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...

Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th lesson in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a formula to find...

This task asks learners to prove that the segment joining the midpoints of two sides of a parallelogram is both congruent and parallel to an adjacent side of the parallelogram. The activity would be good to use in a discussion about how...

To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...

What figure is formed by connecting the midpoints of the sides of a quadrilateral? The geometry assessment task has class members work through the process of determining the figure inscribed in a quadrilateral. Pupils use geometric...

Have learners graph complex numbers to gain a visual and mathematical understanding of the distance and the midpoint between two complex numbers. This lesson is short, but to the point, and addresses an important complex number...

Learners find the midpoint between two numbers, shade fractional amounts of rectangles as well as decimal amounts of rectangles, and explain their mathematical reasoning in words. The assessment is a great way to check for understanding...

A congruent triangles quiz challenges teenage mathematicians to complete a pair of geometric proofs. Each problem includes a picture of the triangles in question, a given set of information, and the five steps needed to finish the proof....

In Utah, one stretch of highway goes for 106 miles without a single gas station. Where should people build one? Scholars face the dilemma of where to place a new gas station between three cities. They consider distance and proximity to...

The task, should your class decide to take it, is to list a series of reflections that transfer a line segment from one position to another. 

Sometimes the best things are already done for you! Here is a six-problem quiz that has a variety of problems ranging from solving quadratic equations to interpreting a function. The piece-de-resistance is the worked out answer key in...

The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...

Given the lines of symmetry in an equilateral triangle, your learners find where the pre-image vertices are mapped onto the new image. They explore the properties of equilateral triangles, the impact of reflections, and the...

What does slope have to do with lines? Pupils work with lines and determine the slope of the lines informally and with the slope formula. Groups use their knowledge to calculate the slopes of parallel and perpendicular lines. They also...

What can symmetry tell us about triangles? After looking at four examples, learners will come to realize that lines of symmetry are different for equilateral, isosceles, and scalene triangles. Use this guided practice activity as an...

Your algebra learners emphasize the"geometric" in geometric series as they use a common ratio between algebraic terms and find that it corresponds to a repeated similarity transformation. 

Learners explore mapping a rectangle onto itself using rigid motion concepts, geometric intuition and experimenting with manipulatives in a collaborative task.

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

Graphs, functions, symbols, and more! Use these strategies to model everything from the flow of a river to the number of cars passing a toll booth. Presented differently but solved similarly, learners consider five different scenarios...

Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is...

Can your classes apply the knowledge they have learned? Use this performance task to find out! Individuals use transformations to explain congruence and angle relationships within parallel lines to find missing values. They show what...

Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The...

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...

Find the midpoint of a segment on the coordinate plane, or find the endpoint of a segment given one point and the midpoint. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or...