, or octagons and the number of sides or vertices Identify or describe quadrilaterals

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8

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Assessment limit: Use squares, rectangles, rhombi, parallelograms, and trapezoids and the length of sides Identify triangles, rectangles, or squares as part of a composite figure Assessment limit: Use a combination of 2 of the stated polygons MAT+ / Understanding Measurement and Geometry / Topic 2-Perimeter and Area of Polygons / Polygons ­ What are they?: Concept, A Triangle is, A Quadrilateral is, A Pentagon is, A Hexagon is, An Octagon is, Classify Polygons 2. Analyze geometric relationships Identify right angles MAT+ / Understanding Measurement and Geometry / Topic 5 ­ Angles and Their Measure / In This Topic; Lines and Rays; Angles ­ An Introduction; the Degree; Classifying Angles: Classifications, Memory Game; Measuring Angles; Practice Questions; Topic Test Solid Geometric Figures 1. Analyze the properties of solid geometric figures Identify and describe cubes, rectangular prisms, and triangular prisms Assessment limit: Use cubes and the number of edges, faces, vertices, or shape of each face MAT+ / Understanding Measurement and Geometry / Topic 4 ­ Solids- Volume and Surface Area / In This Topic; Classifying Solids: A Solid is..., Recall Polygons, A Polyhedron is, A Prism is, Some Special Pyramids, A Cylinder is, A Cone is, Platonic Solids Representation of Geometric Figures 1. Represent plane geometric figues Sketch triangles, quadrilaterals, pentagons, hexagons, octagons, and circles MAT+ / Understanding Measurement and Geometry / Topic 2-Perimeter and Area of Polygons / Polygons ­ What are they?: Concept, A Triangle is, A Quadrilateral is, A Pentagon is, A Hexagon is, An Octagon is, Classify Polygons Congruence 1. Analyze congruent figures Identify and describe geometric figures as congruent Assessment limit: Use the same shape and same size

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8

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Transformations 1. Analyze a transformation Identify and describe the results of a slide, flip, and turn Assessment limit: Use horizontal slide, flip over a vertical line, or turn of 900 clockwise around a given point of a geometric figure or picture MAT+ / Understanding Graphing / Topic 4 ­ Transformations / In This Topic; What is a Transformation?; Introduction to Common Transformations; Translations ­ An Introduction, Slide #1, #2, #3, #4; Reflections ­ An Introduction, Flip #1, #2, #3, #4; Rotations ­ An Introduction, Turn #1, #2, #3, #4; The Transformation Machine: Examples 1 through 5 2. Analyze geometric figures and pictures Identify and describe symmetry Assessment limit: Use no more than 4 lines of symmetry MAT+ / Understanding Graphing / Topic 4 ­ Transformations / Lines of Symmetry ­ An Introduction: Introduction, Examples 1 through 4; Symmetry Match: Puzzle 1,2 STANDARD 3.0 KNOWLEDGE OF MEASUREMENT Students will identify attributes, units, or systems of measurements or apply a variety of techniques, formulas, tools or technology for determining measurements. Measurement Units 1. Read customary and metric measurement units Estimate and determine length Assessment limit: Use the nearest centimeter or ½ inch MAT+ / Understanding Measurement and Geometry / Topic 1 ­ An Introduction to Measurement / Measurements with a Ruler: Introduction to the Ruler, Centimeters #1, #2, Inches #1, #2 Tell time in days, hours, minutes, and seconds Assessment limit: Use the nearest minute using an analog clock NUM / COMPARING AND ORDERING / Understand Measurement of Time / B / The Clock ­ An Introduction; Times to the Hour; Analog and Digital; Times to the Half Hour NUM / COMPARING AND ORDERING / Understand Measurement of Time / C / Times to Five Minutes NUM / COMPARING AND ORDERING / Understand Measurement of Time / D / Times to the Minute

