Scale and Powers of Ten

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Students will be able to relate scale to metric prefixes and the power of ten.

Big Idea

Scientists use instruments and metric units to quantify and understand the size of objects from huge to tiny.


The purpose of this activity is to engage students in the topic at hand, namely that objects appear very differently at different scales, and that we humans have figured out how to look at and analyze very large and very small objects. A lot of work in chemistry involves making macroscopic observations in order to infer what is happening at the nanoscale. In What's the Point? I elaborate on this topic from a lab at the Silvio O. Conte National Center for Polymer Research.

This is an introductory lesson that ties to standard HS-PS1-3--Plan and conduct an investigation to gather evidence to compare the structure of substances at scale to infer the strength of electrical forces between particles. It does this by providing a framework for the structure of matter; as such it also ties into the Crosscutting Concept of Scale, Proportion and Quantity, as students use the metric system to describe the relative sizes of objects, and they observe how the scale in which they are viewing objects changes the characteristics of what is being observed.

Do Now and Activator

10 minutes

I distribute or project the magnified pollen grain for my students and ask them to take a moment to study the photo and then record in their notebooks what the object is. I explain to them that it is an object that they are probably familiar with. Student answers are all over the map--responses based in science fiction, bacteria, viruses--the responses are potentially endless!

I then ask students to share their guesses regarding the object. I accept and enjoy all the guesses until the subject is exhausted and then either recognize or give the correct response by showing the picture of bees collecting pollen at the macroscopic scale. I explain that in class today we will focus on scale and the units and prefixes scientists use to describe the size of objects.

Mini-lesson and Guided Practice

10 minutes

This lesson is about helping students build knowledge and think about very small sizes. Viewing colored newsprint under a microscope is a great way to introduce the idea that objects at different scales have different characteristics.

During this lesson I am hoping to build on prior knowledge. Students have already had biology and they have used microscopes. I want to make sure they understand that chemistry deals with atoms and molecules, and that these are usually much smaller than anything that can be observed using a light microscope. I also want students to understand early on that numbers and units are important in the chemistry.

I begin the lesson by reminding or teaching students how to use the microscope. I use the microscope handout, which is adapted from a biology website. I give students a few objects that look different under a microscope compared to what they look like to the unaided eye. Colored newsprint, textured objects such as sand or salt crystals, and leaves are good examples. I give students time to explore and draw what they see at the macroscopic and microscopic level. I project the microscope graphic organizer to assist students in recording their observations in their chemistry notebook.

Allow students to spend about 10 minutes exploring what different objects look like under the microscope. Students should be encouraged to share with one another the discoveries they make. While my students are working I walk around and help students troubleshoot. Students may need to be reminded to start with the lower magnification to focus in on a sample before increasing the magnification. They may need help focusing, and they may encounter difficulties if their sample is to thick to let light pass through.

Here is one student's microscope observations, and here is another student's microscope observations. While I was not that impressed with what students draw, I am impressed with how they saw and marveled at the microscopic world, which was my intent for having them look at it.

Students may or may not be quite familiar with how to use a microscope. If there are no technical difficulties, I simply enjoy sharing in the discoveries that students make.


25 minutes

In this part of the lesson I want students to do some thinking as they build their understanding of different scales. 

Students watch the video How Small is a Nano? using the How Small is A Nano notecatcher. You may need to show the video more than once if students do not capture all of the information during the first showing. I also rely on showing a couple of examples and then pausing the video if students need to catch their breath.

I then show students the Power of Ten slide show, where the frame of reference goes from 1023 meters down to 10-19 meters! I ask them to observe what happens to the exponent as the frame of reference gets smaller.

Next, students grapple with understanding for how the measurements given in the videos translate into decimals and powers of ten in the last two columns. During this time, my objective is to help students become more comfortable with the fact that smaller numbers mean smaller scales.

My other objective is to help students see the relationship between exponents and decimal places. By completing the worksheet, students should see a pattern. If they do not, the debrief section of the lesson will draw their attention to it. This student work was typical of what students accomplished in this portion of the lesson.


10 minutes

Based on what I am observing as students are working independently, I decide how to proceed. If students effortlessly fill out the last two columns, than less time can be spent in reviewing the How Small is A Nano Answer key. If students struggle, I prompt students to ask questions about the work, and complement those who do so in order to foster a classroom culture that encourages self assessment and critical thinking. My objective is to discuss powers of ten and scientific notation, and how these relate to the prefixes that are attached to the word meter. 

After reviewing the answers, I ask students to complete the Scale and Powers of Ten Exit Ticket. This allows me to assess understanding, and after students do this I ask for volunteers to share their answers. I have students share out so that I can make some final points about what the lesson was about, and to satisfy student curiosity. I collect a piece of paper from everyone so that I can measure understanding of individual students and ascertain whether individual or whole class reteaching is in order.

In this student work sample of scale and power of ten I see that while some progress has been made with exponents, more work is needed as evidenced by the answer given for millionths, and by the student saying that a virus is bigger than bacteria. In this other student's scale and power of ten work it shows even less understanding, so clearly reteaching is in order for some of the students.