Reflection: Developing a Conceptual Understanding How Does It Grow? - Section 2: Whole Class Discussion


Having students reflect on why and how really helps them make sense of and understand the properties. Without this dual reflection, my students often notice the wrong things. They end up failing to conceptualize the math.

It is my experience that traditional textbook questions that ask students to identify the property in (7+4) + 6 = 7 + (4 + 6) are more likely to promote the misconception that the associative property is the one in which parentheses move and will often be mistaken for the distributive property. The idea of flexible regrouping is lost on students, and they never see the value in the property. Yet, this is important for fluency with mental mathematics.

In this lesson I listen for and invite multiple explanations and demonstrations of the same idea because it takes a while for my students to formulate, connect, and solidify ideas. In this case, I am asking my students to think about several different ideas. Making connections takes time, but it helps my students understand more completely.

Today, a student made a comment that initiated an unexpected, but necessary discussion with the class. While I was solving 66 + 7, by breaking down the 7 further (66+4+3) another student said it was easier for him to add 60 and 7 and then break the 6 into two threes (60+7+6=60+7+3+3). This inspired several other students to suggest other orders for the four addends (20+40+6+7, etc.) which in turn led a skeptical student asking if those expressions were really all equal. I turned the question back to the class and asked them to find some way to decide and to prove their conclusion. The most convincing were the ones that used an open number line.


  Concept development
  Developing a Conceptual Understanding: Concept development
Loading resource...

How Does It Grow?

Unit 2: Writing expressions
Lesson 7 of 7

Objective: SWBAT generalize patterns into a verbal description and a variable expression.

Big Idea: Students will verbally generalize the properties of addition as well as write a variable expression to describe a growth pattern.

  Print Lesson
Add this lesson to your favorites
how does it li
Similar Lessons
Determining Solutions
6th Grade Math » Equations
Big Idea: How can we prove equality? In this lesson students determine if a given number is a solution to an equation. Skill mastery is a focus.
New Haven, CT
Environment: Urban
Carla Seeger
Equivalent Numerical Expressions, Day 2 of 2
6th Grade Math » Intro to 6th Grade Math & Number Characteristics
Big Idea: How can you represent the area of a diagram using numerical expressions? Students connect their knowledge of area and equivalent expressions to the commutative and distributive properties for day 2 of this investigation.
Somerville, MA
Environment: Urban
Andrea Palmer
Distributive Property
6th Grade Math » Properties of Math
Big Idea: Students will compare the distributive property to sending invitations at a birthday party.
Brooklyn, NY
Environment: Urban
Ursula Lovings
Something went wrong. See details for more info
Nothing to upload