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MATH LENGTH OF TIME: one year GRADE LEVEL: 2 COURSE STANDARDS: Students will: 1. Use numbers, number systems, and equivalent forms (including numbers, words, objects, and graphics) to represent theoretical and practical situations. (M1a-f, M2ak) 2. Compute, measure, and estimate to solve theoretical and practical problems using appropriate tools which include modern technology such as calculators and computers. (M1a-f, M2a-k, M6a-h) 3. Apply the concepts of patterns, functions, and relations to solve theoretical and practical problems. (M3a,d, M6a-h) 4. Formulate and solve problems while being able to communicate the mathematical processes used and the reasons for using them. (M5a-c, M6a-h, M7a-c) 5. Understand and apply the basic concepts of algebra, geometry, probability, and statistics to solve theoretical and practical problems. (M2a-k, M3a,d) 6. Evaluate and draw references from charts, tables, and graphs showing the relationships between data and real-world situations. (M4a-f, M5a-c, M6a-h) 7. Make decisions based upon the collection, organization, analysis, and interpretation of statistical data and predictions of outcomes based upon the application of probability. (M4a-f, M5a-c, M6a-h) RELATED NEW STANDARDS M1 Arithmetic and Number Concepts count by 2's and 10's from any given 2 or 3 digit number construct fact families and extended fact families for + and understand "What's My Rule?" routine using unknown rule extend addition and subtraction facts to tens and hundreds use a calculator to add 3 or more 2-digit numbers correctly add one digit numbers mentally use comparison symbols add three 1-digit numbers mentally count by 2's and 10's forward and backward from any 2 or 3-digit number multiply numbers with one as a factor solve addition and subtraction fact extensions mentally use multi-digit addition strategies know complements of 10 identify place values in 3-digit numbers write 2 and 3-digit numbers from dictation MATH2\4A 5/8/2017 read 3 and 4-digit numbers read and write (from dictation) 4-digit numbers shade requested fractional parts of a region give fraction name for a shaded part of a region show coins for a given amount of money using penny, nickel, dime and quarter knows cent values of nickel, dime, quarter, half-dollar and dollar knows exchange values among US coins use equivalent coins to show money amounts use a calculator for entering and computing money amounts understand the concept of equivalent number names for 2 and 3-digit numbers M2 Geometry and Measurement use linear measuring tools identify common 3D shapes such as prisms, cylinders, pyramids, cones and spheres draw given line segments use a ruler, tape measure, meter/yard stick correctly show progress with calendar concepts and skills M3 Function and Algebra Concepts use comparison symbols <, >, = correctly uses linear patterns to solve problems: one quantity determines another one (repeated pattern); one quantity determines another quantity in a functional relationship (number of people and total number of eyes) uses letters, boxes or other symbols to stand for any number in simple situations with concrete materials M4 Statistics and Probability Concepts collect and predict class data through daily routines collect and predict individual data use individual and class data to make comparisons (e.g. shortest, tallest, etc.) record and make prediction on the frequency of various events (e.g. weather, bed times) sort groups by attributes use various graphs to display data use a table to display data and frequency of events plot data on various graphs cooperatively graph data share observations about various graphs independently sort groups of attributes compare quantities from graphs read various graphs tally quantities and frequencies of events MATH2\4A 5/8/2017 find median value of a data set compare data from daily activities compare data results of various events finds all possible combinations with a limited number of variables M5 Problem Solving and Mathematical Reasoning draw pictures to solve problems manipulate objects to solve a problem write word stories make a list to solve problems explain a solution to a number story determine which strategy can be used to solve a number problem compare and contrast patterns compare and contrast number stories and their solutions use mathematical rules in different contexts apply strategies to solve curriculum integrated problems M6 Mathematical Skills and Tools tell time to 5 minute intervals use equivalent coins to show money amounts demonstrate calendar concepts and skills use a calculator to add 3 or more 2-digit numbers use a rules, tape measure, meter/yard stick use a calculator for entering and computing money amounts uses recall, mental computations, pencil and paper, measuring devices, manipulatives, calculators, computers to achieve solutions M7 Mathematical Communication write 2 and 3-digit numbers from dictation read 3 and 4-digit numbers write addresses correctly uses appropriate mathematical terms, vocabulary and language based on prior conceptual work shows mathematical ideas in a variety of ways, including words, numbers, symbols, picture, charts, graphs, tables and diagrams explains solutions to problems clearly and logically and supports solutions with evidence in both oral and written work RELATED PENNSYLVANIA STATE STANDARDS 1. Number Sense, Properties, Operations A. Decimals B. Fractions C. Estimation and Rounding D. Whole Number Operations MATH2\4A 5/8/2017 2. Measurement A. Area, Perimeter and Volume B. Reasonable Measurement Units and Estimates C. Solving Problems Involving Measurement Units 3. Geometry A. Identification and Properties