Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 49039
Can You Find the Relationship?
In this lesson students will first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will
take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based
on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two day
lesson.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Computers for Students,
Internet Connection, Java Plugin
Instructional Time: 1 Hour(s) 30 Minute(s)
Freely Available: Yes
Keywords: greatest common factor, lowest common multiple, LCM, GCF
Instructional Design Framework(s): Direct Instruction, Confirmation Inquiry (Level 1)
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
define in their own words the greatest common factor (GCF) and least common multiple (LCM).
find the GCF and LCM of two numbers.
identify when to use GCF or LCM to solve mathematical problems.
summarize their understanding of GCF and LCM by using real world examples.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students will need to know:
1. how to fluently multiply multi-digit whole numbers using the standard algorithm.
2. the relationship between multiplication and division.
3. how to find all factor pairs for a whole number in the range 1 - 100.
4. recognize that a whole number is a multiple of each of its factors.
5. generate a number or shape pattern that follows a given rule.
6. what a prime number is.
7. how to find multiples of a given whole number.
Guiding Questions: What are the guiding questions for this lesson?
How did you redefine GCF? (Possible answer: The biggest number/ they both have/ as a factor (divisor of each number))
How can you use this definition to find the GCF of 12 and 32? (Find the biggest number that both can divided by: 4.)
How might you show the factors of these numbers? How might you decide which is the biggest and is a factor of both? How can I use this definition to find the LCM of
page 1 of 4 12 and 32? (The smallest number that is a multiple for each number: 96.)
How might I show the multiples for each number? How would I find the smallest that is the same for both. If I want to have enough hotdogs and buns to serve each of
24 people exactly one hotdog and bun and have none left over, how many packages of hot dogs and hot dog buns should I purchase? The package of hotdogs contains
8 hotdogs, and the package of buns contains 12 buns. (Answer: LCM is 24/3 bags of hot dogs; 2 bags of buns) How do you know your answer is correct?
Teaching Phase: How will the teacher present the concept or skill to students?
Have a timer with sound running as students walk in. Have the initials GCF and LCM written on bold colored paper and hung on the board. This should be big and bold
enough to catch students' attention. There needs to be space under each sign for students to post sticky notes. Have a blank set of stickies in order of blue, yellow, and
green lined up under each mathematical term. Students will need 2 sets (GCF/LCM) of 3 different colored sticky notes and a dictionary or thesaurus on each desk. The
school media center may have a class supply.
"Today our mission is to break apart the mathematical terms Greatest Common Factor and Least Common Multiple, and then put the terms back together in our own
words. You have three sticky notes for each term and a dictionary or thesaurus. We are going to look up each word and find a more "friendly" way to explain GCF and
LCM. You may use more than one word or a phrase to replace each word (example: criteria/ things you have to have in your project). We will start with the
mathematical term greatest common factor. You will have 4 minutes to find another way to say greatest common factor and post it under GCF on the board. The blue
sticky will represent greatest, the yellow sticky will represent common, and the green sticky will be used to represent factor. On your mark, get set, go!" Have a
silenced timer counting down. Use the same procedure for least common multiple. Only give the students 2-3 minutes. Now the students know what they are doing
and have already redefined the word common.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Review the redefined mathematical term GCF and apply this better understanding to numbers. "How did you redefine GCF?"(Possible answer: The biggest number/ they
both have/ that they can be divided by.) "How can I use this definition to find the GCF of 12 and 32?" (The biggest number that both can divided by is 4.)
"With your partner, find 2 ways you can find two different numbers' GCF, or the greatest number they are divisible by." Write 12 (
) and 32 (
) on the document camera or board to help students that might be stuck. Higher level students might choose 2 more challenging numbers. Use the timer to give
students 5 minutes. Adjust time for student ability. All students might not have finished 2 examples. Explain that they should look at where in the process they began to
feel stuck/unsure. Have them think of a question that would help them become 'unstuck'. (Possible questions: How can I find what numbers 12 and 32 are divisible by?
or I just know that the biggest number both 12 and 32 are divisible by is 4. How do I figure out the GCF if I don't just know the biggest number/factor two numbers are
divisible by?") They should note how other students moved past that point to find the GCF and see if they can answer their own question. Giving students extra points
is a good incentive to ask and answer their own questions.
