THIRD GRADE CURRICULUM MAP - Red Clay Consolidated School .
THIRD GRADE CURRICULUM MAPMATHEMATICSOFFICE OF CURRICULUM AND INSTRUCTION
Third Grade Curriculum MapTo:Third Grade TeachersFrom:Jodi AlbersDate:July 19, 2017Re:Third Grade Math Expressions Curriculum MapMathematicsDear Teachers,This is a draft of the Math Expressions curriculum map that correlates the Common Core State Standards inMathematics. Please note: this is a draft. Your suggestions and feedback should be given to your Math ExpressionsLead Teacher so appropriate changes can be made.This document is divided into the following sections: Instructional Focus Mathematical Practices Scope and Sequence Curriculum MapInstructional FocusThis summary provides a brief description of the critical areas of focus, required fluency for the grade level, majoremphasis clusters, and examples of major within-grade dependencies.The Common Core State Standards for Mathematics begin each grade level from kindergarten through eighth gradewith a narrative explaining the Critical Areas for that grade level. The Critical Areas are designed to bring focus tothe standards by outlining the essential mathematical ideas for each grade level.Mathematical PracticesThe Common Core State Standards for Mathematics define what students should understand and be able to do in theirstudy of mathematics. The Standards for Mathematical Practice describe varieties of expertise that mathematicseducators at all levels should seek to develop in their students. The Standards for Mathematical Practice areincluded first in this document because of their importance and influence in teaching practice.Scope and SequenceThis table provides the unit sequence and pacing for Math Expressions.Curriculum Map – By UnitThe curriculum map provides the alignment of the grade level Math Expressions units with state-adopted standards aswell as unit specific key elements such as learning progressions, essential questions learning targets, and formativeassessments.A special thank you to the Third Grade Math Expressions Lead Teachers who created these documents for the RedClay Consolidated School District.Sincerely,Jodi AlbersRed Clay Consolidated School DistrictDepartment of Curriculum and Instruction(302) 552-3820jodi.albers@redclay.k12.de.usUpdated Summer 2017
Third Grade Curriculum MapMathematics2017 – 2018 Math Expressions Lead TeachersKindergarten TeamMichelle Finegan, Richardson Park Elementary SchoolJackie Gallagher, Highlands Elementary SchoolChristine Saggese, Cooke Elementary SchoolBeth Ann Turner, Forest Oak Elementary SchoolFirst Grade TeamSamantha Ches, Shortlidge AcademySara Edler, Marbrook Elementary SchoolBrandy Wilkins, Lewis Dual Language Elementary SchoolSecond Grade TeamGabriele Adiarte, Mote Elementary SchoolSherri Brooks, Richey Elementary SchoolStephanie Fleetwood, Linden Hill Elementary SchoolThird Grade TeamSarah Bloom, Brandywine Springs Elementary SchoolKaren Cooper, North Star Elementary SchoolKathleen Gormley, Highlands Elementary SchoolKathryn Hudson, Cooke Elementary SchoolAmy Starke, Heritage Elementary SchoolFourth Grade TeamAmber Tos, Baltz Elementary SchoolFifth Grade TeamJennifer Greevy, Forest Oak Elementary SchoolErin McGinnley, Warner Elementary SchoolStacie Zdrojewski, Richey Elementary SchoolUpdated Summer 2017
Third Grade Curriculum MapMathematicsInstructional FocusIn Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication anddivision and strategies for multiplication and division within 100; (2) developing understanding of fractions, especiallyunit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and ofarea; and (4) describing and analyzing two-dimensional shapes.1. Students develop an understanding of the meanings of multiplication and division of whole numbers throughactivities and finding an unknown factor in these situations. For equal-sized group situations, division canrequire finding the unknown number of groups or the unknown group size. Students use properties ofoperations to calculate products of whole numbers, using increasingly sophisticated strategies based on theseproperties to solve multiplication and division problems involving single-digit factors. By comparing a varietyof solution strategies, students learn the relationship between multiplication and division.2. Students develop an understanding of fractions, beginning with unit fractions. Students view fractions ingeneral as being built out of unit fractions, and they use fractions along with visual fraction models torepresent parts of a whole. Students understand that the size of a fractional part is relative to the size of thewhole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a largerbucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to usefractions to represent numbers equal to, less than, and greater than one. They solve problems that involvecomparing fractions by using visual fraction models and strategies based on noticing equal numerators ordenominators.3. Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape byfinding the total number of same-size units of area required to cover the shape without gaps or overlaps, asquare with sides of unit length being the standard unit for measuring area. Students understand thatrectangular arrays can be decomposed into identical rows or into identical columns. By decomposingrectangles into rectangular arrays of squares, students connect area to multiplication, and justify usingmultiplication to determine the area of a rectangle.4. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classifyshapes by their sides and angles, and connect these with definitions of shapes. Students also relate theirfraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.Key Areas of Focus for 3 – 5:Multiplication and division of whole numbers and fractions —concepts, skills, and problem solvingRequired Fluency:3.OA .7 Multiply and divide within 100.3.NBT.2 Add and subtract within 1000.Updated Summer 2017
Third Grade Curriculum MapMathematicsMajor Emphasis Clusters:Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Understand the properties of multiplication and the relationship between multiplication and division. Multiply and divide within 100. Solve problems involving the four operations, and identify and explain patterns in arithmetic.Number and Operations – Fractions Develop understanding of fractions as numbers.Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses ofobjects. Geometric measurement: understand concepts of area and relate area to multiplication and to addition.Examples of Major Within-Grade Dependencies:Students must begin work with multiplication and division (3.OA) at or near the very start of theyear to allow time for understanding and fluency to develop. Note that area models for productsare an important part of this process ( 3.MD.7). Hence, work on concepts of area (3.MD.5.6)should likely begin at or near the start of the year as well.Updated Summer 2017
Third Grade Curriculum MapMathematicsStandards for Mathematical PracticesThe Standards for Mathematical Practice describe varieties of expertise that mathematics educators at alllevels should seek to develop in their students. These practices rest on important “processes andproficiencies” with longstanding importance in mathematics education. The first of these are the NCTMprocess standards of problem solving, reasoning and proof, communication, representation, andconnections. The second are the strands of mathematical proficiency specified in the National ResearchCouncil’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding(comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carryingout procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitualinclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence andone’s own efficacy).Connecting the Standards for Mathematical Practice to the Standards for MathematicalContentThe Standards for Mathematical Practice describe ways in which developing student practitioners of thediscipline of mathematics increasingly ought to engage with the subject matter as they grow inmathematical maturity and expertise throughout the elementary, middle and high school years. Designersof curricula, assessments, and professional development should all attend to the need to connect themathematical practices to mathematical content in mathematics instruction. The Standards forMathematical Content are a balanced combination of procedure and understanding. Expectations thatbegin with the word “understand” are often especially good opportunities to connect the practices to thecontent. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexiblebase from which to work, they may be less likely to consider analogous problems, represent problemscoherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully towork with the mathematics, explain the mathematics accurately to other students, step back for anoverview, or deviate from a known procedure to find a shortcut. In short, a lack of understandingeffectively prevents a student from engaging in the mathematical practices. In this respect, those contentstandards which set an expectation of understanding are potential “points of intersection” between theStandards for Mathematical Content and the Standards for Mathematical Practice. These points ofintersection are intended to be weighted toward central and generative concepts in the schoolmathematics curriculum that most merit the time, resources, innovative energies, and focus necessary toqualitatively improve the curriculum, instruction, assessment, professional development, and studentachievement in mathematics.Standards for Mathematical Practice1. Make sense of problems and persevere in solving themMathematically proficient students start by explaining to themselves the meaning of a problem andlooking for entry points to its solution. They analyze givens, constraints, relationships, and goals. Theymake conjectures about the form and meaning of the solution and plan a solution pathway rather thansimply jumping into a solution attempt. They consider analogous problems, and try special cases andsimpler forms of the original problem in order to gain insight into its solution. They monitor andevaluate their progress and change course if necessary. Older students might, depending on thecontext of the problem, transform algebraic expressions or change the viewing window on theirgraphing calculator to get the information they need. Mathematically proficient students can explainUpdated Summer 2017
