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

CONTENTS OF CURRICULUM UNIT 19.05.02

  1. Unit Guide
  1. Introduction
  2. Student and School Background Information
  3. Unit Learning Goals
  4. The Unit
  5. Strategies
  6. Activities
  7. Appendix
  8. Bibliography
  9. Notes

SmArt Math: Paper Polyominoes and Ceramic Tetradic Cuboids

Tina Marie Berry

Published September 2019

Tools for this Unit:

Unit Learning Goals

In this unit we will explore the concepts of 2D shapes and 3D forms and discuss why they are important in art, math, and real-world scenarios.  This unit aims to solidify students’ conceptual understanding of basic measurement and physical mastery of basic length measuring tools. 

The specific objectives for students in this lesson include:

  1. Demonstrate how to measure properly using a ruler, yard stick, and a tape measure, and which method to use for specific needs.
  2. Understand and apply knowledge of measurement of perimeter, area, and volume and the nature and names of the units associated with each of them.
  3. Use measurement to produce figures on a 2D surface (of the type known as “mathematical nets”) that students will fold up to create a 3D art piece.

Important points that I wish to convey to students:

  1. Unit consciousness is essential in measurement and other applications of math.
  2. Rectangles with whole number side lengths are simple shapes that can be broken down into single square units that are then used to measure perimeter and area.
  3. Complicated planar shapes can be decomposed, or broken down, into simple shapes.
  4. Math does have many true, genuine uses in the practical world, outside of academics.

To reach these ends, my students will be doing various activities to scaffold learning.  They will work with the basic measuring tools to measure area, perimeter, and volume.  They will practice with manipulatives to create and understand polyominoes, then use their knowledge of polyominoes to draw all the hexomino nets that can make a cube.  They will then use the cubes they create to understand tetradic cuboids (solid form made from four cubes).  They will use these cuboids to create their own templates for clay planar tiles.  At the end of the 5-week project each student will have a finished ceramic box that meets given dimension specifications based on the perimeter of a square, the area of a rectangle, and the volume of a cube.  

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