Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.

Students will analyze ratios and use proportions to solve problems using a cooperative, kinesthetic activity in which they will create “human ratios.” Students will apply proportional reasoning to demonstrate application of a multiplicative situation by using cross products to solving proportions.

Students will analyze ratios and use proportions to solve problems using a cooperative, kinesthetic activity in which they will create “human ratios.” Students will use ratios to compare two quantities, then solve problems cooperatively by demonstrating how proportions are written to show equivalent ratios.

This 11-minute video lesson compares population proportions (part 1). [Statistics playlist: Lesson 59 of 85]

This 10-minute video lesson compares population proportions (part 2). [Statistics playlist: Lesson 60 of 85]

This 16-minute video lesson looks at the hypothesis test for comparing population proportions. [Statistics playlist: Lesson 61 of 85]

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.

Explore Proportions in this free video unit. It is comprised of 7 lessons with 4-6 short videos in each lesson. Featuring the reasoning of Grade 6 students, the unit explores how to form and iterate ratios through the use of a dynamic applet. The videos provide a foundation for the Common Core State Standards about using ratios and rates to solve math problems. Showing these videos are helpful for teachers who want to move students from reasoning additively to forming multiplicative comparisons.