Ask a few students to work out their examples on the board or document camera of different ways they can find the GCF. As students work out examples on the
board, have the other students write the examples in their math notebook. Give each example a name or title (factor tree, cake/ladder method, list.). Support
students' organized thinking with the displays, and, if necessary, add to the strategies students display. Ask students to articulate and justify their method and
reasoning. "How does using a factor tree help you find the GCF?" (Possible answer: Finding the GCF means we are looking for the biggest number that both original
numbers can be divided by. When I break the original number down, to where it cannot broken down any further, I have found all the prime numbers that make the
original number. Looking at the primes each original number has in common, shows all the numbers they are divisible by. When I multiply the primes they have in
common, I find the greatest factor each original number is divisible by.)
"With your partner, let's see if your methods will work to find the GCF for 49 and 84." Remind students to refer to the examples they wrote in their math notebook.
"What is the biggest number both 49 and 84 are divisible by?" Work with students that you noted needed more support. Depending on your class dynamics, this time I
would have the teacher work out the GCF using the factor tree, cake method, and the list method on the document camera instead of using student volunteers. Have
students write the examples in their math notebooks. Ask students to justify why these methods work in finding the GCF for 49 and 84 as you work out that specific
method. "How does the list method help me find the GCF for 49 and 84?" ( Possible answer: We are looking for the greatest common factor or the biggest number 49
and 84 are divisible by. The list method lists all of the numbers' factors.(49: 1,7,49 and 84: 1,2,3,4,6,7,12,14,21,28,41,84). Now you can see the biggest factor they
have in common.)
Play a few online GCF games to practice. This can be done whole group or as a center.
Review the redefined mathematical term LCM and apply this better understanding to numbers. "How did you redefine LCM?" (Possible answer: The smallest number/
both / can make.) "How can I use this definition to find the LCM of 12 and 32?" (The smallest number that both can make is 96.)
"With your partner, find 2 ways you can find two different numbers' LCM." Write 12 (12,24,...
) and 32 (32,64,...
) on the document camera or board
to help students that might be stuck. Use the timer to give students 5 minutes. Adjust time for student ability. All students might not have finished 2 examples. Explain
that they should look at where in the process they began to feel stuck/unsure. Have them think of a question that would help them become 'unstuck'. (Possible
questions: How can I find the smallest multiple 12 and 32 can make? or How do I know this is the smallest multiple 12 and 32 can make?") They should note how
other students moved past that point to find the LCM and see if they can answer their own question. Again, giving students extra points is a good incentive to ask and
answer their own questions.
Ask a few students to work out their examples on the board or document camera. As students give examples of different ways they can find the LCM, have the other
students write the examples in their math notebook. Give each example a name or title (factor tree, cake or ladder method, list,Venn LCM Diagram). Ask student
volunteers to explain their reasoning. Students need to see all 4 examples worked out and explained. "How does the factor tree help me find the smallest multiple 12
and 32 have in common?" ( Possible answer: When I break both numbers down to their prime numbers, I am looking at the smallest numbers/factors that make up
that number - the numbers basic building blocks. If I only use the prime numbers from the largest original number and only add prime numbers from the smaller
original number that are not already listed, I have all of the prime numbers or basic building blocks for both 12 or 32. I am making a multiple both 12 and 32 can make
when I multiply the prime numbers for 32 and any missing prime number or building block needed to make 12. I have broken down each number and put it back
together only using the basic building blocks needed to make either 32 or 12. I know this is the LCM or smallest common multiple, because I only used the prime
factors, using the common prime factor/s once.
"With your partner, let's see if your methods will work to find the LCM for 49 and 84." Remind students to refer to the examples they wrote in their math notebook.
"What is the smallest multiple both 49 and 84 can make?" Work with students that you noted needed more support. Again, depending on your class dynamics, this
time I would have the teacher work out the GCF using the factor tree, cake method, list method, and the Venn on the document camera instead of using student
volunteers. Have students write the examples in their math notebooks. Ask students to justify why these methods work in finding the LCM for 49 and 84 as you work
out that specific method. "How does the Venn method help find the LCM for 49 and 84?" ( Possible answer: We are looking for the smallest multiple 49 and 84 can
make. The Venn Diagram (link for example) organizes both of the numbers' factors, putting each list of prime factors inside separate circles that overlap. The
page 2 of 4 overlapping section contains only the prime factor that is common to both.
