You know about the tangent function, but what are tangent lines to a circle? Learners investigate properties of tangents through constructions. They determine that tangents are perpendicular to the radius at the point of tangency,...

What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...

Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.

What does completing the square have to do with circles? Math pupils use completing the square and other algebraic techniques to rewrite equations of circles in center-radius form. They then analyze equations of the form x^2 + y^2 + Ax +...

Don't go off on a tangent while writing equations of tangent lines! Scholars determine the equations for tangent lines to circles. They attempt both concrete and abstract examples, such as a tangent line to the unit circle through...

What does it mean for a quadrilateral to be cyclic? Mathematicians first learn what it means for a quadrilateral to be cyclic. They then investigate angle measures and area in such a quadrilateral.

Fold, fold, and fold some more. In the first installment of a 35-part module, young mathematicians fold a piece of paper in half until it can not be folded any more. They use the results of this activity to develop functions for the area...

(vegetable)^(1/2) = root vegetable? The fourth installment of a 35-part module has scholars extend properties of exponents to rational exponents to solve problems. Individuals use these properties to rewrite radical expressions in...

Won't the other properties be sad to learn that they're not the most important? The 11th installment of a 35-part module is essentially a continuation of the previous lesson, using logarithm tables to develop properties. Scholars...

These aren't models made of clay. Young mathematicians model given population data using exponential functions. They consider different models and choose the best one.

Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

Solve any issues you have with solving linear equations. Learners solve linear equations in one variable, starting with two-step equations, in the first chapter of a 10-part eighth-grade workbook series. They then progress to equations...

A one-stop resource for exponents, square and cube roots, scientific notation, and volume formulas guides learners through properties of exponents. As they learn to apply these properties to operations with scientific notation,...

Now that you know the ocean has layers, let's name them. The seventh installment of a 23-part NOAA Enrichment in Marine sciences and Oceanography (NEMO) program covers terminology associated with ocean layers, such as thermocline and...

Tired of going around and around for a resource on circles? Scholars determine the general equation of a circle on a coordinate plane, then participate in an activity matching equations to the radii and centers of the circles...

The Lotus Effect ... is it not some kind of yoga pose. In the last installment of a nine-part series, young scientists observe the Lotus Effect on lotus leaves and water-repellent cloths. They observe how motion and damage affect the...

How temperature affects the efficiency of a solar panel is the focus of the third in a series of eight resources that presents how engineers are able to control the temperatures of photovoltaic panels. Class members find out how the...

Challenge young minds to build a better world with genetic engineering. Biologists learn potential solutions for environmental issues using genome editing while interacting with three case studies. Scholars read articles and view...

How do major religions, including Judaism, Christianity, and Islam, differ in how they view the role of individual freedoms within society, the definition of morality, and the importance of politically satisfying the greater...

Dig deep into any piece of poetry with a set of analysis questions. Ponder the content, form, and language of poetry and provide some question for critique. The first two pages include general questions, and the remainder of the document...

Test probability concepts with an activity that asks pupils to first complete a task investigating false positive in medical testing and then to evaluate sample responses to the same task.

Solving problems about pen and paper with systems of equations ... or is it the other way around? In the lesson, learners first interpret expressions and use equations in two variables to solve problems about notebooks and pens. They...

Line up to learn about lines! Scholars discover how to express patterns as linear functions. The workbook then covers how to graph and write linear equations in slope-intercept form, as well as how to write equations of...

Conquer any irrational fears you might have of irrational numbers. As class members investigate how to represent numbers geometrically, they learn about rational and irrational numbers, including approximating and ordering rational...