# Uncertainty and Measurement

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## Objective

Students will be able to properly record and calculate data by applying the concepts of accuracy, precision, scientific notation and uncertainty by taking notes and performing a lab.

#### Big Idea

High quality data in science depends on the ability of scientists to properly perform measurements, which are only as precise as the equipment used.

## Introduction

In this lesson students will be working to understand how to perform measurements correctly in science, how to convert their measurements to scientific notation, and how to calculate percent error.

The materials necessary for this lesson include paperclips, ruler, paper, water, colored water, graduated cylinder, temperature probe or thermometer, ER flask with water, balance, and pennies.   If some of these are unavailable you can use different equipment and supplies to have students practice measuring.

This lesson aligns with NGSS Science and Engineering Practice 3 "Planning and Carrying out Investigations" because students are learning how to collect data through correctly measuring and calculating uncertainty of measuring devices.

Furthermore, this lesson aligns with NGSS Crosscutting Concept 3 "Scale, Proportion, and Quantity" because students are using standard units to perform measurements, understanding how to change numbers to scientific notation, and how to use the equation of percent error.

## Engage

15 minutes

To begin the lesson students are asked to perform three measurements for a paperclip using three different paper rulers.  This part of the lesson is found on the first slide of the Powerpoint and students record at the top of their notes

Before class I copy the attached paper clip patterns paper and cut out the three different rulers so that I can pass out each ruler separately.   I label each ruler with an A, B, or C to help students see which ruler we are using.  Each ruler has more certainty, so each measurement that students perform should have more significant figures (See Prior Knowledge Reflection for more details).

I start the lesson by giving each student a paper clip and the first ruler, then after they write down their measurement (which I stress should only have one number), I pass out the second ruler and have them record the length using this more precise ruler (to two sig figs), then I collect this final ruler and pass out the third where they should record to three sig figs.  For example they might have the measurements of 3 cm, 2.9cm, and 2.90cm.... depending on the type of paperclip used.

As students complete their three measurements I take one student's paper (who has the measurements done correctly in terms of 1, 2, and 3 sig figs) and share on the overhead.  I do this to stress that the first measurement should only have 1 number, the second 2 numbers, and the third 3 numbers.

I then have students answer two questions related to what they measured with the rulers to see that although they measured the same paperclip, that the different types of rulers gave them different measurements and required different amounts of estimation.  For the first question most students answer no, but some who measure 3, 3.0, and 3.00 or something similar to that say "yes" and I then explain how those are actually not the same measurement as well will talk about in class.  For the second question most students answer the first ruler.  For those that are confused I stress that it is the one with the "worst" ruler that they probably would not want to use if they had to be sure about their measurement of the paperclip.

## Explain

30 minutes

This next section is the meat of the lesson where I present new information and students take notes and practice uncertainty, accuracy vs. precision, percent error, units, and review scientific notation.  The notes are set up for students to learn/review each concept and then practice each concept as they learn it.

The first section of the notes deals with uncertainty where I continue to stress the need to estimate the last number as students saw in the engage activity.  I show a quick  movie clip on uncertainty to serve as a quick review and to break up the lesson before moving onto the next section.  Students are only responsible for listening as they watch the video clip.

For the accuracy vs. precision part of the notes, I use the example of the dartboard on the notes and then pause and have students practice the concepts with a magnetic dartboard.  I have students try to hit the bulls eye and have the class determine if the student throwing the darts was accurate, precise, neither or both.  I also use a chemistry example of students performing measurements in class.

The second half of the notes is review of units and scientific notation.  Even though this is something that students have often seen in middle school and/or biology, I have found that most of them do not know the correct units or how to correctly perform scientific notation conversions.

For scientific notation I stress that when scientific notation represents numbers less than 1 that the exponent is negative; whereas for those numbers that are greater than 1 that the exponent is positive.  Most students find this helpful, rather than memorizing to move to the left or right as they did in middle school because they forget which direction to move. See this movie about how I explain this to my students when they are reviewing exponents.

When I review units, I make sure to explain, "How there are other units which we use, but that in science class, these are the ones we want to use".  After the units section I show the students a Metric_System_and_SI_Units video to serve as a quick review where students are responsible for listening only.

## Elaborate

20 minutes

In this section I give students a chance to practice measuring, identifying lab equipment, writing uncertainty and calculating scientific notation.

Before students come to class I set up four stations (see attached index cards for examples of what to put at each station) where students go and measure one thing and record on the attached lab sheet

I have students work in their table groups of four and rotate around four different stations (I have 2 sets of the 4 stations so all 8 groups are at a station and then rotate).  I tell students, "Although they are in groups that they should each make sure to record the measurement, and check with their group members concerning the estimated number and uncertainty of the measurement".

I give students 4 minutes per station and then have them rotate.  In order to help students stay on task and know how much time they have at each station I use a countdown timer which I project through my computer/LCD projector.  The timer I use is called TimerTools and is available through Kagan Publishing.  I set the timer for four minutes, and when time runs out it beeps and I have students rotate to the next station.  See the reflection concerning group rotation for a glimpse at how I do this in my classroom.

Finally, as students are working I find it very helpful to walk around and check students' measurements to ensure that they are estimating the last digit and writing uncertainty as well as working well with their groups.  Students continue to struggle with estimating the last number when measuring by hand on graduated cylinders, rulers, or triple beam balances.  This is especially true for graduated cylinders which are not necessary divided into 10 equal divisions and requires students to think a little bit more about the estimated number.

When students complete the lab activity, they place it in their binders (where I will check it for completion at the end of the unit binder check) and begin to work on their homework.

## Evaluate

20 minutes

The evaluation piece is the homework where students have a chance to practice measuring correctly, calculating percent error and writing scientific notation.

When students come into class the following day I stamp their homework for completion, and then go over the answers using the answer key. Some students will still not estimate the last number in their measurements so as I go over the homework I continue to stress the need for estimation and let them know that this is something that we will be doing all year.