Overall Learning Goal
The overall learning goal of this unit is to lead students both to mastering the concepts of perimeter, area, and volume of rectangles and rectangular prisms and to computing the area of a rectangle and the surface area and volume of a rectangular prism. These activities will develop students’ understanding of the properties of rectangles and rectangular prisms. For simplicity, we will restrict attention to shapes with length, and width (and for prisms, height) that are whole numbers. More specifically, in using such manipulatives as unit squares and unit cubes and in using these tiles as polyominoes, students will be able to develop both concepts of and definitions for perimeter, area, and volume while also solving problems before deriving standard formulas (i.e. P = 2l + 2w; A = lw; and V = lwh). When they have derived standard formulas, students will work on their final project where they explore volume of rectangular prisms by constructing planters.
All activities in the unit will help students understand that rectangles are so simple a shape that formulas can take the place of counting with tiles. The final goal is then for students to make a connection between values derived from measurement with unit squares or unit cubes and values derived from the use of formulas. In other words, students should see that patterns occur when working with rectangles, allowing for the use of formulas. The result of achieving the curriculum unit’s main goal will be to emphasize concepts of measurement that can often be quite vague without concrete reinforcement. To do this, the curriculum will seek to re-teach foundational concepts of measurement such as those presented in Beckmann’s Mathematics for Elementary Teachers with Activities while expanding on knowledge necessary to master Virginia Standards of Learning regarding the area of rectangles.4 While this curriculum unit will center only on rectangles and rectangular prisms, students can apply what they have learned about these more rudimentary shapes to a wider array of polygons or solid shapes.
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