This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

This short video and interactive assessment activity is designed to teach third graders an overview of area and perimeter.

Students learn about civil engineers and work through each step of the engineering design process in two mini-activities that prepare them for a culminating challenge to design and build the tallest straw tower possible, given limited time and resources. First they examine the profiles of the tallest 20 towers in the world. Then in the first mini-activity (one-straw tall tower), student pairs each design a way to keep one straw upright with the least amount of tape and fewest additional straws. In the second mini-activity (no "fishing pole"), the pairs determine the most number of straws possible to construct a vertical straw tower before it bends at 45 degrees—resembling a fishing pole shape. Students learn that the taller a structure, the more tendency it has to topple over. In the culminating challenge (tallest straw tower), student pairs apply what they have learned and follow the steps of the engineering design process to create the tallest possible model tower within time, material and building constraints, mirroring the real-world engineering experience of designing solutions within constraints. Three worksheets are provided, for each of two levels, grades K-2 and grades 3-5. The activity scales up to school-wide, district or regional competition scale.

This short video and interactive assessment activity is designed to teach fifth graders about subtracting capacities in compound units (english units).

This short video and interactive assessment activity is designed to teach fifth graders about subtraction in grams.

This short video and interactive assessment activity is designed to teach fifth graders about subtraction in kilograms.

Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.

This learning video presents an introduction to graph theory through two fun, puzzle-like problems: ''The Seven Bridges of Konigsberg'' and ''The Chinese Postman Problem''. Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem.

Roller coasters projects are frequently used in middle and high school physics classes to illustrate the principle of conservation of mechanical energy. Potential energy transforms to kinetic energy and vice versa, with gravity being the driving force during the entire process. Even though friction force is mentioned, it is rarely considered in the velocity calculations along the coasters’ paths. In this high school lesson, the friction force is considered in the process. Using basic calculus and the work-energy theorem for non-conservative forces, the friction along a curved path is quantified, and the cart’s velocity along this path is predicted. This activity and its associated lesson are designed for AP Calculus. Practice problems/answers, a PowerPoint® presentation and student notes are provided.

Students overlay USGS topographic maps into Google Earth’s satellite imagery. By analyzing Denali, a mountain in Alaska, they discover how to use map scales as ratios to navigate maps, and use rates to make sense of contour lines and elevation changes in an integrated GIS software program. Students also problem solve to find potential pathways up a mountain by calculating gradients.

Student teams investigate the migration of small-particle plastic pollution by exposing invertebrates found in water samples from a local lake or river to fluorescent bead fragments in a controlled environment of their own designs. Students begin by reviewing the composition of food webs and considering the ethics of studies on live organisms. In their model microcosms, they set up a food web so as to trace the microbead migration from one invertebrate species to another. Students use blacklights and microscopes to observe and quantify their experimental results. They develop diagrams that explain their investigations—modeling the ecological impacts of microplastics.

In this activity, students explore how trebuchets were used during the Middle Ages to launch projectiles over or through castle walls as well as how they are used today in events such as Punkin’ Chunkin’. Students work as teams of engineers and research how to design and build their own trebuchets from scratch while following a select number of constraints. They test their trebuchets, evaluate their results through several quantitative analyses, and present their results and design process to the class.

This lesson focuses on ultrasound wavelengths and how sound frequencies are used by engineers to help with detection of specific distances to or in materials. Students gain an understanding about how ultrasonic waves are reflected and refracted. Students also see how ultrasound technology is used in medical devices. The activity following this lesson allows students to test their knowledge by using the Sunfounder Ultrasonic sensor and Arduino Mega Microcontroller.

This short video and interactive assessment activity is designed to teach third graders about given the perimeter, find the side length and area - squares.

This short video and interactive assessment activity is designed to teach fifth graders about using the four operations with money - word problems.

This short video and interactive assessment activity is designed to teach fifth graders about multiplication and division with money.

This short video and interactive assessment activity is designed to teach second graders about using symbol maps with compound units.

Students develop a physical understanding for the meaning of equality by trying to find equal lengths using rods.

This short video and interactive assessment activity is designed to teach second graders about visual differences in length (english units).

This short video and interactive assessment activity is designed to teach fifth graders about visual objects: comparing length.