GCF and LCM Word Problems

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SWBAT: • Define LCM, and GCF • Solve word problems involving LCM and GCF.

Big Idea

When would you come across GCF and LCM? Students apply their knowledge of GCF and LCM to solve word problems.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, students are reviewing factors, multiples, GCF, and LCM.  A common mistake is students confuse GCF and LCM.  I quickly go over correct answers with students.


15 minutes

I have students work in partners on these two problems.  I don’t mention anything about LCM and GCF.  If students struggle, that’s okay.  I encourage them to use what they know to do something.  Students will use different strategies to solve these problems, and that’s great!

After about 10 minutes I have students go to the next page.  Students participate in a Think Write Pair Share.

I want students to notice that problem 1 is asking for the smallest number of buns and hot dogs you need to buy if you want the same number of each.  Some students will connect this to finding the LCM of 8 and 10.  I want student to notice that problem 2 is splitting pearls and beads up into equal groups.  The question is asking for the largest number of identical necklaces.  Some students will connect this to GCF. 

More Problems

25 minutes

I use the ticket to go data from the previous lesson (Multiples, LCM, and GCF) to create homogeneous groups for this part of the lesson.  This way students can work with other students who are around their same skill level.  I go over group expectations and pass out the Group Work Rubric.  I have printed one set of GCF and LCM problem cards for each group.  I cut them out and put them in an envelope.  I explain that students will receive an envelope with the problems they will work on.  See my Creating Homogeneous Groups and Using the Group Work Rubric videos in my Strategy Folder for more details.

As students are working I walk around to fill out rubrics and monitor student progress.  I am looking to see what strategies students are using and how they are showing their work.  Students are engaging with MP 1: Make sense of problems and persevere in solving them. 

If students struggle I may intervene in one of these ways:

  • What is the problem asking?
  • What do you know from the problem?
  • What do you see going on in your head when you read this problem?
  • How could you show what is going on in the problem?
  • Look back at problem A and B.  Is this problem similar to either of those problems?  Why or why not?
  • Offer the student(s) a multiplication chart or Factor reference sheet

I Post A Key around the room, so groups can check their answers as the complete them.  If a group successfully completes the problems, they can work on the challenge problems.



10 minutes