I will give students about 5 minutes to work on the following problem. I will remind students to refer to their prior notes, if necessary.
Find the GCF of 72 and 80.
I want students to refer back to their notes and use one or both of the methods we discussed in the GCF lesson.
I will review the definition of multiples with students. This is important because students often confuse multiples with factors.
A multiple of a whole number is the product of the number and any nonzero whole number.
For this activity, I will show students a clip from the movie "Father of the Bride" in which the main character has a breakdown in the grocery store over the amount of hot dogs and hot dog buns he can buy.
We will discuss the following questions:
How many hot dogs came in a pack? Buns?
Why was this a problem for George?
What did he do to solve the problem?
Was there a better way, mathematically, he could have solved the problem?
The overlying problem is the hot dogs come in a package of 8 and the buns in a package of 12. Students should come to the conclusion that George could have bought 3 packs of hot dogs and 2 packages of buns so he could have an equal amount of 24. This will lead to an introduction of the least common multiple.
I will share with students 2 methods of finding the least common multiple. I tell students that both methods are acceptable, but I prefer the second method for a few reasons. One reason being it is easier to use when given large numbers. The other reason being that it is a continuation from the previous GCF lesson.
Method 1 - List the multiples LCM - Method 1
I will work through an example with students explaining that I start with listing 3 - 4 multiples of each number and then list more if necessary. This method is fairly straightforward, but I ask students to consider if it would be as easy if they were given larger numbers.
Method 2 - Division Method and Venn Diagram LCM - Method 2
As I work through an example with students, they may begin to realize that we are using the same steps as method 2 of finding the GCF. I will explain that the only difference is the last step, where it is important to multiply all of the numbers in the diagram to find the LCM.
I will give students a problem to work through on their own. I will suggest that they try both methods, before they decided which method they prefer. As students work, I will circulate to answer any questions and to assess students' understanding. A common mistake when using method 2 is students only multiply the numbers in the non-overlapping sections of the diagram instead of all of the numbers.
Find the LCM of 28 and 90.
I will give each student an index card and the problem "Find the prime factorization of 248" to solve. They will show their work on the index card and hand it in before leaving class. I will explain to students that this is not a quiz or test, but just a way for me to check on their understanding.
I will use these cards to assess students' understanding of prime factorization. This is important because method 2 of finding the GCF and LCM are based on prime factorization.