The Nrich problem offers opportunities to think about area, proportion and fractions, while offering an informal introduction to the mathematics of infinity and convergence which would not normally be met by younger students, to tempt their curiosity.

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

This is course material published for a secondary Math 1 course. Authors of this work are: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius and updated from the original work in 2013 in partnership with the Utah State Office of Education.

Proof that the sum of angles of a triangle equals 180 degrees using vertical angles and corresponding angles.

Course presentation slides for each step of proving vertical angles are congruent, using intersecting lines and supplementary angles.

Definition of circle and similarity, images of circles shown to map to one another after a translation and dilation. Interactive word drag of keywords of steps of proof.

Khan Academy video proving parallel lines have the same slope. Information text added mid video, along with a drag and drop of ordering proof steps at the end of the video.

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.

In this NRich activity students will analyze a pattern on a coordinate plane in order to make predictions.

The Mathematics Vision Project (MVP) curriculum has been developed to realize the vision and goals of the New Core Standards of Mathematics. The Comprehensive Mathematics Instruction (CMI) framework is an integral part of the materials. You can read more about the CMI framework in the Utah Mathematics Teacher Journal. (UCTM, 2009)

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.