KINDERGARTEN CURRICULUM MAP - Red Clay Consolidated School .
KINDERGARTEN CURRICULUM MAPMATHEMATICSOFFICE OF CURRICULUM AND INSTRUCTION
Kindergarten Curriculum MapTo:Kindergarten TeachersFrom:Jodi AlbersDate:October 2, 2017Re:Kindergarten 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, andAssessments.A special thank you to the Kindergarten 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
Kindergarten 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
Kindergarten Curriculum MapMathematicsInstructional FocusCritical Areas of Focus:In Kindergarten, instructional time should focus on two critical areas: (1) representing and comparing wholenumbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergartenshould be devoted to number than to other topics.1. Students use numbers, including written numerals, to represent quantities and to solvequantitative problems, such as counting objects in a set; counting out a given number ofobjects; comparing sets or numerals; and modeling simple joining and separating situationswith sets of objects, or eventually with equations such as 5 2 7 and 7 – 2 5. (Kindergartenstudents should see addition and subtraction equations, and student writing of equations inkindergarten is encouraged, but it is not required.) Students choose, combine, and applyeffective strategies for answering quantitative questions, including quickly recognizing thecardinalities of small sets of objects, counting and producing sets of given sizes, counting thenumber of objects in combined sets, or counting the number of objects that remain in a setafter some are taken away.2. Students describe their physical world using geometric ideas (e.g., shape, orientation, spatialrelations) and vocabulary. They identify, name, and describe basic two-dimensional shapes,such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways(e.g., with different sizes and orientations), as well as three-dimensional shapes such ascubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to modelobjects in their environment and to construct more complex shapes.Required Fluency:K.OA.5 Add and subtract within 5.Major Emphasis Clusters:Counting and Cardinality Know number names and count sequence. Count to tell the number of objects. Compare numbers.Operations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apartand taking from.Number and Operations in Base Ten Work with numbers 11-19 to gain foundations for place value.Updated Summer 2017
Kindergarten 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 theirUpdated Summer 2017
Kindergarten Curriculum MapMathematicsgraphing calculator to get the information they need. Mathematically proficient students can explaincorrespondences 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. Students at all grades can listen or read the arguments ofothers, decide whether they make sense, and ask useful questions to clarify or improve the arguments.4. Model with mathematicsMathematically proficient students can apply the mathematics they know to solve problems arising ineveryday life, society, and the workplace. In early grades, this might be as simple as writing anaddition equation to describe a situation. In middle grades, a student might apply proportionalreasoning to plan a school event or analyze a problem in the community. By high school, a studentmight use geometry to solve a design problem or use a function to describe how one quantity ofinterest depends on another. Mathematically proficient students who can apply what they know arecomfortable making assumptions and approximations to simplify a complicated situation, realizing thatthese may need revision later. They are able to identify important quantities in a practical situationand map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts andformulas. They can analyze those relationships mathematically to draw conclusions. They routinelyinterpret their mathematical results in the context of the situation and reflect on whether the resultsmake sense, possibly improving the model if it has not served its purpose.Updated Summer 2017
Kindergarten Curriculum MapMathematics5. Use appropriate tools strategicallyMathematically proficient students consider the available tools when solving a mathematical problem.These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, aspreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.Proficient students are sufficiently familiar with tools appropriate for their grade or course to makesound decisions about when each of these tools might be helpful, recognizing both the insight to begained and their limitations. For example, mathematically proficient high school students analyzegraphs of functions and so
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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