Day 2: Chemistry Math Boot Camp
Lesson 2 of 9
Objective: TSWBAT solve non-related chemistry problems using scientific notation, conversions and factor labeling.
Many of my students enter into this unit lacking the necessary math skills needed to successfully understand the mole. So to start the unit I teach students how to do basic unit conversions before introducing the mole as a counting unit. Day 2 of Chemistry Math Boot Camp the focus is on students understanding scientific notation and reinforcing how to factor label. The mole can be a difficult concept for many students, so giving them a chance to practice the necessary math conversions first makes the transition to the mole easier. I typically spend several days letting students work on factor labeling and scientific notation before introducing the mole.
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).
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.
Today’s class starts off with a check-in of the previous day’s assignment and a bell ringer. As students are walking in I instruct them to take out the previous day’s assignment and a half sheet of paper that will be used to complete the bell ringer.
The check-in consist of me walking around the class with a student rooster, giving students 10 pts (completed), 5 pts (partially completed) or 0 pts (not completed). Most students receive full or partial credit due to the fact that they had 30 minutes the previous period to complete the assignment. While I am check-in the assignment I have the answer key showing on the overhead so that students can check there work after completing the bell ringer.
While I am checking-in their assignment students have a short bell ringer assignment complete. The bell ringer is two dimensional analysis problems that I have on the board as they come into class:
- How many feet are in 500 inches? 41.7 ft.
- If 1 byte equals 8 bits, 1 kilobyte equals 1,024 bytes, and 1 byte equals 2 nibbles. How many kilobytes is 36 nibbles? 0.018 kilobytes
They are instructed to show their work and turn it in when completed. The first problem is an easy problem that requires only one step to complete. I do this to see if all students are capable of solving a one-step problem that has a simple ratio used. The second problem is a little more unconventional and requires higher-thinking skill to solve. I use this problem because I want to see how many students are able to solve a multistep problem using dimensional analysis with an unconventional ratio. The students that are able to solve the second problem should have a good foundation for setting up stoichiometry problems later in the unit. I don’t provide points for the bell ringer, it is meant to show me what students understand dimensional analysis. The following day I will return the bell ringer and work with the students that got both problems wrong and still need help after today’s lesson
After all the homework assignments have been checked, I will ask if students have any questions. Generally students that did the assignment do not have any questions because working through 30 problems provided enough practice. The students that did not complete the assignment will need to complete the assignment before completing this lessons assignment. I will give them partial credit if the assignment is completed before the end of the period.
After completing the bell ringer I hand out page 6 of the factor label worksheet for scientific notation(Key). I got this packet from the internet on Mrs. Crane’s website and modified it slightly to accommodate my class. The beginning of the packet gives several examples of what an exponent looks like and how to convert a large number into scientific notation. The first example is 2,500,000 = 2.5 x 106. I start this portion of the lesson by doing guided practice with the class. This method gives students an opportunity to practice problems while being shown how solve the problems.
My standard method for guided practice is to provide students with a couple of examples, have them work on a couple problems and then solve the practice problem as a class to illustrate the correct way to solve the problem. Overall students do not have a problem with converting from standard notation to scientific notation. If students are to show some difficulty it is converting a decimal number smaller one into a negative exponent. If students have difficulty with this I tell them that smaller numbers will have negative exponents and larger numbers will have positive exponents. Practicing the class problems should provide enough practice understand scientific notation.
At this point in the unit I do not instruct students how to enter scientific notation into their calculators. This type of instruction will be part of the unit that introduces problems that involve Avogadro's number. Till then students only need to know how to recognize scientific notation, what type of numbers exponents represent (positive exponents > 1 and negative exponents < one) and how to convert from from standard notation to scientific notation and vice versa on paper.
After completing the standard notation to scientific notation, we work on converting from scientific notation to standard notation. We again work these problems through guided practice and most students understand the concept by the end of the lesson. Most students find these conversions easier than the previous ones. Attached is an example of student work illustrates the majority of the students in the class. This students and the majority of my students have very little difficult with scientific notation.
Very little time is spent on scientific notation because the only need to use in this unit when solving moles to atoms (molecule) problems which only makes up one lesson and two problems on the unit exam.
After completing the guided practice the remainder of the class period (20 mins) is a quiz white board review. The review is done in groups of two on white boards (14” x 14”) and is a mixture of dimensional analysis problems and scientific notation.
I tell each group they will need a calculator, the conversion table from Day 1 Boot Camp, a white board and marker. I leave white board and markers out at lab tables for easy access and quick reviews. I tell the class that this will be a review for a quiz tomorrow on dimensional analysis (factor labeling) and scientific notation. Each problem students will be given 45 sec to 90 secs to complete the problem depending on the difficulty. I tell the class that problems will be alternated between partners (one will solve one problem and the next will be solved by the other problem…so on and so forth) and they should turn over the board once completed until instructed to raise the board. I have them work in groups of two that way is someone is struggling the other person can help them solve the problem. This method is a great way to review especially when little practice has been issued (see reflection). Here are the problems I used:
- How many milliliters are in 0.255 liters? 2.55x10^2 mL (255)
- How many liters are in 233 milliliters? 2.33x10-1 L (0.233)
- How many grams are in 125 pounds? 5.675x10^4 g (56750)
- How many days are in 520 minutes? 3.61x10-1 day (0.361)
- How many eggs are in 12 dozen? 1.44 x 10^2 eggs (144)
- 2.81 x 10-2 0.0281
- 3.77 x 105 377000
- 1.05 x 101 10.5
- 6.02 x 1023 602000000000000000000000
- 15678 1.57 x 104
- 0.00456 4.56 x 10-3
- 0.00000067 6.7 x 10-7
- 1,234,567 1.23 x 106
I tell the students that if they want to put the dimensional analysis problems in scientific notation it will help them on the quiz. Therefore, I have provide the answers for 1-5 in scientific notation.
I do not assign a homework assignment, I just tell students to study for the quiz using the worksheets that we did in class.
Mastery of this lesson was achieved by most students. The area where some students struggled was converting from a small number (such as problem 11 above) into scientific notation. Some students tend to move the decimal all the way to the end of the number, or forget that the exponent will be negative for small numbers. These students will need more practice before working on mole to particle problems (Avogadro's number).
Overall the review was successful in providing students with practice, mainly in part to students working together in a group. The only two problems that groups struggled with were 4 because it was a two-step problem and 11 & 12 because the were problems converting a small number into scientific notation.