Mathematics. Curriculum Content for Elementary School Mathematics. Fulton County Schools Curriculum Guide for Elementary Schools


 Raymond Copeland
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1 Mathematics Philosophy Mathematics permeates all sectors of life and occupies a wellestablished position in curriculum and instruction. Schools must assume responsibility for empowering students with the mathematical skills necessary for functioning in and contributing to today's complex society. Instruction should emphasize the application of mathematics to real world problems; allow the use of calculators and computers as tools in problemsolving and allow students to develop their own mathematical understanding through the use of concrete materials. The Elementary Mathematics Program is developmentally appropriate and designed to meet students intellectual, social, and emotional needs. The curriculum and assessment components of the program are conceptually oriented and contain a broad range of content. Curriculum and assessment activities allow students to experience success and helps students build positive attitudes toward mathematics and toward themselves as mathematical problemsolvers. Development of students abilities to think, to reason, to solve problems, and to communicate their understanding of mathematical concepts is a major focus of the program. Goals The goals of the K12 mathematics program are to: Meet the needs of individual students be that student is onlevel, advanced, or accelerated (working a year ahead); Build students' appreciation of mathematics and its relationship to other disciplines; Promote students' confidence in their own mathematical abilities; Assist students in becoming mathematical problemsolvers; Provide opportunities for students to communicate their ideas about mathematics; Develop students' mathematical reasoning skills; Enable students to utilize calculators and computers as problemsolving tools; Encourage participation in cooperative learning; Develop concepts and skills measured on standardized tests; and Enable parents to understand and support the program. Curriculum Content for Elementary School Mathematics
2 Fulton County Schools implements the Common Core Georgia Performance Standards for mathematics. The Fulton County Schools Mathematics curriculum stresses rigorous concept development, presents realistic and relevant applications, and keeps a strong emphasis on computational skills. Teachers utilize a standards based direct instruction delivery model. A direct instruction approach provides students with specific skillsbased instruction from their teachers at the beginning of new lessons followed by both guided and independent practice. It includes continuous modeling by the teacher, followed by more limited teacher instruction and then fading teacher instruction as students begin to master the material. Engaging students in problem solving and realworld applications are important aspects of mathematics instruction. The use of technology and manipulatives support the conceptual development of mathematical concepts and skills. The Common Core Georgia Performance Standards for mathematics are organized into content standards and standards for mathematical practice. The content standards are organized into domains: counting and cardinality, operations and algebraic thinking, number and operations, measurement and data, and geometry. The standards for mathematical practice are an essential part of learning for all students. Students will use these standards as a way of acquiring and using content knowledge.
3 Kindergarten By the end of Kindergarten, students will understand the following concepts: Know number names and the count sequence Count to tell the number of objects Compare numbers Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from Work with numbers to gain foundations for place value Describe and compare measurable attributes Classify objects and count the number of objects in categories Identify and describe shapes Analyze, compare, create, and compose shapes Grade 1 K CONTENT DOMAINS Counting and Cardinality Operations and Algebraic Thinking Number and Operations Base 10 Fractions Measurement and Data Geometry Ratios and Proportional Relationships The Number System Expressions and Equations Functions Statistics and Probability STANDARDS FOR MATHEMATICAL PRACTICE Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make sense of structure Look for and express regularity in repeated reasoning Students will represent mathematics in multiple ways.
4 By the end of Grade 1, students will be able to: Represent and solve problems involving addition and subtraction Understand and apply properties of operations and the relationship between addition and subtraction Add and subtract within 20 Work with addition and subtraction equations Extend the counting sequence Understand place value Use place value understanding and properties of operations to add and subtract Measure lengths indirectly and by iterating length units Tell and write time Reason with shapes and their attributes Grade 2 By the end of Grade 2, students will be able to: Represent and solve problems involving addition and subtraction Add and subtract within 20 Work with equal groups of objects to gain foundations for multiplication Understand place value Use place value understanding and properties of operations to add and subtract Measure and estimate lengths in standard units Relate addition and subtraction to length Work with time and money Reason with shapes and their attributes Grade 3 By the end of Grade 3, students will be able to: Represent and solve problems involving multiplication and division Understand properties of multiplication and the relationship between multiplication and division
5 Multiply and divide within 100 Solve problems involving the four operations, and identify and explain patterns in arithmetic Use place value understanding and properties of operations to perform multidigit arithmetic Develop understanding of fractions as numbers Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Geometric measurement: understand concepts of area and relate area to multiplication and to addition Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures Reason with shapes and their attributes Grade 4 By the end of Grade 4, students will be able to: Use the four operations with whole numbers to solve problems Gain familiarity with factors and multiples Generate and analyze patterns Generalize place value understanding for multidigit whole numbers Use place value understanding and properties of operations to perform multidigit arithmetic Extend understanding of fraction equivalence and ordering Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers Understand decimal notation for fractions, and compare decimal fractions Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit Geometric measurement: understand concepts of angle and measure angles Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Grade 5 By the end of Grade 5, students will be able to:
6 Write and interpret numerical expressions Analyze patterns and relationships Understand the place value system Perform operations with multidigit whole numbers and with decimals to hundredths Use equivalent fractions as a strategy to add and subtract fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions Convert like measurement units within a given measurement system Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition Graph points on the coordinate plate to solve realworld and mathematical problems Classify twodimensional figures into categories based on their properties Grade 6 By the end of Grade 6, students will understand the following concepts: ratio concepts and use ratio reasoning to solve problems further applications and extensions of multiplication and division to divide fractions by fractions computations with multidigit numbers and determination of common factors and multiples further applications and extensions of previous understandings of numbers to the system of rational numbers further applications and extensions of arithmetic to algebraic expressions how to reason about and solve onevariable equations and inequalities how to represent and analyze quantitative relationships between dependent and independent variables solving realworld and mathematical problems involving area, surface area, and volume statistical variability distributions Prentice Hall Mathematics Course 1, 2008 edition
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