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 6

NUM / COMPARING AND ORDERING / Describe Elapsed Time ­ Hours, 5 Minutes / C / Elapsed Time in Hours; Elapsed Time ­ 5 Minutes NUM / COMPARING AND ORDERING / Describe Elapsed Time ­ Minutes / D / Time Goes By ­ Analog; Time Goes By ­ Digital; Elapsed Time NUM / COMPARING AND ORDERING / Describe Back in Time ­ Hours, 5 Minutes / C & D / Back in Time in Hours; Back in Time ­ 5 Minutes; Early and Late Estimate and read temperature Assessment limit: Use the nearest degree (°F or °C) Estimate and determine weight of objects Assessment limit: Use the nearest pound or ounce Measurement Tools 1. Measure in customary and metric units Measure length of objects and pictures of objects using a ruler, a tape measure, a yardstick, or a meter stick Assessment limit: Use a ruler and the nearest centimeter or ½ inch MAT+ / Understanding Measurement and Geometry / Topic 1 ­ An Introduction to Measurement / Measurements with a Ruler: Introduction to the Ruler, Centimeters #1, #2, Inches #1, #2; Calculating Distances: Using Centimeters, Examples 1 through 6, Using Inches, Examples 1 through 6; Benchmarks: Establishing Benchmarks, Meter Benchmarks, Foot Benchmarks, Centimeter Benchmarks, Inch Benchmarks, Yard Benchmarks Measure capacity of containers to the nearest cup, pint, quart, gallon, milliliter, and liter using graduated containers Measure weight of objects to the nearest ounce and pound and the mass of an object to the nearest gram and kilogram Applications in Measurement 1. Apply measurement concepts Estimate and determine the perimeter of geometric figures and pictures on a grid Assessment limit: Use counting and whole numbers (0 ­ 50) Estimate and determine the area of geometric figures and pictures on a grid Assessment limit: Use counting of whole units and whole numbers (0 ­ 50) MAT+ / Understanding Measurement and Geometry / Topic 2-Perimeter and Area of Polygons / Polygons ­ What are they?: Concept, A Triangle is, A Quadrilateral is, A Pentagon is, A Hexagon is, An Octagon is, Classify Polygons; Walk Around a Polygon: Joan Walks, Perimeter of Various Shapes, Examples 1,2,3; Perimeter of the Ranch; Amount of Surface: The Driveway ­ An Introduction to Area; Area ­ Estimation; Area of

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 7

a Rectangle; Relationship ­ Area and Perimeter: The Information, The Graph; Given Area and Perimeter ­ Create Shapes: Examples 1 through 4; Practice Questions 2. Calculate equivalent measurements Determine equivalent units of length Assessment limit: Use 12 inches = 1 foot and 3 feet = 1 yard and whole numbers (0 ­ 30) MAT+ / Understanding Measurement and Geometry / Topic 1 ­ An Introduction to Measurement / Metric and U.S.A. Standard Measurement Systems: Searching for the Standard Unit, Related Units for Metric Prefixes, Metric Prefixes at Work, Converting Between Metric Prefixes STANDARD 4.0 KNOWLEDGE OF STATISTICS Students will collect, organize, display, analyze, or interpret data to make decisions or predictions. Data Displays 1. Collect, organize, and display data Collect data by conducting surveys Organize and display data to make tables using a variety of categories and sets of data Assessment limit: Use no more than 4 categories from one set of data and whole numbers (0 ­ 1000) MAT+ / Understanding Graphing / Topic 1 ­ Reading and Sketching Graphs / In This Topic; Graphs without a Scale: Concept ­ Age and Weight, Examples 1 through 13; Graphs with a Scale: Concept ­ Distance and Time, Examples 1 through 14; Discrete Data; Continuous Data; Extrapolation; Practice Questions; Topic Test Organize and display data to make pictographs using a variety of scales Assessment limit: Use scales of 2:1, 4:1, or 10:1 and whole numbers (0 ­ 100) Organize and display data to make single bar graphs using a variety of categories and intervals Assessment limit: Use no more than 4 categories of data with intervals of 1, 2, 5, or 10 and whole numbers (0 ­100) Organize and display data to make line plots using a variety of intervals MAT+ / Understanding Graphing / Topic 2 ­ Statistics / An Introduction: Tally Chart, Pictographs 1 & 2, Bar Graph 1 & 2, Line Graph 1 & 2; Data ­ What is it?; Examples of Data: Examples 1 through 6, Summary

