The basic question that we ask in this lesson is "how far is that?" We find different ways to quantify "far" by looking at time, distance, rate, and cost. We examine different objects in space and calculate how far that object is by understanding how long it would take to get there.
We start with a quick review of the formula distance = rate * time by asking a simple question:
An object is 100 kilometers away and you are driving 5 kilometers per hour. How long would it take you to get there?
The conversation is not just about the answer here, but about the relationship between distance, rate, and time. Students need to recognize that d = rt and t = d/r and r = d/r. Having this flexibility and understanding this fact family will help them navigate the questions we will ask them in this lesson.
Here we combine science and make believe. I show the class this image of the andromeda galaxy and then show them the image of this road bike. I ask, "how long would it take to ride this bike to that galaxy?"
Here the conversation takes on the imagined parts of this question, where students need to imagine that there is a way to simply ride your bike in space and we need to imagine that the speed on that journey has some type of average. I tell the class that a fast average speed accomplished by Tour de France riders is 28 mph or about 45 kph. Together we create the imaginary scenario for this problem and agree upon the imaginary speed the bike would take on to get there.
Whatever the speed, we know that the andromeda galaxy is about 2.5 million light years or 2.4 x 10^19 km from Earth. I give the students around 3 minutes to solve the problem and then we share.
I start with the bicycle problem because it avoids the need to calculate fuel. But I use the problem as an opportunity to start discussing variables in cost.
The goal is to get students ready for a future project in which they will model the cost of a trip to a far away place.
In this part of class, students pick two vehicles and one new object in space. They need to figure out how long it would take to drive to the Andromeda Galaxy and to new object with either vehicle. I also give them opportunities to calculate cost in terms of food, gas and repairs.
I print the vehicles and objects in space on cards and tape them to the board. Students pick one object and pick two vehicles. The cards are taped with the image side down. These keeps the choices somewhat random. The cards contains photos and distances in light years. The vehicles contain images and speeds in kilometers per hour.
The instructions for the activity are simple:
Before the students begin, I ask them how they will solve these problems and what they need to know in order to be successful. When they mention something like, "we need to know how far a light year is," I give them the print out with that information. I give them a print out because I like to give them a sheet that I can collect.
I use about 8 destinations, but print out 16 copies so that each partnership can work on their own destination.
Resource Note: I tried to pick images that aren't heavy on black ink, but since each image is intense, I print out one set for all the classes to use and laminate the images. I set the printer to print at a reduced darkness to save ink as well. If ink is a major issue, just give them the numbers on the cards and display the digital images on the projector when you do your summary.
Sources for Eye Candy and other fun things:
The goal here is for the students to share their findings. I have few groups present and display the photos of their vehicles and space destinations and share results. I record their findings on a table for all to see and talk about the impact of speed on time.
Students are surprised to see the time differences in vehicles fairly close in speed. The idea is that these incredible distances magnify the impact of a small change in speed. This is a sharp contrast to our daily lives. If we are driving 5 miles with an average speed of 40 mph versus 50 mph, how much time would we save? Does this small change in speed have a big impact?
I end the discussing by discussing the resources I used to find these images (mentioned in the previous section here) and ask student to start thinking about their own comparisons for one of the projects in this unit (described in another lesson section here. The project is called "Long Distance Relationships.")