# Significant Figures

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## Objective

Students will be able to properly record and calculate data with proper significant figures by taking notes, practicing, and performing a lab.

#### Big Idea

When calculating and measuring in chemistry it is important to use significant figure rules.

## Introduction

This lesson gives students the opportunity to determine the rules concerning significant figures and learn how to perform calculations using significant figure rules.  The lesson builds on the previous lesson (Unit 1 lesson 3) where students learned about performing measurements correctly in chemistry, how to determine the uncertainty of measurements, and how to perform scientific notation.  This lesson also requires that students are able to perform basic math skills such as addition, subtraction, multiplication, division, and rounding.

This lesson involves NGSS Science and Engineering Practice 5: "Using Mathematics and Computational Thinking" because students are learning how to correctly record values following math problems.

This lesson also is aligned with NGSS Crosscuting Concept 3: "Patterns" because it encourages students to use patterns when determine the rules for significant figures during the explore section of the lesson.

## Engage

5 minutes

I engage students in the lesson by asking them, "What is the difference between the values of 3, 3.0 and 3.00".

I have students use the strategy of think, pair, share.  I give students a minute on their own and have them share with their elbow partner (the person sitting next to them) and then their table groups.  After I give them a few minutes to talk with their groups I call on one or two groups to share their thoughts.

The goal is for students to remember from the previous lesson that the more "values" the number has the more certain of the measurement, and the more precise the measuring device.

I then tell students that, "We will be learning about significant figures today which will help determine how precise measurements are".

## Explore

10 minutes

In this section I lead students in determining the significant figure rules through giving them examples and having them notice the patterns (it is the first part of the PowerPoint). I have found that by leading students into determining the rules they are much better at remembering the rules throughout the year.

I do this one rule at a time following these steps:

1.) I give students a set of numbers with how many significant figures there are in each.

2.) I have students think about the patterns on their own and then share with their groups.

3.) I ask if any groups think they have it figured out and call on those groups.

4.) I then go over the rule with an additional example and have them write it down on their notes as can be seen in the PowerPoint and the filled in notes.

This is especially difficult with the first rule where they are not quite sure where I am going, so if they are struggling once they begin to work with their groups I give them hints such as "Do you see any zeroes?" or, "How many numbers are there in each box and how does that relate to the number of significant figures?".

After we have determined the rules together I point to the poster in the classroom where I have the rules for them to refer to throughout the school year.

## Explain

30 minutes

In this section I go over the rules in more detail while having students perform examples.  I start by showing students a significant figures video clip for them to see the use of sig figs.

The general flow of the lesson can be seen on the PowerPoint where students learn about how to determine sig figs, how to round numbers to sig figs, and how to perform calculations with sig figs.  While performing the sig fig calculations I encourage students to use calculators and then make sure to have correct number for the answer (see reflection on Calculator Use for how I use calculators in my classroom).

I introduce parts of significant figures gradually while students take notes and then perform practice questions within their notes.  When students perform the practice questions I give students a few minutes to try several problems on their own, and then go over as a group.  I tell them if they are done before the rest of the class they can check with their partners if their partners are also done.   I walk around the classroom and help students as they are working, making sure to pay attention to those who are struggling.

## Elaborate part I

20 minutes

I find it extremely helpful to allow students time to practice their sig fig skills using whiteboards.  When using whiteboards in my class I have students work with partners to encourage them to discuss why they think that a certain answer is correct.  I periodically remind them to switch partners in terms of who is doing the writing throughout the whiteboard session.

I lead student through the practice questions in three steps:

1. I put up a problem on the PowerPoint and then have students hold up their answers.

2. I either give thumbs up or down and if they get it incorrect they should retry.

3. After most students answer I go onto the next answer.  If it is one that many get wrong I go over why the correct answer is correct either by myself explaining or having a student explain how they determined the answer.

The most common mistake that students make with significant figures is rounding numbers to specific significant figures.  This class video shows an example of my using whiteboards with a class and how I go over common mistakes regarding rounding.

If you do not have access to whiteboards you can have your school order some such as these at Office Max or you can also have students write answers on a sheet protector with a piece of paper in the middle.

## Elaborate part II

30 minutes

As another way to reinforce significant figures while also reviewing measurement I have students perform a Measurement Lab.   In this lab students perform various measurements and then use them in a calculation.   The resources I use are listed on the lab paper.

In the first procedure students the area of a piece of paper using lenght and width measurements.

In the second procedure students find the average volume of an approximate 8 mL when poured into a graduated cylinder.

In the third procedure students find the mass of individual objects and then perform addition to find the total mass.  The individual objects can vary.  This year I had students use a rubber band, penny, metal ball, and paperclip which I gave to them in a Ziploc bag labeled procedure 3, as an see in this picture.

For the final and fourth procedure students find the temperature of boiling water and then calculate the percent error given the accepted value of 100.0 degrees Celsius.

This lab is different from the uncertainty measurement lab found in Unit 1 Lesson 3 because I have students write their own data table, and they are using their measurements to perform calculations using significant figures.

This lab can be tricky for students in terms of measurement and calculating with significant figures, so it is helpful to remind students to bring their significant figure notes with them to their lab tables and to help their group members. As in other labs I always walk around and help individual groups.

If time is an issue then I sometimes will do the lab on another day or have students only do one or two of the procedures, because students will still have a chance to practice calculations with significant figures.

## Evaluate

20 minutes

This last section is the homework where students will practice their significant figure skills.

Most students do well on the homework, but some of the common struggles are the section where students perform scientific notation and record the number of significant figures as well as the multiplication and rounding to correct number of significant figures.  I make sure to remind students that they should have the same number of sig figs BEFORE and AFTER they convert to scientific notation.

I check the homework the following day where I stamp for completion and then go over the answers using the answer key.