Base plans

Learning Objectives Identify the purpose of a base plan in representing 3D figures. Interpret a given base plan to visualize the corresponding 3D figure. Construct a base plan from a given 3D figure made of unit cubes. Determine the number of unit cubes required to build a 3D figure from its base plan. Calculate the volume of a 3D figure given its base plan. Distinguish between a base plan and other 2D views (front, side). Ever tried to build something with LEGOs just by looking at a picture from above? 🏗️ That's kind of like what we do with base plans in math! In this lesson, we'll explore base plans, a powerful tool for representing three-dimensional figures on a two-dimensional surface. You'll learn how to create and interpret these plans, which are essent...

TermDefinitionExample Three-Dimensional (3D) FigureA figure that has length, width, and height, occupying space.A cube, a rectangular prism, a pyramid, or a stack of blocks. Two-Dimensional (2D) RepresentationA drawing or plan that shows a 3D object on a flat surface, lacking actual depth.A photograph of a building, a map, or a blueprint. Base Plan (Top View with Heights)A 2D drawing that shows the arrangement of the base of a 3D figure, often indicating the height (number of unit cubes) of each section or stack from a top-down perspective.A grid with numbers in each cell, where '3' means a stack of 3 unit cubes. Unit CubeA cube with side lengths of 1 unit, used as the basic building block for many 3D figures.A 1x1x1 cube, often used to construct larger composite figures. Volume...

Interpreting a Base Plan Each cell in a base plan grid represents a column of unit cubes, and the number in the cell indicates the height of that column. Use this rule to visualize the 3D structure by imagining stacks of cubes on each square of the base. A '0' indicates an empty space on the base. Calculating Volume from a Base Plan $V = \sum_{i=1}^{n} h_i$ To find the total volume ($V$) of a figure represented by a base plan, sum the numbers ($h_i$) in all the cells of the plan. Each number represents the number of unit cubes in that stack, and $n$ is the total number of cells. Constructing a Base Plan Observe the 3D figure from directly above. For each square on the base, count the number of unit cubes stacked vertically at that position and write this numb...