In this concurrent circles using GeoGebra worksheet, students solve 2 short answer problems. Students construct concurrent circles using the GeoGebra software and determine why their construction of circles are concurrent. Students...

In this Pascal's Theorem worksheet, high schoolers prove 1 theorem. Students use GeoGebra to construct lines given three points and prove Pascal's Theorem.

Students investigate the area of squares and circles. For this geometry lesson, students calculate the area and probability of simple events. They work on a laptop using Safari.

Uncover the properties of translations through this exploratory lesson. Learners apply vectors to describe and verify transformations in the second installment of a series of 18. It provides multiple opportunities to practice this...

The task at hand is to partition a hexagon into two, four, and eight congruent figures. Make sure to give your wizards a sheet of triangle grid paper on which to decompose the hexagons. Have them explain which rotations, reflections, or...

Will someone please constrain those pets? Pupils create two constraint equations on the number of cats and dogs for a pet sitter. They choose specific points and determine whether the point satisfies one or both constraints. The...

Find the best way to maximize the profit. Pupils graph four constraints of a pet-sitting company, using a revenue equation to find a maximum amount the sitters can earn. By using the equation, scholars determine the number of cats and...

Take a ride on a Ferris wheel. Using sliders to adjust the parameters of a Ferris wheel, pupils investigate the height of a point over time. The interactive traces out the curve on a time-height graph. Learners use what they learned to...

Stretch your knowledge of ratios to the coordinate plane. The interactive allows pupils to set the endpoints of a directed line segment and form a right triangle. Using rubber bands, users visualize the line segment divided into equal...

Transform proofs using triangle rotations. By rotating a triangle around various points, class members develop proofs. Participants prove relationships of alternative interior angles formed by parallel lines and the sum of the interior...

Predict an equation that waves up and down. Pupils set the height, radius, and period of a Ferris wheel. The learners write a sine equation to match the graph of the height of a point on the wheel as a function of time. Running the...

Stretch the class' knowledge of dilations. With the aid of the rubber band stretcher tool, learners perform dilations. They dilate the triangle by a whole number scale and a fractional scale from two centers of dilation.

Determine whether the point is just right. The interactive allows participants to input a constraint equation. Pupils pick a point and determine whether it is too big, not too big, or just right for the constraint. Using the graphing...

Eleventh graders explore the three basic trigonometric functions. In this trigonometry/Algebra II instructional activity, 11th graders use GeoGebra and the unit circle to define the ratios of sides is a right triangles as they examine...

Discover the connection between vectors and translations. Through the lesson, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...

What do you get when you combine a matrix and a cube? Well that depends on the matrix! Pupils use online software to graph various transformations of a cube. Ultimately, they are able to describe the matrix that is responsible for a...

Learners discover that multiplying transformation matrices produces a composition of transformations. Using software, they map the transformations and relate their findings to the matrices. 

This a fun problem for young geometers to play with while gaining important insight into deductive reasoning. Some will find the answers very quickly, others might take a less direct path, but all will use their knowledge of the sum of...

Geometers prove that triangle PQR is congruent to triangle ABC by describing any combination of rotations, reflections, and translations that would prove it so. There is only this single task on the handout, but a detailed explanation of...

Teach your class how to apply their knowledge of geometry as they explore the unknown. In order to find an unknown angle, learners must understand that rectangles have four interior right angles, that right angles have 90 degrees, and...

Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...

Scholars take transformations from the second to the third dimension as they extend their thinking of transformations to include three-dimensional figures. They explore how to use matrices to represent compositions of...

Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...

Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic...