# Moles <--> Numbers of Particles Conversions

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## Objective

SWBAT convert between numbers of particles and numbers of moles.

#### Big Idea

There are 6.02 x 10^23 things in 1 mole of things; We can convert between number of particles and moles based on this equivalence.

## Why This Lesson?

This lesson seeks to help students understand how to convert from numbers of particles to numbers of moles and vice versa.  This mathematical understanding is crucial to the foundation of stoichiometry.  It also serves to address the NGSS Crosscutting Concept of Scale, Proportion, and Quantity, particularly XC-SPQ-HS-4.  Students later need to convert from moles to grams (and vice versa) in predicting amounts of product that can be made in particular chemical reactions and will need to understand the scale of the mole.

The student activity in this lesson addresses the Science and Engineering Practice 5 since students will use mathematics and computational thinking.

## Warm-Up

5 minutes

While I take attendance, students do a warm-up activity in their composition Warm-Up/Reflection books.  I use warm-ups to either probe for students' prior knowledge about the day's upcoming lesson or to have them bring to mind and review what they should have learned previously.  (To read more about Warm Up and Reflection Books, please see the attached resource.)

Today's Warm-Up: "If 1 mole equals 6.02 x 10^23, what are two conversion factors we can make using this equality?"

In this case, the warm-up is asking students to prepare for the conversions in today's lesson and to recall how to make conversion factors (something covered in a lesson from Unit 1, Dimensional Analysis).

If time permits, I walk around with a self-inking stamp to stamp the completed warm-ups indicating participation, but not necessarily accuracy.  On days when there is too much business keeping, I do not stamp.  Students have been told that warm-ups are occasionally immediately checked and other times not.  At the end of each unit, Warm-Up/Reflection Books are collected and spot-checked.

Today, I do not walk around to stamp because the top of our activity handout will ask students to write their two conversion factors again and we will discuss our answers as an introduction to today's calculations.

## Introduction to Activity

10 minutes

After students have had a chance to complete their warm-ups, I will ask a student who I know had the correct answers to give us one of the conversion factors.  He or she will write it on the whiteboard.  At this point, students who had forgotten what a conversion factor is should be prompted to get the correct remaining conversion factor.  I will call a student who has this "a-ha" type of moment to share the second conversion factor with us.  I am looking for two conversion factors:

Then I will model converting first from moles to atoms using the following example:

After, I model converting from atoms to moles, as shown here:

## Partners Activity

30 minutes

Students are told to work with their "North" partners (as explained in this video).  They should move so that both partners are seated next to each other.  I will differentiate between "left" side partners and "right" side partners as we go through a cooperative partnering process.

I pass out the activity handout titled Moles <--> # Particles Conversions.  Then, I pass out index cards, one to each student.  I tell students to write their conversion factors on the index card as the handout directs.

I give the following directions, pausing in between steps to allow for students to complete the work.

1.  Pairs will need one calculator.  If you need to borrow a calculator from me, the "left" partner should get one now.

2.  The right partner should set up problem 1 on the handout.  Include the correct conversion factor.  You have 90 seconds.  (I use a countdown clock to keep track of time and announce time left at 60 s, 30 s, 15 s, and countdown from 5 s.)

3.  The left partner should double-check the set-up.  Do you agree?  Or are there changes that should be made?  You have 60 seconds to discuss together.

4.  The right partner should enter the calculation into the calculator while the left partner watches to make sure it is being entered correctly.  You have 90 seconds to write down your final answer.

5.  Now, reverse roles.  The left partner will set up problem 2 on the handout.  Include the correct conversion factor.  You have 90 seconds.

6.  The right partner should double-check the set-up.  Do you agree?  Or are there changes that should be made?  You have 60 seconds to discuss together.

7.  The left partner should enter the calculation into the calculator while the right partner watches to make sure it is being entered correctly.  You have 90 seconds to write down your final answer.

8.  The correct answer to #1 is:

9.  The correct answer to #2 is:

10.  Are your answers correct?  Are they incorrect, and if so, can you determine where the misstep happened?   You have 2 minutes to confer with other groups to find your mistakes.

11.  Now you are going to work together to finish the rest of the calculations.  You may use your index card with conversion factors to help.  Remember to pay attention to the units you want (which should be on the top of your conversion factor) and the units you want to cancel out (which should be on the bottom of your conversion factor).

Students continue working until we reach time for the Student Reflection.

**Students who are having trouble remembering how to use scientific notation on their calculators will often have answers that are off by one power of ten.  This is because they are using the notation of x10^ as well as the EXP/EE notation button.  This is another reason to have students show all of their conversion work so that I can tell if the mistake is happening with the problem set-up or with the calculator use.  We cover calculator use for scientific notation in an early lesson (Subatomic Particles and Relative Masses), but students often need re-teaching on this application.

## Student Reflection

5 minutes

In student's Warm-Up/Reflection Books, students should spend about 3-5 minutes writing a response to the day's reflection prompt.  Prompts are designed to either help students focus on key learning goals from the day's lesson or to prompt deeper thinking.  The responses also allow me to see if there are any students who are missing the mark in terms of understanding.  The collection of responses in the composition books can also show a progression (or lack thereof) for individual students.

Today's Reflection Prompt:  "Imelda Marcos, former first lady of the Philippines, was rumored to have over 3000 pairs of shoes (that's 6000 shoes?!!).  How many moles of shoes is that?"

Desired student responses should indicate that:

• 6000 shoes should be multiplied by (1 mole)/(6.02 x 10^23 shoes) = 9.97 x 10^-21 moles

Students first questioned if they could use "shoes" as a unit instead of "atoms" when they began work on the reflection.  It is important that students understand that "atoms" or "particles" or "molecules" can be used interchangeably when completing these calculations and this understanding will be necessary in additional practice problems assigned as homework later.

I am always most concerned about conversion factors being shown in student work and emphasize that when grading.  Here are student samples of the homework assignment (Moles-#particles Conversions, More Practice) that we later graded in class: