Fluency with Large Numbers

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SWBAT solve a variety of conversion problems with Large Numbers

Big Idea

We need to be flexible and efficient when converting to and from scientific notation.

Start Up

15 minutes

I like to arrange students based on the results of their exit tickets (Deconstructing_Standard_Form_Exit_Ticket).

I may tell them this explicitly, but I usually keep it to myself. The idea is that I arrange groups that are having similar issues, but throw-in one person that can help the group (I might let this person know who they are in a discrete way, depending on how shy they are). My goal is to empower "the ringer" and help them recognize that they need to lead the group.

I give the class 5 minutes to discuss the three problems from yesterday with the expectation that they write notes in their book and share their solutions. For the group that did well on all the problems, I have them review other exit tickets and give advice to struggling students. They sign their names next to their advice and answers so that the students they help can find them for future reference.

Once this process is done, I present the class with The Chicken Problem.

I let students know that chickens in fact run this world, since the greatly outnumber humans. Here is the current approximation of chicken eggs produced annually: 390,000,000,000.

I ask them to write the name of this number, then write it in scientific notation. Next, I ask the class to make this number 1000 times larger, write the result in standard form, and write it in scientific notation. I also ask for the name of this number.

Afterward, when reviewing their work, I hope to bring out the idea that we can just multiply by 10^3 and then add the exponents (spiraling back to their previous work with exponents).  


30 minutes

I let students know that the focus today is on fluency and individual work. As they complete Fluency with Large Numbers, I let them work in a cycle of 10s. Where they work individually for 10, then with a partner for 10 and so forth. I circulate and help students as they practice a wide variety of problems. 


20 minutes

I review the problems from the investigation with students. Depending on the class, I split up the problems by difficulty. The first group are all about mild (grade level) or medium (grade level but a little tricky). However, the last three questions are certainly spicy and worth talking about. I like to extend the problem by substituting trillion or higher for the word million. 


The way I review the group of problems is to have students code their sheets before we review. I ask them to mark which problems they didn't start because they ran out of time and which they skipped because they felt lost. Then they mark their responses write or wrong and fix their work on their sheet. I like to collect this worksheet to help me design future lesson discussions and assessments. This is especially relevant as the next lessons require students to use large numbers fluently.