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MATH LENGTH OF TIME: One year GRADE LEVEL: 4 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-e) 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) 8. Conducts one large scale mathematical investigation and communicates the mathematical processes used, the reasoning, and the results found. (M7a-e, M8a-e) RELATED NEW STANDARDS M1 Arithmetic and Number Concepts solves addition and subtraction facts with multi-digit numbers gives equivalent names for numbers reads and writes numbers to millions gives values of digits in numerals to millions identifies and uses square numbers identifies fractional parts of a region and collections of objects makes magnitude estimates for multiplication problems identify place value to trillions and thousandths have a successful strategy for adding multi-digit numbers have a successful strategy for subtracting multi-digit numbers explain the relationship between multiplication and division solve basic multiplication facts solve extended multiplication facts MATH4\H: 05/03/17 use and explain strategies for solving multiplication and division stories have a successful strategy for solving multi-digit multiplication problems identify fractional parts of regions identify fractional parts of collections of objects use a map scale to estimate distances M2 Geometry and Measurement names, draw and labels line segments, lines and rays names and draws angles, triangles and quadrangles identifies and describes right angles and parallel lines uses personal references to estimate lengths in US customary units identified lines of symmetry draws the reflection of a figure using appropriate tools measures feet and inches describes properties of parallelograms uses two dimensional coordinate system to find locations on map or grid estimates and measures length, width, perimeter, and area calculates simple unit conversions (examples - between cm and m, hours and minutes) uses scales on maps M3 Function and Algebra finds missing numbers on a number line uses rate tables to solve problems uses linear equations (repeated patterns and functional relationships) recognizes that an equality remains the same, when the same change is made to both quantities uses letters, boxes, or symbols to stand for any number in an equation recognizes simple non-linear patterns (example - growing patterns, squaring, etc.) M4 Statistics and Probability Concepts finds the median of a set of data collects and organizes data to create line plots, graphs, tables and charts finds statistical landmarks for a set of data uses appropriate vocabulary to describe the probability of chance events uses statistical landmarks maximum and minimum calculates the probability of a simple event determine the fairness of the design of a spinner determine the patterns generated as a result of an experiment list all possible combinations within a limited number of variables MATH4\H: 05/03/17 M5 Problem Solving and Mathematical Reasoning has a successful strategy for solving multi-digit multiplication problems has a successful strategy for solving multi-digit addition problems has a successful strategy for solving multi-digit subtraction problems explains the relationship between multiplication and division uses and explains strategies for solving multiplication and division stories uses tables to solve problems solves elapsed time problems uses appropriate mathematical terms, vocabulary, symbols and graphs to clearly and logically explain solutions to problems solves problems that make demands on all three aspects of the solution process - formulation, implementation, and conclusion M6 Math Skills and Tools uses a map scale to estimate distances uses a calculator to rename any fraction as a decimal measure and draws angles with a protractor uses recall, mental computations, pencil and paper, measuring devices, manipulatives, calculators, and computers to achieve solutions M7 Math Communication uses and explain strategies for solving multiplication and division number stories describes properties of a parallelogram uses appropriate mathematical vocabulary and language in written and oral work shows mathematical work in a variety of ways (example - graph, chart, table) considers audience and purpose when communicating M8 Putting Mathematics to Work conducts one large scale project, drawn from the following: data study science study design of a physical structure management and planning pure mathematics investigation RELATED PENNSYLVANIA STATE STANDARDS 1. Number Sense, Properties, Operations A. Decimals B. Fractions C. Estimation and Rounding D. Multiples and Factors E. Whole Number Operations MATH4\H: 05/03/17 2. Measurement A. Area, Perimeter and Volume B. Customary and Metric Conversion C. Reasonable Measurement Units and Estimates D. 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. Interpreting Tables C. 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. Group and individual mathematical investigations. (Course Standards 8) 10. Free response questions with/without rubrics. (Course Standards 1-7) 11. Class and homework assignments. (Course Standards 1-7) DESCRIPTION OF COURSE: This course stresses the fundamentals, application, and appreciation of mathematics. Students will solve problems using skills commensurate to those standards indicated above and communicate effectively using mathematical language. Students will demonstrate number sense, problem solving skills, reasoning abilities, and technological skills throughout the course. Instruction will include, but not be limited to: Numeration through the million’s period; addition of 2, 3, or more addends into the thousand’s period with regrouping to include money; subtraction into the thousand’s period with regrouping to include money; multiplication and division facts through the nine’s table; multiplication of three-digit MATH4\H: 05/03/17 factors by two-digit factors with regrouping; division with two-digit divisors and threedigit dividends; adding and subtracting decimals to the hundredth’s place value; renaming fractions to lowest terms; addition and subtraction of fractions with unlike denominators; tell time to the nearest minute; metric and standard measurements in length, capacity, and weight; find perimeter, area, and volume of geometric figures; with problem solving skills, estimation abilities, and technology integrated throughout the course. TITLES OF UNITS: 1. Place Value 2 weeks 2. Whole Number Sense and Operations 18 weeks 3. Measurement 4 weeks 4. Decimals 3 weeks 5. Geometry 4 weeks 6. Fractions 5 weeks Technology, estimation, and problem solving (including algebra, graphs, charts, patterns, and interpretation of data) are integrated throughout the year. 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. Volunteer tutors MATH4\H: 05/03/17 6. Flexible/modified grouping 7. Re-teaching with alternative strategies 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 task 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 MATH4\H: 05/03/17 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 MATH4\H: 05/03/17