Comparing different scales

0:00- [Instructor] We're told a scale drawing of Denali National Park uses a scale of one centimeter to 200 meters. Marta made a smaller drawing of Denali National Park. Which scales could Marta have used for her drawing? Choose all answers that apply. So pause this video, have a go at that before we do this together.

0:21Okay, so if her drawing is smaller, then that means a smaller distance is going to represent, say, 200 meters. One way to think about it, if in this original drawing this is one centimeter, and if it represents 200 meters, maybe that could be a hill like that.

0:40Well, now you're going to represent that hill. You're gonna draw it smaller. So maybe a half a centimeter would represent that same 200 meters. So we have to look for something where the ratio between this number and the 200 meters, or the larger number, is even smaller.

1:01So let's see, one centimeter to 250 meters, yes, that would make sense because now we have the same distance that representing more, or the same distance on the map representing more distance in real life. So it will be a smaller map, so we like that one. One centimeter to 125 meters.

1:19No, that won't be the case because that means that that one centimeter is now representing less. So if you had to draw it, it would have to be a bigger map. One centimeter to 400 meters. Yeah. So now each centimeter is representing twice as much. So if you were to draw that hill in this world, that hill would have, now, that same 200 meters would now be half a centimeter in width, so I like that choice as well.

1:44Let's do another example. So here we are told that a scale drawing of a roller coaster uses a scale of one centimeter to four meters. In the drawing, the roller coaster's height is 15 centimeters. Jeremiah made a new drawing of the roller coaster, using a scale of one centimeters to one meters.

2:08What is the height of the roller coaster in Jeremiah's drawing? Alright, pause the video and have a go at this one, too. Alright, so the way my brain likes to tackle it is let's use this initial information to just think about how big that roller coaster is in real life.

2:24And then think about using Jeremiah's scale, how big he would have to draw it. So in the original drawing, the scale is one centimeter is four meters in real life. One centimeter in the drawing is four meters in real life. In the drawing, the roller coaster's height is 15 centimeters, so that would be 15 times four meters.

2:46So in real life, so real life, the roller coaster is going to be 15 centimeters times, we could write it this way, times four meters per every one centimeter. That is the scale. So we are going to get it to be 60 meters in real life. And just think about what's going on here.

3:1215 centimeters is 15 times that one. So the real life distance is gonna be that times 15, or the real life height, so that's going to be 60 meters. So that's in real life, but that's not what they're asking us. They're asking us how tall would this roller coaster be on Jeremiah's drawing?

3:29So Jeremiah made a drawing of the roller coaster using a scale of one centimeter to one meter. So if one centimeter in his drawing represents one meter in real life, and this is 60 meters, well then that means that his drawing is going to be 60 centimeters. Each meter corresponds to a centimeter in his drawing.

3:48So that's how tall the roller coaster would be in his drawing.