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8

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Data Analysis 1. Analyze data Interpret data contained in tables using a variety of categories and intervals Assessment limit: Use no more than 4 categories from one set of data and whole numbers (0 ­ 1000) Interpret data contained in pictographs using a variety of categories and intervals Assessment limit: Use scales of 2:1, 4:1, or 10:1 and whole numbers (0 ­ 100) Interpret data contained in single bar graphs using a variety of categories and intervals Assessment limit: Use no more than 4 categories of data, intervals of 1, 2, 5, or 10 and whole numbers (0 ­ 100) Interpret data contained in line plots using a variety of intervals MAT+ / Understanding Graphing / Topic 2 ­ Statistics / An Introduction: Tally Chart, Pictographs 1 & 2, Bar Graph 1 & 2, Line Graph 1 & 2; Data ­ What is it?; Examples of Data: Examples 1 through 6, Summary STANDARD 5.0 KNOWLEDGE OF PROBABILITY Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Sample Space 1. Identify possible outcomes Identify possible outcomes that make up the sample space for a given real life situation Identify possible outcomes that make up the sample space for a given experiment such as: flipping a coin, spinning a spinner, and rolling a number cube MAT+ / Understanding Probability / Topic 1 ­ An Introduction to Probability / The Language of Chance; Impossible to Certain: Activities 1 & 2; Probability Lines: Lines 1 & 2; Experiments with Spinners: Experiments 1 through 6; The Spinner Game: Boards 1 & 2; IT's in the Bag; Tree Diagrams: Meals, Socks; Practice Questions; Topic Test Theoretical Probability 1. Identify the probability of one event Describe the probability of an event using words Assessment limit: Use probability terms of more (or most) likely, less (or least) likely, or equally likely

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8

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MAT+ / Understanding Probability / Topic 2 ­ What's the Chance? / Probability: What is it? Introduction 1, Introduction 2; Probability Examples 1 through 12; The Probability Scale: Examples, Summary, Follow Up, Soccer Example; Experimental Probability: Introduction; Examples 1 & 2; Practice Questions STANDARD 6.0 KNOWLEDGE OF NUMBER RELATIONSHIPS AND COMPUTATION/ARITHMETIC Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology. Knowledge of Number and Place Value 1. Apply knowledge of whole numbers and place value Read, write, and represent whole numbers using symbols, words, and models Assessment limit: Use whole numbers (0 - 10,000) Express whole numbers in expanded form Assessment limit: Use whole numbers (0 - 10,000) MAT+ / Understanding Whole Numbers and Integers / Topic 1 ­ The Meaning of Whole Numbers CAN/US / Seeing the Number: To Tens ­ Examples 1& 2, To Hundreds ­ Examples 1 & 2, To Thousands ­ Examples 1,2,3; Expanded Notation: To 999 ­ Examples 1 & 2, To 9999 ­ Examples 1 & 2, Write as Numerals ­ Examples 1 & 2, The Number Line Identify the place value of a digit in a whole number Assessment limit: Use whole numbers (0 - 9,999) MAT+ / Understanding Whole Numbers and Integers / Topic 1 ­ The Meaning of Whole Numbers CAN/US / Place Value to 999 999: Examples 1 through 5, The Number Line ­ Examples 1 & 2 Compare, order, and describe whole numbers with or without using relational symbols (<, >, =) Assessment limit: Use no more than four whole numbers (0 - 10,000) MAT+ / Understanding Whole Numbers and Integers / Topic 1 ­ The Meaning of Whole Numbers CAN/US /Represent Numbers in Many Ways: Examples 1 through 5 2. Apply knowledge of fractions Read, write, and represent fractions as parts of a single region using symbols, words, and models Assessment limit: Use fractions with denominators of 2, 3, or 4 MAT+ / Understanding Fractions / Topic 1 ­ The Meaning of Fractions / Fractions in the News; Introduction ­ Think, Write, Say: Circle, Squares, Balls, Examples; Parts of a Fraction; Introduce Fractions: Part of a Whole, One Half, One Third, One Quarter

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 10

Read, write, and represent fractions as parts of a set using symbols, words, and models Assessment limit: Use fractions with denominators of 2, 3, or 4, and use sets of 2, 3, 4 items, respectively MAT+ / Understanding Fractions / Topic 1 ­ The Meaning of Fractions / Fraction of a Set: Examples 1 through 3 3. Apply knowledge of money Represent money amounts in different ways Assessment limit: Use money amounts ($0 - $100) Determine the value of a given set of mixed currency Assessment limit: Use coins and bills ($0 - $100) Compare the value of two sets of mixed currency Number Theory 1. Apply number relationships to: Identify and describe whole numbers as even or odd Assessment limit: Use whole numbers (0 ­ 100) Number Computation 1. Analyze number relations and compute Add numbers using a variety of strategies Assessment limit: Use no more than 3 addends, with no more than 3 digits in each addend and whole numbers (0 ­ 1000) Subtract numbers using a variety of strategies Assessment limit: Use no more than 3 digits in the minuend or subtrahend and whole numbers (0 ­ 999) MAT+ / Understanding Whole Numbers and Integers / Topic 2 ­ Adding and Subtracting Whole Numbers / Add - Partial Sums: Examples 1 through 6; Add ­ Trade First: Examples 1 through 6; Add ­ Right to Left: Examples 1 through 6; Subtract ­ Right to Left: Examples 1 through 6; Subtract ­ Trade First: Examples 1 through 6; Subtract ­ Add Up: Examples 1 through 6; Subtract ­ Add up to Zero: Examples 1 through 4 Solve addition and subtraction word problems Add and subtract money amounts Identify and apply the concept of inverse operations to addition and subtraction MAT+ / Understanding Whole Numbers and Integers / Topic 2 ­ Adding and Subtracting Whole Numbers / Whole Numbers Around Us: Examples 1 through 11 Represent multiplication and division basic facts using number sentences, pictures, and drawings