Play a few LCM online games.docx to practice. This can be used during whole group or as a center.
End of day one. Review students' redefinitions for GCF and LCM. Have students vote on the best one for each mathematical term. Write this redefinition on the colorful
GCF and LCM signs.
Day 2:
Play the video clip with the father of the bride is getting frustrated because hotdogs are packaged in quantities of 8 and hotdog buns are packaged in quantities of 12.
Ask students if they have ever had a similar situation of trying to purchase items with different quantities. Display word problem document and work it out with the
students.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
"Hot dog come in packages of 8. Hot dog buns come in packages of 12. If I want to buy enough buns and dogs and have none left over, how many packages of hot dogs
and hot dog buns should she purchase?" (Answer: LCM is 24/ 3 bags of hot dogs 2 bags of buns)
Each group is responsible for creating a poster that illustrates how they solved their word problem. Have one person from each pair get a word problem, poster
rubric, scissors ,glue , poster paper, and markers. Have sets of these supplies prepared before class, including one word problem. Cut the individual word problems
from the word problems examples supplied. Remind students to use their examples from their math notebooks. (word problem worksheet with answers)
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Each pair will have 2-3 minutes to present their poster. Students can be given the first 10 minutes of each class to finish up presentations. An alternative approach could
be to have students make a video of their presentation or create power points instead of posters. The teacher could choose 2 or 3 to show the whole class. Students
could, also, simply display their posters and have students choose 2 or 3 for whole class presentation.
End the lesson by pointing to and reading the GCF and LCM re-definitions. Then display your power point that reviews GCF and LCM word problem strategies.
Summative Assessment
The rubric will be used to assess students' posters that illustrate their understanding of Greatest Common Factor and Least Common Multiple.
Ask students to independently answer the following two questions:
What is the Greatest Common Factor for the two numbers 15, 21? answer: 3
What is the Least Common Multiple for the two numbers 14, 10? answer: 70
Formative Assessment
The teacher will use students' comments during the whole group discussion to gauge students' understanding. Please refer to the guided questions section. Walk to
each group when they are creating their posters during independent practice. Note students' use of resources (class created definitions, notes, and poster rubric) and
application of them to solving their word problem and illustrate their understanding on the word problem poster.
The teacher will use this information to guide instruction throughout the lesson.
Feedback to Students
During whole group discussion respond and elaborate on students' comments. Walk to each group when they are creating their posters and comment on their
organization and accuracy. Remind the students to refer to their notes, class created definition, and poster rubric.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: Students can use an online dictionary and thesaurus.
Display examples of GCF and LCM using smaller numbers.
Students can create power point presentations instead of posters.
English Language Learners may need extra support with unfamiliar vocabulary. Provide definitions and examples.
Extensions: Students can throw a mock party and find when they have to use GCF and LCM during the planning.
Students can create their own GCF and LCM word problems.
Suggested Technology: Document Camera, Computer for Presenter, Computers for Students, Internet Connection, Java Plugin
Special Materials Needed:
Students will need:
1. enough sticky notes for each student to have 2 sets of three different colored sticky notes
2. class set of dictionaries or thesaurus
3. poster paper, scissors, glue, and markers for pairs of students
4. magazine that can be cut up and odds and ends pieces for students to use as manipulatives for their poster (straws, tooth picks, beads)
5. the word problems
Further Recommendations: Students have already worked with finding the GCF and LCM while solving fraction math problems. They are learning how GCF and
LCM can be used to work with numbers more efficiently by understanding numbers relationship. Give students time to reason and apply their understanding of GCF and
LCM.
The video is from Youtube. Download the video or prepare the screen, such that no advertisements are displayed.
Additional Information/Instructions
page 3 of 4 By Author/Submitter
This resource is likely to support student engagement in the following the Mathematical Practice: MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
SOURCE AND ACCESS INFORMATION
Contributed by: Kellyann Cox
Name of Author/Source: Kellyann Cox
District/Organization of Contributor(s): Brevard
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.NS.2.4:
Description
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of
two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–
100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express
36 + 8 as 4 (9 + 2).
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