When teaching students how to convert numbers from standard notation to scientific notation and back the other way, it’s a common practice to teach them the steps. The danger is that this approach reduces this concept to a series of steps that students may or may not remember later. Instead of approaching converting with scientific notation as a set of procedures, I find that teaching students how to think about the process really helps it stick. Here’s how I use 4 questions when teaching scientific notation to get students thinking about numbers and converting between standard and scientific notation.
Before getting into the four questions, let me show you what I mean about how we traditionally teach scientific notation. When teaching the procedures of converting between scientific and standard notation, it goes something like this: First, look at the number. If it is a big number, then you’ll move the decimal point left until you have a number between 1 and 10. Second, count how many places you moved the decimal point and write as a power of ten. If a number is written in scientific notation, then move the decimal point right the number of spaces shown with the power of ten. But, if it is a small number, then move the decimal point right until you have a number between 1 and 10. Then, count the number of places you moved the decimal point and write as a negative power of 10. And if you’re converting to standard notation, then you’ll move left. Students can get really fluent with these steps, but then down the road they start getting mixed up- is this where I go right? Or left? Or right and then left? It turns into a bad square dance 🙂
By teaching students questions to help them think about the numbers they’re working with, they understand not just how to convert numbers, but mathematically WHAT they are doing when writing numbers in different formats. This helps my students remember how to convert with scientific notation long after our unit is over!
Four Questions to Use for Teaching Converting with Scientific Notation
Question #1: Is this a big number or a small number?
Question #1 gets to the heart of what the heck we’re trying to accomplish when using scientific notation. It’s not just some abstract concept- it’s actually an incredibly useful way to write numbers that are exceptionally large or exceptionally small.
To help students understand just how big or small some of these numbers are, it’s helpful to give them some concrete examples. For instance:
How long is a red blood cell? Not very long! This is a teeny, tiny number. Wow!How many stars are in the Milky Way Galaxy? This is clearly a very, very big number. Who wants to write all those zeroes!
With these examples in their mind, I want students to look at a number and think about what this number represents. Is a really big number, or a really small number? Answering this basic question is an important first step, and helps them understand what these numbers mean.
Question #2: Will the exponent be positive or negative?
Once students have identified whether the number is a very large or very small number, this is an easy next step. Students need to remember that if the number is very large, the exponent on the power that 10 is raised to will be positive. Likewise, if the number is very small, then it is a number between 0 and 1 and will have a negative exponent.
Question #3- How many places will the decimal move?
Now that students have identified what power 10 will be raised to, they need to start thinking about how to rewrite the coefficient. They need to start by asking themselves, where is the decimal point now? Then, it’s a matter of counting how many places the decimal needs to move until there is just one digit to the left of the decimal point.
Question #4- How do we rewrite the number in scientific notation?
This is the final question for students to answer using the information from the previous three questions. Students produce their answer, and then double check it by thinking through the previous three questions. Is the 10 raised to the number of spaces the decimal point moved? Does the 10 have the exponent raised to a positive number for a large number or a negative number for a small number? Is the coefficient written with one digit to the left of the decimal point?
Students always enjoy thinking about really, really, ridiculously big numbers and teeny, tiny numbers. And I find that by starting with this question really helps students understand the overall picture of what they’re doing, whether the number is written in scientific or standard notation. When moving from scientific notation to standard notation, students apply the same thought process in reverse and quickly seem to get the hang of converting numbers between scientific and standard notation.
I hope these questions help your students become scientific notation pros! The presentation and student notes I use to teach students about scientific notation and practicing with these four questions is available in my TPT store. Check it out 🙂 Until next time, let’s keep making math class awesome!
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