Model a bicycle chain with circles and tangent lines. Given the dimensions of the sprocket wheels, young scholars calculate the length of the chain that surrounds them. A second task has learners write a function for the length of a...

High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve...

Circles, and triangles, and tangents, oh my! In the assessment task, learners first answer questions leading to the radius of an inscribed circle for a given right triangle. They then use the result to independently determine the...

Go around the unit circle and create triangles. Pupils move a point around the unit circles to visualize the triangle associated with the angle in standard position. The three main trigonometric functions are defined in terms of the legs...

Solve problems around a circle. Pupils watch a video that shows how to apply concepts about circles and related angles and segments to find solutions to word problems. Learners then review the different concepts from the unit in...

In this circles and ellipses worksheet, students solve and complete 5 different types of problems. First, they write each equation in standard form. Then, students graph and label Write the equation of the ellipse whose center is the...

In this circles and ellipses instructional activity, students solve and complete 12 different types of problems. First, they find the distance between the given pair of points. Then, students find the center and radius of each circle and...

Construct tangent lines and make the connection to tangent functions. An informative activity reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a circle from a...

You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their...

Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...

What do skateboarding and baked goods have in common with math? You can use them to connect half-pipe ramps and cakes to arcs and sectors. Pupils compare the lengths of three different ramp options of a skate park. They calculate the...

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 +...

Show budding mathematicans how to find the sine of pi over 12. The third lesson plan in a series of 16 introduces the addition and subtraction formulas for trigonometric functions. Class members derive the formulas using the...

In this equations of circles instructional activity, 10th graders solve 10 different problems that include graphing different circles. First, they convert the equations into center-radius form given the coordinates of the center of the...

In this circles worksheet, 10th graders solve 10 different problems that include determining the chords, secants, and tangents of circles shown. First, they determine 4 different line segments given a circle with secants and chords with...

In this geometry worksheet, students find the sum of the perimeters of three small circles.  These small circles are tangent to each other and to a larger circle.  The centers of the small circles have their centers on the...

In this circles activity, students solve 10 multiple choice problems. Students use a diagram of a circle with tangent lines and segment bisectors to answer each question. Students find unknown segment lengths using the given information.

For this circle worksheet, learners solve classic chord-chord angle problems with the angle on, in, and outside the circle as well as chord-tangent problems. There are 20 questions. 

Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the instructional...

From a circle to a cycle! The final lesson plan of a five-part series challenges learners to use points from the unit circle to plot a repeating pattern. The repeating patterns become the graphs of the trigonometric functions....

Students construct tangent lines. In this geometry lesson, students identify the point of tangency, secant and tangent lines. They graph the lines on the Ti and make observations.

Your Geometry learners will collaboratively prove that the tangent line of a circle is perpendicular to the radius of the circle. A deliberately sparse introduction allows for a variety of approaches to find a solution. 

Students differentiate between the slope and the tangent of the horizontal. In this precalculus instructional activity, students examine slopes created by tangent lines. They observe the angle formed using properties of the unit...