Building on the previous lesson in the 29-part series, the ninth lesson asks individuals to construct a triangle given specific criteria. First, they are given three specific side lengths, followed by two sides and the included angle....

Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...

Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

Create concrete examples of triangle congruence for your classes. The eighth installment of the 29-part module sets the stage for studying triangle congruence. Given a set of criteria, math scholars use constructions to build a specific...

Construct an understanding of triangle congruence through a visual analysis. Young scholars find that given two sides and a non-included angle, sometimes two possible triangles are produced. Their analysis shows that if the non-included...

Learn about constructing figures, proofs, and transformations. The seventh unit in a course of nine makes the connections between geometric constructions, congruence, and proofs. Scholars learn to construct special quadrilaterals,...

Construct yourself a winning geometry unit. A set of lessons introduces geometry scholars to constructions and proofs with compasses and straightedges. It also covers triangle congruence through transformations. This is the second of...

Triangles, triangles, and more triangles! In this second installment of a 36-part series, your young mathematicians explore two increasingly challenging constructions, requiring them to develop a way to construct three triangles that...

Drawing circles isn't the only thing compasses are good for. In this first installment of a 36-part series, high schoolers learn how to draw equilateral triangles by investigating real-world situations, such as finding the location of a...

Your geometry learners will discover and show the construction of the circumcenter of a triangle. Guided by the steps in the activity, they construct perpendicular bisectors of each side that have a point of concurrency called the...

Young mathematicians build an understanding of area and perimeter with their own two hands in a series of interactive geometry lessons. Through the use of different math manipulatives, children investigate the properties of...

Middle schoolers study the triangle inequality. They will identify, compare, and analyze attributes of two and three-dimensional shapes. Then they develop vocabulary to describe the attributes. They also use manipulatives to analyze the...

More constructions! In this third installment of a 36-part series, learners watch a YouTube video on creating door trim to see how to bisect an angle. They then investigate how to copy an angle by ordering a given list of steps.

Try to figure out what happens with shadows as a person moves between two light sources. A formative assessment activity has individuals work on an assessment task based on similar triangles, then groups them based on...

Add up areas of squares to discover the pythagorean relationship. Small groups create right triangles with squares along each side. They calculate the areas of each square and notice the relationship. Groups construct other types of...

Use the parallel lines to find your way. After first reviewing geometric constructions and the relationships between angles formed by parallel lines and a transversal, young mathematicians write proofs for theorems relating to parallel...

Ever dream of becoming an architect? Here's your chance to give it a try. After reviewing facts about triangles and quadrilaterals, pupils learn about the basics of architecture by talking to an architect or housing expert. They use...

Your learners connect the new concepts of transformations in the coordinate plane to their previous knowledge using the solid vocabulary development in this unit. Like a foreign language, mathematics has its own set of vocabulary terms...

You say that perpendicular bisectors intersect at a point? I concur! Learners investigate points of concurrencies, specifically, circumcenters and incenters, by constructing perpendicular and angle bisectors of various triangles.

Your geometry learners are guided by questions that help them use the language of reflections to explain the Side-Angle-Side congruence between two triangles in this collaborative task. Given a sample solution, declaring the...

Most adults remember learning about the Pythagorean theorem, but they don't all remember how to use it. The emphasis here is on developing an intuitive understanding of how and when to use the theorem. Young mathematicians explore...

It's time to get crafty with shapes! Your future farmers demonstrate their geometric ability by building a farm using triangles, circles, rectangles, and squares. But first, scholars take part in a brainstorm session inspired by their...

Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from...