Shapes, Space, and Structure

You spent the last unit thinking like a mathematician about data and probability. Starting today, you'll use those exact same five habits, just aimed at a new target: shapes, space, and measurement. Mathematicians who study geometry still make sense of a problem and stick with it even when their first plan fails (Problem SolvingMaking sense of a problem and persevering even when a first plan fails.). They still notice that one math idea shows up in different forms, and connect it to the real world (ConnectionsNoticing that math ideas are the same idea in different forms, and connecting math to real life.).

They explain their thinking with precise language, models, and tools so someone else can follow exactly what they did (Representation & CommunicationExplaining thinking with precise language, models, and tools so someone else can follow it exactly.). They check whether an argument, theirs or someone else's, actually makes sense, and revise their thinking when new evidence shows up (Analyze & JustifyChecking whether an argument makes sense and revising thinking when new evidence appears.). And they hunt for patterns in repeated work, because a pattern is often a shortcut in disguise (Structure & PatternsHunting for patterns in repeated work because a pattern is often a shortcut in disguise.).

This strand is called Measurement, Geometry & Spatial Reasoning, MGSR for short, and it has three big chapters. First, you'll measure and build shapes: finding the area of flat figures, folding three-dimensional shapes into flat nets, and using those nets to find surface area. Later, you'll measure angles with a protractor, and finally you'll locate and move points on a full four-quadrant coordinate plane. Today you're starting chapter one with a shape you may not have named before: the trapezoid, a four-sided figure with exactly one pair of parallel sides. By the end of this week, you'll be finding the area of triangles, squares, rectangles, parallelograms, and trapezoids, and you'll lean on Structure & Patterns to do it: every one of those shapes can be broken into pieces you already know how to measure.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.