Third Grade Curriculum MapMathematicscorrespondences between equations, verbal descriptions, tables, and graphs or draw diagrams ofimportant features and relationships, graph data, and search for regularity or trends. Younger studentsmight rely on using concrete objects or pictures to help conceptualize and solve a problem.Mathematically proficient students check their answers to problems using a different method, and theycontinually ask themselves, “Does this make sense?” They can understand the approaches of others tosolving complex problems and identify correspondences between different approaches.2. Reason abstractly and quantitativelyMathematically proficient students make sense of quantities and their relationships in problemsituations. They bring two complementary abilities to bear on problems involving quantitativerelationships: the ability to decontextualize—to abstract a given situation and represent it symbolicallyand manipulate the representing symbols as if they have a life of their own, without necessarilyattending to their referents—and the ability to contextualize, to pause as needed during themanipulation process in order to probe into the referents for the symbols involved. Quantitativereasoning entails habits of creating a coherent representation of the problem at hand; considering theunits involved; attending to the meaning of quantities, not just how to compute them; and knowingand flexibly using different properties of operations and objects.3. Construct viable arguments and critique the reasoning of others.Mathematically proficient students understand and use stated assumptions, definitions, and previouslyestablished results in constructing arguments. They make conjectures and build a logical progression ofstatements to explore the truth of their conjectures. They are able to analyze situations by breakingthem into cases, and can recognize and use counterexamples. They justify their conclusions,communicate them to others, and respond to the arguments of others. They reason inductively aboutdata, making plausible arguments that take into account the context from which the data arose.Mathematically proficient students are also able to compare the effectiveness of two plausiblearguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in anargument—explain what it is. Elementary students can construct arguments using concrete referentssuch as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, eventhough they are not generalized or made formal until later grades. Later, students learn to determinedomains to which an argument applies. Student
Red Clay Consolidated School District Department of Curriculum and Instruction (302) 552-3820 . Michelle Finegan, Richardson Park Elementary School Jackie Gallagher, Highlands Elementary School Christine Saggese, Cooke Elementary School Beth Ann Turner, Forest Oak Elementary School . Linden Hill Elementary School Third Grade Team Sarah .
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Grade 4 NJSLA-ELA were used to create the Grade 5 ELA Start Strong Assessment. Table 1 illustrates these alignments. Table 1: Grade and Content Alignment . Content Area Grade/Course in School Year 2021 – 2022 Content of the Assessment ELA Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
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Second Grade Curriculum Map Mathematics Updated Summer 2017 To: Second Grade Teachers From: Jodi Albers Date: July 19, 2017 Re: Second Grade Math Expressions Curriculum Map Dear Teachers, This is a draft of the Math Expressions curriculum map that correlates the Common Core State Standards in
Fifth Grade Curriculum Map Mathematics Updated Summer 2017 To: Fifth Grade Teachers From: Jodi Albers Date: July 19, 2017 Re: Fifth Grade Math Expressions Curriculum Map Dear Teachers, This is a draft of the Math Expressions curriculum map that correlates the Common Core State Standards in Mathematics. Please note: this is a draft.
Fourth Grade Curriculum Map Mathematics Updated Summer 2017 To: Fourth Grade Teachers From: Jodi Albers Date: July 19, 2017 Re: Fourth Grade Math Expressions Curriculum Map Dear Teachers, This is a draft of the Math Expressions curriculum map that correlates the Common Core State Standards in Mathematics. Please note: this is a draft.
