Reflection: Discourse and Questioning Connecting Multiplication and Division - Section 2: Connecting Multiplication and Division


Over the three sets of problems, students were able to see a pattern connecting the multiplication and division problems.  They were able to see that dividing a number by 2 is the same as multiplying that number by ½.  They were also able to extend this pattern to divisors other than 2.  At the end of this section, I posed a question: 10 divided by 'w' will result in the same answer as 10 x ______ .  Some students immediately reacted to my use of a variable with “I don’t know!” and “W?! How are we supposed to know what w is?!”  I explained that we had been working on finding a connection between multiplication and division, and that I wanted to see if they could use what they’ve learned to demonstrate the connection using variables.  I asked if someone had a number we could substitute in for w.  One student said we could use 5 for w.  10 divided by 5 = 2, so 10 x _____ will also result in 2?  Students participated in a Think Pair Share with their partners.  Students were able to conclude that 10 x 1/5 would also result in 2.  After a bit more discussion, a couple students were able to explain that 10/w is equivalent to 10 x 1/w.  I substituted 2 in for w to demonstrate that it indeed worked.

One of my classes had a little extra time, so I asked them what w divided by w would equal.  Students were able to say that any number divided by itself will result in 1, so w divided by w will equal 1.  Then I asked students what the missing factor would be to also create an answer of 1:  w x ______ = 1.  Students participated in a Think Pair Share.  Some students said w, and I explained that w times w would result in w squared.  I connected this to multiplication, 3 x 3 is equal to 3 squared, or nine.  A student figured it out and I asked her to come to the board to explain her answer.  She said w x 1/w would equal one, because if you multiply the two amounts you would get w/w and any number over itself (like 2/2, 3/3, 4/4, etc) equals one. 

Some students continue to struggle to extend patterns using variables and this is okay.  I think it is important to expose students to these questions and have them work through them.  Some students struggle with the idea that a variable could stand for any number.  The more I push students to extend patterns using variables, the more skilled they will become.

  Extending Patterns Using Variables
  Discourse and Questioning: Extending Patterns Using Variables
Loading resource...

Connecting Multiplication and Division

Unit 4: Fraction Operations
Lesson 12 of 19

Objective: SWBAT: • Demonstrate the relationship between multiplication and division involving fractions. • Use visual models to divide whole numbers by unit fractions. • Develop strategies for dividing a whole number by a unit fraction.

Big Idea: How are multiplication and division connected? Why do 11 divided by 2 and 11 times ½ result in the same answer? Students make connections between multiplication and division and work to develop strategies for dividing whole numbers by unit fractions.

  Print Lesson
Math, Number Sense and Operations, division, multiplication, 6th grade, master teacher project, fraction division
  60 minutes
unit 4 11 image
Similar Lessons
Expressing Fractions, Mixed Numbers, and Division Expression
5th Grade Math » Adding and Subtracting Fractions with Unlike Denominators
Big Idea: 0.25 is the same as 25/100. And ½ is the same as 5/10 is the same as .5
Seattle, WA
Environment: Urban
James Ewing
Introduction to Dividing Whole Numbers by Fractions
5th Grade Math » Multiplying and Dividing Fractions
Big Idea: Students learn a rap song to help them divide with fractions.
Tyngsborough, MA
Environment: Suburban
Julie Kelley
Dividing Fractions: Twisting Twizzlers
5th Grade Math » Multiplying & Dividing Fractions
Big Idea: In this lesson you will learn how to divide fractions by using models.
Kenansville, NC
Environment: Rural
Jessica Field
Something went wrong. See details for more info
Nothing to upload