Lesson: GCF

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Lesson Objective

SWBAT find the GCF of any set of numbers

Lesson Plan

Lesson Steps:  Wednesday

Do Now-8 min

·         Students work on 2 problems on do now sheet to review content ( 4 minutes)

·         Teacher walks around to check HW for completion and process on do now problems (while students complete problems)

·         Pull two sticks – students complete answers on whiteboard – students check work against students boardwork (2 minutes) Teacher walks around still to check understanding while students are working on board.



HW Check- 6 min

·         Check All – put up all answers on whiteboard

·         Students check all problems on homework (3 minutes – 1 minute front, 1 minute back)

·         Teacher walks around while students are checking work to intervene.

·         Teacher identifies the one or two most common mistakes on homework and reviews it whole class on transparency.  (1 – 2 minutes)  Before review – ask students to think about the steps I am taking while I solve the problem(s) – they will share whole class afterwards.

Paper Pass in Transition:


Mental Math: 5min  

·         Teacher reads and shows problem

·         Student pulls a stick to call on student to answer

·         Last problem string – all students complete and answer by raising hand – fastest hand called on


Mini-Lesson: (40 mins)  Parallel TEACHING

·         Discuss with students that today we are going to be working on two different ways that will help us to solve the problem above. 

·         Group 1: (Froehlich)

o    Opening:  Present students with the following problem:

Coach Jones is bringing 24 pretezels and 36 cookies for the mudball team.  These have been carefully counted so that each team member gets the same number of pretzels and the same number of cookies?  What’s the largest amount of members that can be on the team?  How many of each snack would the members receive?

o    Teacher will review prime factorization – what is prime factorization?  A way to break down numbers into a product of primes, The longest string of factors for a number, a unique i.d. for a number.

o    Teacher will review factors – what is a factor?  A way to break down a number as whole number parts that can be multiplied to get the number, a whole number divisor of a number.

o    Today we will use prime factorization to help us find the greatest common factor of two or more numbers.  When we are talk about greatest common factor we are thinking about what factors two numbers share. Sometimes two numbers will share many factors.  Today we are looking for the greatest factor two number share.  What’s another word for greatest?  Largest, biggest. 

o    One way that we can find the largest common factor for a number is to use prime factorization. 

o    Step one – we should prime factorize both numbers:   24: 2 x 2 x 2 x 3    36:  2 x 2 x 3 x 3   Show with trees.

o    Next we should circle all the factors they have in common.   Circle the 2, 2, and 3

o    Next we will multiple the factors they have in common.  Multiply 2 x 2 x 3 = 12.  12 is the greatest common factor of 24 and 36.

o    Practice with other examples: 

§  12 and 18

§  14 and 15 – Explain what happens if they don’t have any common prime factors – the answer is 1. 

§  24, 32 and 16

·         Group 2 (Ivory):

o    Problem:  A band of pirates divided 32 pieces of silver and 48 gold coins.  These pirates were known to be absolutely fair about sharing equally.  How many pirates were there?

o    Teacher will review factors:  What is a factor?  A way to break down a number as whole number parts that can be multiplied to get the number, a whole number divisor of a number.

o    Today we are going to use a list to help us to solve the problem presented.  One way we can solve the problem is we can think about which numbers go into the two numbers evenly.  Then we need to think about of those numbers which ones do they share.  To do this, we can write a list of all of the factors of each number.

o    What are the factors of 32?  (Really focus on naming factor pairs and starting from 1 and moving to two and so on…)

o    What are the factors of 48?  List the factors

o    Which factors do both numbers share?  What factors are common?  What is the greatest common factor ? 

o    Practice with other examples:

§  Including one where 1 is the gcf.

·         Summarize:

o    Today we learned about two different ways to find the greatest common factor of two or more numbers.  What are they?  Using prime factorization or making a list.

o    Complete the exit ticket on GCF.  Know that you should always use which ever method is easier for you to do.

§  On exit ticket, include question about which method do you prefer?

§  Find GCF



Lesson Resources

GCF reteach  
GCF prac  
CW Bagging Snacks GCF to problems  
HW GCF to solution of problems  
U4 L7 Notes Prime Time GCF  


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