# Understanding Scale

Teacher Toolbox - The Purpose of This Page

The purpose of this page is to provide practice and context for the scaling that the students will need to complete in Designing and Scaling a Race Course and later in the Robo Rally Challenge.

Engage the students in a whole class discussion to review the Motivate Discussion questions. Ask the students to write their work and thoughts in their engineering notebook.

### What is "Scale"?

Scale is the relationship or ratio between a set distance on a map or drawing and its corresponding distances in real life. Materials that use scale, such as blueprints, are often considered more valuable because they allow the user to perceive distance visually, therefore making them more effective models. Being able to convert measurements when working with scale is important for careers that incorporate maps, blueprints, and architectural models. Professionals such as architects, engineers, military soldiers, and set designers all use scale in some fashion in their industry.

Developing a detailed sketch as a plan is an important step in the engineering design process. When we make a scaled copy of an object, the original and the copy must have the same proportions. To present how much an object has actually been scaled down (or up), we often use ratios. These ratios are displayed on the scaled copy so that the real-life object can be represented correctly. For example, a scale on a drawing may be represented as 1 cm = 20 m. This lets a team know that for every 1 cm on the sketch, the real-life measurement is 20 m. So, if a wall is represented on the sketch as 4 cm, the real-life wall needs to be 80 m. When engineers construct things like highways or buildings, the scaled plans are checked continuously to make sure the proportions are always correct. Breaking the real-life model down into sections and checking that the proportions are correct while completing each section is one way teams work to make sure that they are keeping to scale. Mistakes can cause a loss of substantial time, money and materials, so keeping with the accuracy of the scale is essential.

Motivate Discussion

Scaling can be a difficult concept for some students to apply. Instead of having students drill and practice the mathematics involved, have a discussion so that students can explain to classmates how they reason about scaling.

**Q:** A red building in a drawing of the city is 2 centimeters tall but it is really 50 meters tall. The gray building next to it in the drawing is only 1 centimeter tall. How tall is that next building really?

**A:** It is really 25 meters tall. See the explanation below:

**Q: **What if we wanted to add a brick building that is really 80 meters tall to the drawing? How many centimeters should it be?

**A:** 3.2 centimeters. See the explanation below: