Perimeter, Area, Volume, and All That: A Study of Measurement

CONTENTS OF CURRICULUM UNIT 19.05.01

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Academic context and learners
  4. Learning Goals of the Unit
  5. Background knowledge for teachers
  6. The sequence of the Unit and Implementation
  7. Teaching strategies
  8. Classroom Activities
  9. Bibliography
  10. Endnotes
  11. Appendix

A Pathway to Understanding Area and Perimeter

Lianne Aubert Sanfeliz

Published September 2019

Tools for this Unit:

Appendix

The academic standards this unit is intended to cover are listed and described below.

All the standards refer to 3rd-grade mathematical content and mathematical practices.

As the Oklahoma Department of Education didn’t adopt the Common Core State Standards (CCSS), I have included in this appendix, the Oklahoma Standards for Geometry and Measurement that pertain to this unit, as well as the Common Core State Standards, and the Mathematical Practice standards.

Oklahoma Academic Standards for Mathematics 3rd Grade.

Geometry and Measurement:

3.GM.2.1 Find perimeter of a polygon, given whole number lengths of the sides, in real-world and mathematical situations.

3.GM.2.2 Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns.

3.GM.2.8 Find the area of two-dimensional figures by counting the total number of same size unit squares that fill the shape without gaps or overlaps.

Mathematical Actions and Processes:

Develop a Deep and Flexible Conceptual Understanding. Students will demonstrate a deep and flexible conceptual understanding of mathematical concepts, operations, and relations while making mathematical and real-world connections.

Develop the Ability to Make Conjectures, Model, and Generalize. Students will create, identify, and extend patterns as a strategy for solving and making sense of problems.

Develop the Ability to Communicate Mathematically. Students will discuss, write, read, interpret, and translate ideas and concepts mathematically. 19

Common Core State Standards for Mathematics 3rd Grade.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.C.6 Measure areas by counting unit squares.

3.MD.C.7 Relate area to the operations of multiplication and addition.

Geometric measurement: recognize perimeter.

3.MD.D.8 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.20

Standards for Mathematical Practice:

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, and knowing and flexibly using different properties of operations and objects.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure.

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