of Geometric Shapes B. Lines and Angles C. Visualizing Constructed and Changed Shapes 4. Data Analysis, Statistics and Probability A. Interpreting Graphs B. Probability and Statistics 5. Algebra and Functions A. Finding Unknown B. Patterns PERFORMANCE ASSESSMENTS: Students will demonstrate achievement of the standards by: 1. Objective tests using pencil, paper, and calculator activities with/without rubrics. (Course Standards 1-7) 2. Demonstration of the problem solving process with routine and non-routine problems. (Course Standards 1-7) 3. Oral questioning and interviewing. (Course Standards 1-7) 4. Self and peer assessment. (Course Standards 1-7) 5. Teacher observation at completion of task or activity. (Course Standards 1-7) 6. Student portfolio to maintain student work. (Course Standards 1-7) 7. Math journal. (Course Standards 1-7) 8. Oral or written presentation to demonstrate a solution, concept, project, survey, etc. with/without rubrics. (Course Standards 1-7) 9. Free response questions with/without rubrics. (Course Standards 1-7) 10. Class and homework assignments. (Course Standards 1-7) DESCRIPTION OF COURSE: This course stresses the fundamentals, application, and appreciation of mathematics. The course focuses on the NCTM Standards suggested for second grade to include problem solving, communication with the use of math language, reasoning ,estimation, number sense and numeration, whole number concepts and computation, geometry, measurement, fractions, patterns, statistics, and probability. Technology will be integrated throughout the course. The course will be presented to the students in a manner that appropriately follows the district’s Developmentally Appropriate Practices Program. Instruction will include, but not be limited to: addition and subtraction facts through 18; numeration and place value through 999 (including skip counting 2,3,5,10); identifying coin currency; comparing money amounts through $1.99; determine and compare times by the hour, half-hour, and five minutes; calendar days, weeks, and months; measurement units including centimeter, MATH2\4A 5/8/2017 inch, liter, cups, pints, quarts, gallons, kilogram and pound; addition and subtraction of two and three digit whole numbers with limited renaming; multiplication by twos, threes, fours, and fives; construct and name squares, rectangles, triangles, circles; writing fractions and diagrams including halves, thirds, fourths, and tenths; constructs bar graphs, charts, pictographs, surveys, and tallies; with problem solving skills, estimation abilities, and technology integrated throughout the course. TITLES OF UNITS: 1. Number sense and operations 12 weeks 2. Measurement 4 weeks 3. Probability and statistics 6 weeks 4. Patterns and geometry 4 weeks 5. Time and money 4 weeks 6. Problem solving, estimation, and technology are appropriately integrated throughout SAMPLE INSTRUCTIONAL STRATEGIES: 1. Teacher/student made activities 2. Teacher/student led discussions and activities 3. Problem solving strategies 4. Calculators and computers 5. Individual and group explorations and investigations 6. Games and manipulatives 7. Written explanations and journal activities 8. Teacher/peer modeling 9. Math Word Wall MATERIALS: 1. Everyday Mathematics: The University of Chicago School Mathematics Project, Everyday Learning Corporation, 1999, Chicago, Illinois. 2. Calculators 3. Computers 4. Enrichment materials 5. Computer software 6. Standard related games and manipulatives 7. Base 10 blocks METHODS OF ASSISTANCE AND ENRICHMENT: A. Assistance 1. IST 2. Cooperative groups 3. ADAPT 4. Peer helpers 5. Volunteers/tutors 6. Flexible/modified grouping 7. Re-teaching with alternative strategies MATH2\4A 5/8/2017 8. Extended instructional time B. 1. 2. 3. 4. 5. 6. 7. Enrichment Modified curriculum Peer tutoring Modified testing Math journal and/or projects Individual mathematical investigations IST PAL PORTFOLIO DEVELOPMENT: 1. Teacher/student assessments 2. Math journals 3. Individual/group investigations, projects, and/or activities 4. Written explanation of problem solving strategies 5. Student reflections 6. End of the year assessment task (measure all skills) 7. District developed four problem solving tasks (measure all focused problem solving strategies) METHODS OF EVALUATION: 1. Teacher/student checklists 2. Individual/group tests 3. Investigations, projects, and/or journals 4. Problem solving activities 5. Written and oral presentations 6. End of the year assessment tasks 7. District developed four problem solving tasks INTEGRATED ACTIVITIES: 1. Concepts -demonstrate knowledge of the basic concepts and principles for the above mentioned standards 2. Communication -compose and make oral presentations using appropriate mathematical language -written entries in math journal using appropriate mathematical terms and vocabulary -explains solutions and strategies clearly and logically with supporting evidence -listen to, and understand, oral math presentations MATH2\4A 5/8/2017 3. Thinking/Problem Solving -apply the concepts of the above mentioned standards to formulate and solve problems -make critical judgments using the learned skills -draw conclusions and show relationships in mathematical settings -make decisions and predictions based upon the application of learned skills 4. Application of Knowledge -use learned skills to solve authentic problems -exhibit skills with calculators and computers -examine, evaluate, and solve routine and non-routine problems 5. Interpersonal Skills -work cooperatively with others on projects and investigations -work effectively with others on projects and investigations -communicate effectively using appropriate mathematical language MATH2\4A 5/8/2017