Curated OER
The Pythagorean Puzzle
An engaging hands-on activity is presented. Learners of all ages are addressed in thie unique plan. K-5 learners identify, name, and define a rectangle, square, triangle, and the concept of area. Older learners prove the Pythagorean...
Curated OER
Worksheet 6: Functions
In this math worksheet, young scholars answer 7 questions having to do with continuous functions, the Squeeze Theorem, and the Product Rule for differentiation.
Curated OER
Pascal's Theorem
In this Pascal's Theorem activity, students prove 1 theorem. Students use GeoGebra to construct lines given three points and prove Pascal's Theorem.
EngageNY
Similarity and the Angle Bisector Theorem
Identifying and verifying reproducible patterns in mathematics is an essential skill. Mathematicians identify the relationship of sides when an angle is bisected in a triangle. Once the pupils determine the relationship, they prove it to...
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
Illustrative Mathematics
Area of a Trapezoid
Here is a straightforward example of how to apply the Pythagorean Theorem to find an unknown side-length of a trapezoid. Commentary gives additional information on proving that the inside of the trapezoid is a rectangle, but is...
Curated OER
The Notorious Four-Color Problem
Take a walk through time, 1852 to 2005, following the mathematical history, development, and solution of the Four-Color Theorem. Learners take on the role of cartographers to study a United States map that is to be colored. One rule: no...
Curated OER
Logical Relationship of Postulates & Theorems
For this postulates and theorems worksheet, students explore a concept map containing information about angles and sides, alternate interior angles, and diagonals of a parallelogram. They use the concept map to prove theorems dealing...
Curated OER
The Pythagorean Theorem
Young scholars create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. They construct a square and conjecture the following theorem: The sum of the areas...
Curated OER
Fundamental Theorem of Algebra
In this learning exercise, learners identify the Fundamental Theorem of Algebra. They solve polynomial functions and simplify expressions and equations.
Mathematics Vision Project
Connecting Algebra and Geometry
Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates including...
EngageNY
What Is a Trigonometric Identity?
Protect yourself from identity theft! Establishing a strong understanding of the Pythagorean identity allows learners to prove that sine^2x + cos^2x = 1. They then use the identity to find sine or cosine ratios given the other.
University of Utah
Geometry: Angles, Triangles, and Distance
The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.
Illustrative Mathematics
Shortest Line Segment from a Point P to a Line L
One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the class...
Curated OER
Proving Triangles Congruent
In this proving triangles congruent worksheet, 10th graders solve 5 different problems that include proofs and proving congruence in triangles. First, they determine which postulate can be used to prove the triangles congruent and mark...
Curated OER
Pythagorean Theorem
Students investigate the Pythagorean Theorem. In this seventh through twelfth grade geometery lesson, students explore the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right triangle.
Curated OER
Investigating the Pythagorean Theorem
Students problem solve a series of problems based on the Pythagorean Theorem. They apply the theorem to a number of scenarios.
Curated OER
Central Valley Math Project
Middle schoolers study the Pythagorean Theorem. They describe what it means to square a number. Pupilsuse the Pythagorean Theorem to prove the sides of given triangles, and use geometric pieces of paper to create a right triangle and...
Curated OER
Analyzing Congruence Proofs
Looking at numerous examples of triangles, each with different properties, geometers develop their understanding of congruency. They use the notation of a counter-example to disprove certain conjectures and prove geometric theorems and...
Curated OER
Calculus 2.1 day 2 - Step Functions
"Step functions" are sometimes used to describe real-life situations. This extensive lesson with many practice examples demonstrates two such functions: the Greatest Integer Function and the Least Integer Function. The commands on the...
EngageNY
Unknown Angle Problems with Inscribed Angles in Circles
We know theorems about circles—now what? Class members prove a theorem, with half the class taking the case where a point is inside the circle and half the class taking the case where a point is outside the circle. The lesson then...
EngageNY
Comparing the Ratio Method with the Parallel Method
Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...
EngageNY
Circles, Chords, Diameters, and Their Relationships
A diameter is the longest chord possible, but that's not the only relationship between chords and diameters! Young geometry pupils construct perpendicular bisectors of chords to develop a conjecture about the relationships between chords...
Mathematics Vision Project
Module 6: Connecting Algebra and Geometry
A geometry module connects algebraic reasoning to geometry. It challenges scholars to investigate the slope criteria for parallel and perpendicular lines, prove theorems involving coordinate geometry, and write equations for circles and...