Concord Consortium
Three Rubber Bands
Stretch your mind about triangles. Given a triangle, scholars consider a smaller triangle formed when they stretch three rubber bands from each vertex to the opposite side. They determine the ratios of the areas and perimeters of the...
101 Questions
Transforming Houses
Moving a house is hard work. Given a diagram of a row of houses, scholars determine a set of transformations that would map one house to the next. A second diagram with a coordinate plane helps with the task.
CK-12 Foundation
Angle-Side-Angle Triangles: Caution Tape
Don't lose your marbles. Scholars use an interactive to create a triangle that closes off a portion of a sidewalk with loose marbles. The Law of Sines helps them find the side measures of such a triangle.
CK-12 Foundation
Identify Accurate Drawings of Triangles: Law of Cosines
Drawing triangles is easy, even if you have to calculate the exact length of its sides. Scholars use the Law of Cosines to find missing sides of triangles. An interactive helps them check their answers.
Virginia Department of Education
Similar Solids and Proportional Reasoning
Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral...
Virginia Department of Education
The Exercise Fields
Horses need exercise, too. Scholars create linear equations to model the perimeter of exercise fields for horses. They finish by solving their equations for the length and width of the fields.
Mathed Up!
3-D Pythagoras
Apply the Pythagorean Theorem in three-dimensional shapes. Young mathematicians watch a video that takes them through several examples of using the Pythagorean Theorem to solve problems involving lengths in three-dimensional figures. A...
Mathed Up!
Sine and Cosine Rules and Area of Triangles
Learners discover how to find missing sides and angles using trigonometry. Scholars first watch a video covering the Law of Sines and Cosines, as well as the area formula for a triangle. To test their knowledge, they complete a...
Mathed Up!
Spheres and Cones
Class members learn how to apply formulas for spheres and cones with a video that begins with a review of the formulas for surface area and volume of spheres and cones. Pupils use these formulas to solve problems on a worksheet.
Mathematics Assessment Project
Hopewell Geometry
Right triangles from 2,000 years ago? Learners investigate different right triangles found in the earthworks of the Hopewell people, a Native American culture that populated the United States from 200BC to AD 500. Learners apply concepts...
Mathematics Assessment Project
Pythagorean Triples
What special relationships exist in right triangles? In the high school performance task, learners investigate Pythagorean triples. They then determine rules for the perimeter and area of right triangles given the shortest side.
Mathematics Assessment Project
Triangular Frameworks
What did the triangle say to the circle? You're pointless! Class members will get the point when they investigate relationships between side lengths of a triangle using the Triangle Inequality Theorem. Pupils then create an algebraic...
EngageNY
Construct a Nine-Point Circle
There are an infinite number of points on a circle; can you find nine of them? After putting together a nine-point circle, pupils use constructions and their knowledge of triangle segments to determine the center of the circle. Learners...
Wake Forest University
Authentic Activities for Connecting Mathematics to the Real World
Check out the handout from a presentation that contains a collection of high school algebra projects connecting a variety of mathematics to the real world. Activities range from simple probabilities to calculus. The activities can be...
Harvard University
The Nouns of Geometry
Socratic questioning to teach Euclidean geometry? "The Nouns of Geometry," followed by "The Verbs of Geometry," and the misfit, "A Beginner's Story - The Equilateral Triangle" are designed to encourage learners to explore various topics...
West Contra Costa Unified School District
The Parallelogram Law
Use your pupils' sense of curiosity to explore the Parallelogram Law. Here is an activity that outlines a complete lesson plan from beginning to end, allowing pupils to follow a conjecture through to the proof stage.
Curated OER
Parallel and Perpendicular Lines
Young geometers get some solid skills practice in evaluating slopes. Beginning with the basics of slope through two points and progressing through properties of parallel and perpendicular lines, the building of skills is gradual and...
Illustrative Mathematics
Global Positioning System II
Intricate details of a modern technology that many of us take for granted in our phones, computers (and some cars) are laid bare in a short but deeply investigative activity. The math behind a seemingly simple GPS device is...
Lone Star College
Geometry Worksheet II
Young geometers get practice with the algebra of angles in an extensive skills practice learning exercise. Supplementary, complementary, and vertical angle relationships are used, along with parallel lines cut by a transversal and angle...
Illustrative Mathematics
Slopes and Circles
An upper-level treatment of what is often presented as a basic concept (the right angle of an inscribed circle on the diameter), this activity really elevates the mathematical thought of the learner! Expected to develop formulas from...
Illustrative Mathematics
Use Cavalieri’s Principle to Compare Aquarium Volumes
Learners are designing a stunning new water feature for an aquarium, but they soon discover that more than just a pretty home for their fishy friends is required. From calculating the volume of a composite shape through the abstract...
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using information about...
Kim Brassard
Solving Right Triangles
Solve that triangle! Your class examines angles and side measurements on 20 right triangles to determine the missing measurements. For some, they are given two sides while for others, they are given an angle and a side.
Curated OER
Solidly Platonic
When they do, they learn. Using this resource, young mathematicians learn about platonic solids by actually building, touching, and examining the shapes. They connect their observations about the shapes to Euler's formula.