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Mathematics
Grade: Middle
Subject: Mathematics

#4765. GDC and LCM

Mathematics, level: Middle
Posted 09/08/2014 by Doug Lewis (Doug Lewis).
Boring Middle School, Boring, Oregon
Materials Required: Internet Access, Projector, Printer
Activity Time: 3 or 4 days/ 50 minutes a day
Concepts Taught: Greatest Common Factor and Least Common Multiple

Doug Lewis • ED 551b • Assignment #6
Beginning of year Review Unit
In years past this has been a very fluid unit, and probably will remain for the foreseeable future. As a sixth grade math teacher, I welcome students with a variety of skills and backgrounds into my classroom each fall. We pull from three different elementary schools, so one can imagine the different content that has been covered in grades 1-5.
However, Common Core is supposed to remedy a lot of those issues. This will be the first year I am working with sixth graders in which the full previous year our district implemented Common Core. I am hoping kids will be on a more universal level.
Regardless of what happens this year, I will be reviewing factors and multiples at the beginning of the year; more specifically, Greatest Common Factor (GCF) and Least Common Multiple/Denominator (LCM/LCD). Under previous standards we went over this quite a bit as a lead in to operations with fractions, but that has been pushed into lower grades. Below are the plans for my unit.

Day 1
Objective- Find the greatest common factor (GCF) of a set of numbers. CCSS- 6.NS.4
For the first few weeks of school I really emphasize the "I do, we do, you do," as it slowly and comfortably brings kids into the fold. First up is an intro to Khan Academy with a video explaining how to determine the GCF of two or more numbers:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-and-multiples/cc-6th-gcf/v/greatest-common-divisor
I decided to begin with a video to show them how accessible Khan Academy is. I only use about the first four minutes, stopping at specific points to make sure they are keeping up with notes (students are writing basically everything Sal is writing), and to challenge them to figure things out before he gives them the answer.
We then go over a few more examples on the board, and I generally let students pick the numbers that we work with. After doing a few together, I ask them to do some with a partner, then challenge them to do some on their own.
I will assign them a worksheet that is tied into our curriculum as homework. Required work is on the front, and I try to include a more enjoyable, optional assignment on the back. Something that relates to our topic, but had a riddle or maze or joke or something like that.
Day 2
Objectives- Find the least common multiple for a set of numbers. CCSS- 6.NS.4
Find the least common denominator for a set of fractions.
Begin class by posting a warm-up on the board/screen and I go around checking their practice work (homework). If a student is completely done with their homework, they earn a stamp. This helps me keep track of who is completing things on time, and I can easily transfer that info into our grading program, which our parents can access.
We go through homework as a group, with students checking their own work. After going over the correct answers, give students five minutes to make their own corrections and do a few on the board if necessary. Practice work is collected daily and entered in to our grading program.
For today's video, I chose to use one from a site called Virtual Nerd. I want to expose students to multiple sites, and this is another good one.
http://www.virtualnerd.com/middle-math/number-theory-fractions/least-common-multiple/least-common-multiple-all-multiples
After the video, I will again model some examples, have students work in small groups, then complete some problems on their own
Day 3 (if necessary)
I say if necessary because maybe this will be the year students enter sixth grade with a more well rounded skill set as far as fractions are concerned. If this is the case, I will skip this day and go directly to the quick assessment of day four.
Objective- Review GCF and LCM/LCD CCSS- 6.NS.4

Another warm-up and another round of checking in with kids and their homework completion.
On this day I usually show them a little shortcut for finding both GCF and LCM. This was shown to me by a colleague a few years ago. I never really used it until last year, when a different teacher explained it to me once again. I tried finding a link for it online, but have not been able to yet. Suffice it to say that this day is a review of the first two days. This year I am giving them specific problems from our text book. I have, for the most part, chosen word problems that are the first step in preparing my students for the Smarter Balanced performance task this spring.
Day 4
Objective- Students will show their mastery of identifying the GCF, LCM, and LCD.
I give them a quick assessment on these skills. It consists of eight or nine problems and takes about 20 minutes.
Follow-Up
We will go over the assessment and give students a chance to work on any mistakes they might have made. For those students whom grasped the concepts well, I have a series of challenge problems for them to tackle while other kids are working on corrections.