Reflection: Developing a Conceptual Understanding Common Factor the Great! - Section 1: Warm up


Finding the greatest common factor (GCF) of two numbers is a process of identifying how the numbers are related to each other. This is a different way of thinking for my students. They are not often more comfortable reasoning by rote, than looking for patterns relating math facts.

I find that many of my students have learned their multiplication facts by rote memorization alone. In my view they have missed out on the opportunity to develop good mathematical practices. For instance, rote memorization may involve perseverance, but it does not encourage reasoning concretely and abstractly or developing an understanding of the structure of a number.

My students often measure their proficiency with math facts in terms of the speed of their recall. In order to slow them down to engage their reasoning I ask them to compare two numbers (18 & 12) in a Venn Diagram and include every way the two numbers differed or were the same. When they take the time to consider these numbers they come up with facts like:

  • factors of 1, 2, 3, 6
  • even numbers
  • both have a 1 in them

These are all interesting observations and they can be discussed meaningfully.

  • We can discuss the meaning of the GCF in terms of all of the factors
  • We can consider the importance of the designation even and odd in terms of factors
  • We can discuss place value and the idea that they both numbers have a 10, not a one, which is also a helpful idea with respect to flexible multiplicative reasoning

When students learn their math facts through number sense routines that teach them how to decompose and recompose the numbers flexibly, they learn to look for and use the relationships between the numbers to solve problems. 

  Thinking about Factoring
  Developing a Conceptual Understanding: Thinking about Factoring
Loading resource...

Common Factor the Great!

Unit 3: Equivalent Expressions
Lesson 16 of 23

Objective: SWBAT use the distributive property to factor out the greatest common factor in a polynomial.

Big Idea: Students will relate factoring a variable expression to a real world situation.

  Print Lesson
1 teacher likes this lesson
Math, factoring polynomial expressions, Expressions (Algebra), area model, white boards, real world
  54 minutes
Similar Lessons
Multiples and Least Common Multiples (LCM)
6th Grade Math » Number Sense
Big Idea: A multiple is a product of a number and another whole number greater than 0.
New Haven, CT
Environment: Urban
Carla Seeger
Brownies & Factors
6th Grade Math » Intro to 6th Grade Math & Number Characteristics
Big Idea: How many different rectangular boxes can you design to fit 100 brownies? Students explore the relationship between factors and area models.
Somerville, MA
Environment: Urban
Andrea Palmer
Divisibility Rules for 2 and 3
6th Grade Math » Divisibility Rules
Big Idea: Students will work with calculators to discover the divisibility rules
Brooklyn, NY
Environment: Urban
Ursula Lovings
Something went wrong. See details for more info
Nothing to upload