Let’s answer this question using the Understand-Solve-Explain procedure.

Step 1 – Understand the problem. The question asks how far, so we are looking for a distance. In this case, the definition of a light-year tells us that we are looking for the distance that light can travel in 1 year. We know that light travels at the speed of light, so we are looking for an equation that gives us distance from speed. If you don’t know this equation, think of a simpler but similar problem, such as “If you drive at 50 kilometers per hour, how far will you travel in 2 hours?” The answer is 100 kilometers, because you will travel 50 kilometers in the first hour and another 50 kilometers in the second hour. Notice that we can get the same answer by multiplying the speed (50 km/hr) by the time (2 hr). This give us a general formula for calculating distances:

distance = speed × time
For the question of “how far is a light-year?,” the speed is the speed of light, or 300,000 km/s, and the time is 1 year:

1 light-year of distance = speed of light × 1 yearStep 2 – Solve the problem. We need to carry out the multiplication in the above formula, but there is a small issue: The speed of light is given in units of kilometers per second, but the formula multiplies by 1 year. We therefore need to make the units consistent by doing it all in either seconds or years. In this case, it is easier to convert 1 year into seconds, which you can do by remembering that there are 60 seconds per minute, 60 minutes per hour, 24 hours per day, and 365 days per year.

We can now show all the math like this:

Step 3 – Explain and Check your result. In sentence form, the answer is “One light-year is about 9.46 trillion kilometers.” Notice that this answer makes sense: It has the expected units of distance (kilometers) and it is a long way, as we expect for the distance that light can travel in a year. We say “about” in the answer because we know it is not exact. For example, a year is not exactly 365 days long. In fact, for most purposes, we can approximate the answer further as “One light-year is about 10 trillion kilometers.”

Now, put your skills to the test. Use what you learned in the example above to calculate the distance in kilometers to at least one star from the list below:

Alpha Centauri: distance = 4.4 light-years

Barnard’s Star: distance = 6.0 light-years

Sirius: distance = 8.6 light-years

Vega: distance = 25 light-years

Aldebaran: distance = 65 light-years

Record all your work and your answer(s) in your task book. After you have done this, find another student who has calculated the distance to the same star(s). Do your answers match? 

• If so, write the name of the student with the matching answer in your task book and note that you both got the same answer. 
• If not, discuss together until you figure out what the correct answer should be, then each of you should write the revised calculation in your task books. (Do not erase your original answer; just add a note with the other student’s name and explain that the two of you decided that your original answer should be revised, and show your revised work.)

Just as a light-year is the distance that light travels in one year, a light-day is the distance that light travels in one day. How far is a light-day, in kilometers?

Follow the example above to calculate an answer in kilometers. Show your work and write down the answer in your task book.

Teacher Notes: The plan here is that, starting in 6th grade, we will introduce the following general problem solving procedure, which you see referred to in this box.

The key to problem solving with mathematics is to approach problems in a clear and organized way. Here is a simple, 3-step approach that we recommend you follow:
Step 1 Understand the problem: Ask yourself what the solution will look like (for example, what units will it have? will it be big or small?) and what information you need to solve the problem. Draw a diagram or think of a simpler, similar problem to help you decide how to solve it.
Step 2 Solve the problem: Carry out the necessary calculations.
Step 3 Explain your result: Be sure that your answer makes sense, and think about what you’ve learned by solving the problem.
You can remember this process as “Understand, Solve, and Explain,” or U-S-E for short. You may not always need to write out the three steps explicitly, but they may help if you are stuck.

Answers to the Check Your Math Skills Tasks:

Calculating distance to nearby star

There are several procedures that students could use, but the easiest is simply to use the fact already found in the example, which is that 1 light-year = 9.46 trillion km. Therefore:

Alpha Centauri distance in km: 4.4 ly x 9.46 trillion km/ly = 41.6 trillion km

Barnard’s Star distance in km: 6.0 ly x 9.46 trillion km/ly= 56.8 trillion km

Sirius distance in km: 8.6 ly x 9.46 trillion km/ly = 81.4 trillion km

Vega distance in km: 25 ly x 9.46 trillion km/ly = 236.5 trillion km

Aldebaran distance in km: 65 ly x 9.46 trillion km/ly = 614.9 trillion km

Calculate a light-day in km

Following the Do the Math example, the correct answer is 1 light-day=25,920,000,000 km. Students should show their work for calculating how many seconds are in a day:

And for calculating the distance in kilometers: