Birthday Goodie Bags: GCF & LCM

Introduction (5 minutes):

Start by reviewing the definitions of factors and multiples.

Factor: A factor is a number that divides evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Multiple: A multiple is the product of a number and any other whole number. For example, the multiples of 3 are 3, 6, 9, 12, and so on.   
 

Activity 1: Finding the GCF (15 minutes)

Introduce the concept of GCF: The Greatest Common Factor (GCF) of two numbers is the largest number that is a factor of both numbers.
Example: Let's find the GCF of 12 and 18.
List the factors of 12: 1, 2, 3, 4, 6, 12
List the factors of 18: 1, 2, 3, 6, 9, 18
Identify the common factors: 1, 2, 3, 6
The greatest common factor is: 6

Practice: Have students work in pairs to find the GCF of the following number pairs:
16 and 24
15 and 25
36 and 48

Activity 2: Finding the LCM (15 minutes)

Introduce the concept of LCM: The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.
Example: Let's find the LCM of 4 and 6.
List the multiples of 4: 4, 8, 12, 16, 20, 24...
List the multiples of 6: 6, 12, 18, 24, 30...
Identify the common multiples: 12, 24...
The least common multiple is: 12

Practice: Have students work in pairs to find the LCM of the following number pairs:
5 and 7
8 and 10
9 and 12
Wrap-up (5 minutes)

Review the key concepts of GCF and LCM. Ask students to summarize the steps involved in finding each.

Assessment:

Give each student a copy of the performance task linked in the resources tab. Observe students during the activities and provide feedback.
Collect student work and assess their understanding of GCF and LCM.
Assign homework problems to reinforce the concepts learned in class.

differentiation: Students who do not have multiplication fact fluency may struggle with this lesson. Provide them with a multiplication chart to help them identify factors and multiples. 

extension: Have students create a real-world scenario where finding the GCF or LCM is useful (e.g., dividing objects into equal groups, finding the next time two events will coincide). OR Increase the LCM/GCF to include 3 numbers instead of 2.

Use the performance task (linked in the resources section) to assess student learning outcomes.