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 11

Assessment limit: Use basic facts of no more than 9 x 9 = 81 Identify and use properties of multiplication Assessment limit: Use the properties of commutative, identity, or zero and whole numbers (0 ­ 20) Multiply a one-digit factor by a two-digit factor using models, pictures, and drawings Divide a two-digit dividend by a one-digit divisor using models, pictures, and drawings Identify and apply the concept of inverse operations to multiplication and division Write a word problem based on multiplication or division number sentences MAT+ / Understanding Whole Numbers and Integers / Topic 3 ­ Multiplying and Dividing Whole Numbers / Multiplication Facts: Groups of 6,7,8,9; Commutative Property: 5x1 = 1x5, etc.; The 10x10 Multiplication Table: User Picks, Computer Picks; The 12x12 Multiplication Table: Associative Property, Examples 1,2; Multiples of 10, 100, 1000: Patterns in Multiplication by 10, Patterns in Multiplication by 100, Patterns in Multiplication by 1000, Examples 1,2,3; Multiplying by a Single Digit Number: Repeated Addition: Repeated Addition Examples 1 through 4; Partial Products Examples 1 through 6, Questions 1,2,3; Distributive Property; Lattice Method; The Standard Method; Multiply by a Two Digit Multiplier: Partial Products; The Distributive Method; The Lattice Method; The Standard Method; Divide by a Single Digit Divisor: Fair Sharing Examples 1& 1, Questions 1 through 6; Whole Numbers Around Us: Examples 1 through 11 2. Estimation Determine the reasonableness of sums and differences MAT+ / Understanding Whole Numbers and Integers / Topic 2 ­ Adding and Subtracting Whole Numbers / Whole Numbers Around Us: Examples 1 through 11 STANDARD 7.0 PROCESS OF MATHEMATICS Students demonstrate the processes of mathematics by making connections and applying reasoning to solve and to communicate their findings. Problem solving 1. Apply a variety of concepts, processes, and skills to solve problems Identify the question in the problem Decide if enough information is present to solve the problem Make a plan to solve a problem Apply a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation Select a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation Identify alternative ways to solve a problem Show that a problem might have multiple solutions or no solution Extend the solution of a problem to a new problem situation

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8 12

MAT+ / Understanding Whole Numbers and Integers / Topic 2 ­ Adding and Subtracting Whole Numbers / Whole Numbers Around Us: Examples 1 through 11 MAT+ / Understanding Whole Numbers and Integers / Topic 3 ­ Multiplying and Dividing Whole Numbers / Whole Numbers Around Us: Examples 1 through 11 Reasoning 1. Justify ideas or solutions with mathematical concepts or proofs Use inductive or deductive reasoning Make or test generalizations Support or refute mathematical statements or solutions Use methods of proof, i.e., direct, indirect, paragraph, or contradiction Communication 1. Present mathematical ideas using words, symbols, visual displays, or technology Use multiple representations to express concepts or solutions Express mathematical ideas orally Explain mathematically ideas in written form Express solutions using concrete materials Express solutions using pictorial, tabular, graphical, or algebraic methods Explain solutions in written form Ask questions about mathematical ideas or problems Give or use feedback to revise mathematical thinking

Understanding Math PLUS ... ALL SECTIONS

Connections 1. Relate or apply mathematics within the discipline, to other disciplines, and to life Identify mathematical concepts in relationship to other mathematical concepts Identify mathematical concepts in relationship to other disciplines Identify mathematical concepts in relationship to life Use the relationship among mathematical concepts to learn other mathematical concepts

Understanding Math PLUS ... ALL SECTIONS

Neufeld Learning Systems Inc., February 2005 Source: Maryland Voluntary State Curriculum Mathematics Grades 3-8

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