In preparation for today's lesson, the Warm Up problems I wrote include two questions that ask students to write a number in standard form given it in scientific notation and a number in scientific notation given it in standard form.
I then asked students to solve two bare computation problems with scientific notation in which the numbers have the same exponents. I selected these because I have found that students struggle to add and subtract decimals as they often forget to align their decimal points. These problems will provide teachable moments, if needed.
Building on the previous day's learning, I remind students about the conversation from the day before and our discovery of a strategy that was much more efficient at problem solving with scientific notation. I asked a student to explain what we had figured out, which was that if numbers had the same exponents, it was much easier to conduct operations with them.
I explained that today, we were going to practice writing equivalent numbers. I pointed out that half the numbers we would be using would not be in proper scientific notation because we would be intentionally changing the representation of one of the two numbers in each problem so the exponents would match.
I then displayed three samples and asked for someone to explain how we would change the first one to an equivalent number with the new exponent. One student volunteered that I should just move the decimal three places to the right, so my new representation would be 34,000 x 10^5. To verify, I wrote the first number in expanded form as 340,000,000. I then wrote 34,000 and showed the decimal moving five places to the right. I asked, "So do we have proof that these two representations are equivalent?"
Moving on, I asked students to tell their shoulder partners what I would need to do to create equivalent numbers on the second example. I then pulled a stick (from the cup of sticks with names on them) and asked the student to come to the smartboard and write the number she thought should go in the blank.
She wrote 179, which I then verified by writing both representations in standard form. We continued with the next four examples. At the end of these examples, I took a survey of learning levels from the class. I asked them to show me where they were on the learning scale (5 fingers = I could teach this to someone; 4 = I understand this; 3 = I am starting to understand; 2 = I understand a little; 1= I don't understand at all). Student responses range from 3 to 5, so I feel confident in moving to the next part of the lesson.
Now that students have practiced writing equivalent numbers, I present them with a problem that will require them to convert one number. I ask the students to raise their hands if they know what equivalent number I could convert to. I select one who knows and record her answer under the original number. I ask students to give me a thumbs up if they agree. I then ask what I need to do next to actually solve this problem. One student calls out, "Line up your decimals!"
Feeling grateful that this concept is no longer foreign to the class, I select a student to solve. Once he has written and added the decimals to find the coefficient, I encourage him to finish the problem by asking, "So is your answer in proper scientific notation?" He nods his head no and moves the decimal point two places to the left. I then ask the class if it is okay to just move the decimal without changing anything else in the number. Several students respond that he should add two to the exponent.
I guide the students through another example using the same strategies. I then reveal the third and then the fourth question for students to work on independently before I select a student to answer each one.
For closure, I want students to show what they have learned by completing two problems based on a table of pet ownership. The numbers of pets vary, so students will have an opportunity to use the strategies learned in class today.
As students finish, they raise their hand so I can check their work. I make note of the students who are struggling with the concept so I can provide them additional support during tutorial (which is held two days per week during advisory).