# Using Mass to Determine Quantity

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## Objective

TSWBAT calculate the quantity of objects in a sample based on the mass of the sample.

#### Big Idea

Students measure a the mass of a small sample of paperclips and use factor labeling to estimate the mass and number of large quantities of paperclips to prepare them for the conversions they will use in stoichiometry.

## Introduction and NGSS Alignment

Performance Expectation (PE)/Disciplinary Core Idea (DCI)

This lesson is not directly aligned with HS-PS1-7, the uses of mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction; and DCI-PS1.B, the fact that atoms are conserved, together with knowledge of the chemical properties of the elements involved, can be used to describe and predict chemical reactions.  However, students will need to perform mathematical computations to understand HS-PS1-7 which will require student to have a basic understanding of scientific notation, unit conversions and factor labeling (or proportions).  This lesson is introduction to concept that mass can be used to determine the quantity of a substance

Science and Engineering Practices (SP)

HS-PS1-7 is one of the few high school Performance Expectations with the primary focuses on the use of mathematics to explain a concept.  Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses using algebraic thinking and analysis.  Using computational thinking, students will convert from one unit to another, helping them develop the skills necessary to understanding the mole as counting unit for the atom.

Crosscutting Concept (CCC)

This lesson is not aligned with any Crosscutting concept.

## Warm-up

10 minutes

The previous two days students were to be working independently on either a quiz, quiz corrections or a reading assignment.  Instead of collecting the reading assignment or checking it in for points, I am giving them a short “open note” quiz before we start the day’s activity.

As student walk into class they are instructed to pick up the Inquiry paper clip activity and take out the reading assignment that was assigned the previous day.  I then tell them they can use the reading assignment to answer the four questions I am going to give them.  Next, there is room on the back of the worksheet to number it 1-4.  I give them a minute to do this.

I then read the following questions to them:

1. What 3 important concepts relate mass in grams of a substance to the number of atoms?  The mole, Avogadro’s number and molar mass
2. What is the abbreviation for the mole?  Mol
3. What is the definition of Avogadro’s number and the exact number?  The number of particles in exactly one mole of a substance, 6.02 x 10^23
4. In chemical reactions, what must be true about the total mass of the reactants and total mass of the products?  They must be equal.

## Explore

30 minutes

This activity is meant to be an inquiry activity that shows students that mass can be used to determine the quantity of a substance and vice versa.  After exploring the relationship between mass and quantity during this activity, students should start to develop a basic understanding that industry --and later in the unit, chemists -- can determine how much of substance is in a sample based on its mass.  Prior to this activity students gained a basic understanding of the mole by reading the textbook. This foundation will eventually be used in the next lesson as a scaffold for development of understanding of the mole.

Material need for this activity:

• Scale for each group (2 students per group)
• Small plastic cups to hold paper clips
• Enough small paper clips for ~100 paper clips per group (7 boxes)
• Activity sheet for each student

After students complete the quiz I explain the activity and the materials they will be using.  Since this is an inquiry-based activity, I try to provide them only with a basic understanding of what they will be doing.

Students Directions

• In front of you have a scale and some paper clips, your job is going to be to determine how many paper clips are in a random sample without counting them.
• In step 1 you will need to calculate an average, does everyone know how to calculate an average?  This is important to cover because there might be students who don’t remember how to calculate an average.
• In step one you will take two separate 25 clip samples, calculate the mass of each sample and determine the average mass of one paper clip.  Write these in these down.
• In step two you are not to count the clips, you are only supposed to estimate 75% of the pile and try to guess how many are in the sample.
• In step three now you will count the number of clips to determine how close your educated (mathematically calculated) guess was.
• Step four you are to repeat steps 2 and 3.  I also ask students, why do a repeat of steps 2 and 3? Their answer should be to get more data samples.
• After completing steps 1-4 answer the analysis questions.  These will require you to use dimensional analysis to determine your answer.

After provide the instructions I give students about 30 minutes to complete the activity.  Many students will need help working through some of the problems, but I try to assist only if they refuse to solve the problem on their own.  I try to encourage groups to work through the problem by discussing possible solutions before giving up.  With this approach most groups will work through the problems and finish in 30 minutes.

When I first performed this activity I thought that the instructions were clear enough that students would have no difficulty, I was mistaken.  Only a small percentage of students have the critical thinking and math skills necessary to solve these problems without asking questions.  Common questions are:  1) how do I do this?  2) Or why can’t I just count the paper clips and just weigh them one at a time? 3) How do I determine the mass of one paper clip in a 25 paper clip sample if I have to weigh them all?

Because this is an inquiry-based activity, I really want to limit the amount of information they receive from me.  I would rather see them struggle and come up with the wrong answer then give the answer and have them miss the vital component of exploration necessary for true inquiry.  By limiting the amount of information, some students may not come up with correct answers and the activity may take longer, but in the long term students will gain more from the activity because it will have more intrinsic meaning to them.

## Explain

10 minutes

After about 30 minutes of monitoring student progress I stop them and have a group discussion about what can be determined from this activity.  I like to start out by taking volunteers to explain the process by which they solved the problems and what the benefits are to using mass to calculate quantity. While students are explaining the activity, I engage student conversation by asking if anyone would like to add to the group’s thoughts.  This takes makes me more of a facilitator instead of telling them what they should have learned.  This again is an important part of inquiry. Some questions I might add to the conversation to guide the conversation in the direction of understanding the difference between mass and quantity:

1. Were you able to determine the mass of a sample of paper clips?  Did each paper clip have the same mass?
2. Did determining the mass of a paper clip help you determine quantity?  Are the two the same thing?
4. Is there a benefit to using mass to determining quantity?  Describe some benefits?
5. How do you think we can use the relationship between mass and quantity in chemistry?

Most these questions can stimulate good conversation.  The main goal is to guide students to the understanding that mass and quantity are not the same thing; however both can provide information that is useful when solving a problem.

As a summary, I explain that in chemistry we will often use mass to determine the quantity of a substance.  The quantity of a substance can tell us how many atoms or molecules will be interacting.  In the reading assignment you heard about the mole and Avogadro’s number, these two terms will be used to determine the quantity of a substance in a chemical reaction and the mass of the substance.  In addition we often need to use dimensional analysis to solve problems to determine quantities and masses of substances.

Overall the big picture of the mole is still being painted for students after the activity and discussion. However, even though they don’t understand the mole this activity gives them practice converting between units using dimensional analysis, and can help scaffold the transition between understanding how mass and quantity are related to the mole and stoichiometry.

After completing the discussion, I have students turn in the assignment so it can be graded.  Below is a Screencast of typical student work.