In this video segment from Cyberchase, the CyberSquad must get into a vault before Hacker, Buzz and Delete by cracking a code of shapes and numbers.

How do shape and weight impact the performance of a fidget spinner? This challenge will explore how shapes, weight and force impact the performance of a fidget spinner. Engineering a mechanical device involves designing with a result in mind. This challenge will ask students to explore math, science and engineering design through the device of a fidget spinner.

This is a 3-hour lesson that includes a self-paced interactive module and classroom activities. The teacher guide includes a challenge sequence (timeline), relevance to standards, materials list, assessment, evaluation rubric, and learning extensions.

Lesson objectives: (1) Investigate the basic shapes that make up a fidget spinner. (2) Explore how a fidget spinner works. (3) Design, build and test your own fidget spinner.

This short video and interactive assessment activity is designed to teach fourth graders about describing patterns using letters.

This short video and interactive assessment activity is designed to teach third graders about describing patterns using letters.

Students learn how to use wind energy to combat gravity and create lift by creating their own tetrahedral kites capable of flying. They explore different tetrahedron kite designs, learning that the geometry of the tetrahedron shape lends itself well to kites and wings because of its advantageous strength-to-weight ratio. Then they design their own kites using drinking straws, string, lightweight paper/plastic and glue/tape. Student teams experience the full engineering design cycle as if they are aeronautical engineers—they determine the project constraints, research the problem, brainstorm ideas, select a promising design and build a prototype; then they test and redesign to achieve a successful flying kite. Pre/post quizzes and a worksheet are provided.

Students learn about the mathematical characteristics and reflective property of ellipses by building their own elliptical-shaped pool tables. After a slide presentation introduction to ellipses, student “engineering teams” follow the steps of the engineering design process to develop prototypes, which they research, plan, sketch, build, test, refine, and then demonstrate, compare and share with the class. Using these tables as models to explore the geometric shape of ellipses, they experience how particles rebound off the curved ellipse sides and what happens if particles travel through the foci. They learn that if a particle travels through one focal point, then it will travel through the second focal point regardless of what direction the particle travels.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in parallelograms.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach fourth graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles within rectangles and squares.

This short video and interactive assessment activity is designed to teach fifth graders about determining unknown angles within rectangles and squares.

This short video and interactive assessment activity is designed to teach third graders about determining the unknown angle in an isosceles triangle.

This short video and interactive assessment activity is designed to give fourth graders an overview of special triangles.

This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.

Students use constructions to explore dilations in order to define and establish similarity, and they prove and use similarity criterion and theorems in the solution of problems.

Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.

Using circumference, this segment measures the total distant traveled by two carousel riders after the carousel has rotated 10 times.

The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.