In this video, Harry finds money on the sidewalk. He uses ratio, proportion, and some knowledge about shadows to return it to the rightful owner. In the accompanying classroom activity, students investigate whether there is a consistent relationship between the height of objects and the length of their shadows.

Students work together in small groups, while competing with other teams, to explore the engineering design process through a tower building challenge. They are given a set of design constraints and then conduct online research to learn basic tower-building concepts. During a two-day process and using only tape and plastic drinking straws, teams design and build the strongest possible structure. They refine their designs, incorporating information learned from testing and competing teams, to create stronger straw towers using fewer resources (fewer straws). They calculate strength-to-weight ratios to determine the winning design.

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.

Students are introduced to the concept of ratios, learning ratio language to describe the association between two or more quantities and different strategies to solve ratio problems.

Students investigate rates and percentages by identifying the rates associated with a ratio, defining a percent as a rate per 100, and applying strategies to solve rate and percent problems.

Students "go fishing" and use proportions to learn how estimating is used to determine the size of a population.

Find a quick, concise explanation of rates and ratios. Examples are given and clearly explained.

If you're looking for the measurements of the interior angles of a triangle you can use this tutorial to see how to use a given ratio of the interior angles and the Triangle Sum Theorem to find those missing measurements. [5:39]

A trigonometric ratio is a ratio between two sides of a right triangle. The cosine ratio is one of these ratios. Take a look at this tutorial to see how to find the cosine of a particular angle in a right triangle. [3:22]

Take a look at this tutorial to learn about line segments, how to name them, and what the midpoint of a line segment is. [3:13]

Scale drawings make it easy to see large things on paper. Watch this tutorial to learn all about them. [3:54]

Watch this tutorial to learn why proportions are actually equations with equal ratios. [3:45]

Students apply their knowledge of scale and geometry to design wearables that would help people in their daily lives, perhaps for medical reasons or convenience. Like engineers, student teams follow the steps of the design process, to research the wearable technology field (watching online videos and conducting online research), brainstorm a need that supports some aspect of human life, imagine their own unique designs, and then sketch prototypes (using Paint®). They compare the drawn prototype size to its intended real-life, manufactured size, determining estimated length and width dimensions, determining the scale factor, and the resulting difference in areas. After considering real-world safety concerns relevant to wearables (news article) and getting preliminary user feedback (peer critique), they adjust their drawn designs for improvement. To conclude, they recap their work in short class presentations.

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.