Grade 5 Mathematics MATHEMATICS Frameworks .17/02/2010  Grade 5 Mathematics Frameworks Unit 4

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Transcript of Grade 5 Mathematics MATHEMATICS Frameworks .17/02/2010  Grade 5 Mathematics Frameworks Unit 4

  • Grade 5 Mathematics Frameworks

    Unit 4 Geometry and Measurement Plane Figures

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  • Georgia Performance Standards Framework Fifth Grade Mathematics Unit 4 1st Edition

    Georgia Department of Education Kathy Cox, State Superintendent of Schools

    MATHEMTATICS GRADE 5 UNIT 4: Geometry and Measurement Plane Figures February 17, 2010 Page 2 of 91

    Copyright 2010 All Rights Reserved

    Unit 4 Geometry and Measurement Plane Figures

    (6 weeks) TABLE OF CONTENTS

    Overview..............................................................................................................................3 Key Standards & Related Standards ....................................................................................4 Enduring Understandings.....................................................................................................6 Essential Questions ..............................................................................................................6 Concepts & Skills to Maintain.............................................................................................7 Selected Terms and Symbols ...............................................................................................8 Classroom Routines .............................................................................................................9 Strategies for Teaching and Learning ..................................................................................9 Evidence of Learning...........................................................................................................9 Tasks .................................................................................................................................10

    Archimedes Box ...................................................................................................11 Who Put the Tang in Tangram?.............................................................................23 Whats My Area?...................................................................................................36 King Arthurs New Table ......................................................................................41 Its As Easy As Pi ..................................................................................................48 The Circles Measure.............................................................................................52 Circle Cover-Up.....................................................................................................61

    Culminating Task Stained Glass Designs........................................................................................................74

  • Georgia Performance Standards Framework Fifth Grade Mathematics Unit 4 1st Edition

    Georgia Department of Education Kathy Cox, State Superintendent of Schools

    MATHEMTATICS GRADE 5 UNIT 4: Geometry and Measurement Plane Figures February 17, 2010 Page 3 of 91

    Copyright 2010 All Rights Reserved

    OVERVIEW

    In this unit students will: derive the formula for the area of a parallelogram derive the formula for the area of a triangle find the area of regular and irregular polygons estimate the area of circles derive the formula for the circumference and area of a circle find the area of plane figures using formulae understand congruence of geometric figures and their corresponding parts understand the relationship of a circles circumference, diameter, and pi use variables for unknown quantities use formulae to represent the relationship between quantities Although the units in this instructional framework emphasize key standards and big ideas at

    specific times of the year, routine topics such as addition and subtraction of decimals and fractions with like denominators, whole number computation, angle measurement, length/area/weight, number sense, data usage and representations, characteristics of 2-D and 3-D shapes and order of operations should be addressed on an ongoing basis.

    To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under Evidence of Learning be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.

  • Georgia Performance Standards Framework Fifth Grade Mathematics Unit 4 1st Edition

    Georgia Department of Education Kathy Cox, State Superintendent of Schools

    MATHEMTATICS GRADE 5 UNIT 4: Geometry and Measurement Plane Figures February 17, 2010 Page 4 of 91

    Copyright 2010 All Rights Reserved

  • Georgia Performance Standards Framework Fifth Grade Mathematics Unit 4 1st Edition

    Georgia Department of Education Kathy Cox, State Superintendent of Schools

    MATHEMTATICS GRADE 5 UNIT 4: Geometry and Measurement Plane Figures February 17, 2010 Page 5 of 91

    Copyright 2010 All Rights Reserved

    STANDARDS ADDRESSED IN THIS UNIT

    Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics. KEY STANDARDS M5M1. Students will extend their understanding of area of geometric plane figures.

    a. Estimate the area of geometric plane figures. b. Derive the formula for the area of a parallelogram. c. Derive the formula for the area of a triangle. d. Find the areas of triangles and parallelograms using formulae. e. Estimate the area of a circle through partitioning and tiling. f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles,

    and/or triangles and find the sum of the areas of those shapes. g. Derive the formula for the area of a circle. h. Find the area of a circle using the formula and pi 3.14.

    M5M2. Students will extend their understanding of perimeter to include circumference.

    a. Derive the formula for the circumference of a circle. b. Find the circumference of a circle using the formula and pi 3.14.

    M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles. M5G2. Students will understand the relationship of the circumference of a circle to its diameter is pi ( 3.14). RELATED STANDARDS

    M5A1. Students will represent and interpret the relationships between quantities algebraically.

    a. Use variables, such as n or x, for unknown quantities in algebraic expressions. b. Investigate simple algebraic expressions by substituting numbers for the unknown. c. Determine that a formula will be reliable regardless of the type of number (whole

    numbers or decimals) substituted for the variable. M5P1. Students will solve problems (using appropriate technology).

    a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving.

  • Georgia Performance Standards Framework Fifth Grade Mathematics Unit 4 1st Edition

    Georgia Department of Education Kathy Cox, State Superintendent of Schools

    MATHEMTATICS GRADE 5 UNIT 4: Geometry and Measurement Plane Figures February 17, 2010 Page 6 of 91

    Copyright 2010 All Rights Reserved

    M5P2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.

    M5P3. Students will communicate mathematically.

    a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and

    others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely.

    M5P4. Students will make connections among mathematical ideas and to other disciplines.

    a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a

    coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.

    M5P5. Students will represent mathematics in multiple ways.

    a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical

    phenomena.

  • Georgia Performance Standards Framework Fifth Grade Mathematics Unit 4 1st Edition

    Georgia Department of Education Kathy Cox, State Superintendent of Schools

    MATHEMTATICS GRADE 5 UNIT 4: Geometry and Measurement Plane Figur