##
* *Reflection: Conferencing
÷ Represents "Put Into Groups of" - Section 3: Active Engagement

As I visited with the partnerships, I realized that some of them are still a bit confused about how the equations themselves work. They are able to solve the problems, but were at a standstill when creating their fact triangles, or even writing them correctly at times.

This student was working on figuring out how to make the triangle work as a representation. She knows the "fact family", so I worked on helping her **show **her idea. Notice when I say the dividend is usually at the top, though it really doesn't have to be, she says "Oh! That makes so much more sense." This is when I knew that this model really isn't something she really understands, though she knows they are used to represent the fact family. I am still not convinced she understands "why" the numbers are in a family.

I prompted her to use arrows and really I should have talked less. As I watched this, I realized I was doing the thinking and having her write down my thoughts…not hers. This is a BIG NO NO! I was reminded today to stop talking and listen!

*Not What I Expected*

*Conferencing: Not What I Expected*

# ÷ Represents "Put Into Groups of"

Lesson 10 of 13

## Objective: Students will be able to use grouping to solve and write division problems.

## Big Idea: Division is a critical concept for students to understand. In this lesson, they will explore grouping division and write story problems to explain a division problem.

*55 minutes*

#### Warm Up

*10 min*

My students have done several activities involving division and are moving more deeply into their understanding of the division standards. Now that they have a basic understanding of how to solve division sharing and grouping stories, I decide to teach the "language" of division today by discussing the terms DIVISOR, DIVIDEND, and QUOTIENT.

To do this, I have the words, with an example, written on cards hanging on the board. I ask the students to bring their math reflection journals to the community area, then silently read the vocabulary cards to prepare to describe the words. You will notice in the picture that the digit explained is in red in each equation.

After students review the cards on their own, I ask them to try to turn and talk, explaining each word to their partner. Then we discuss and write the definitions as a class.

It is important here to remember that because this vocabulary is important, I'm focusing on making sure everyone has this as a common language for use when describing their learning. Also, it is developing precision in using mathematical language, a skill that will be needed as they move to the middle grades.

#### Resources

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#### Mini Lesson

*10 min*

To introduce today's activity, I ask a student volunteer to come up and roll two dice under the document camera. I tell the class that these two numbers will be used to create a division problem. We roll a 3 and a 5.

Students are asked to turn and tell their partner what is needed to make a division equation using these two numbers. I am so pleased they all know they need to find the product of the numbers first, in order to build the division problem.

After we write 3 x 5 = 15, we discuss that the "dividend" was 15. I continue the discussion until students note that we also have a choice to make. The divisor could either be 3 or 5, meaning we can build the equation as 15 ÷ 3 = 5, or 15 ÷ 5 = 3. Don't skip this step, as student success in division rests, in part, in understanding the commutative property of multiplication (they do not need to know its name, however).

Next, we choose our equation. I get their attention to make sure they know that I want us to only focus on grouping problems today, so every time we see the **"÷" we say "put into groups of"**.

I then model the steps in creating a poster representing the equation using a story problem, a drawing, number representations, and one other way of their choice.

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#### Active Engagement

*25 min*

I supply the students with 12 x 18 white paper and two dice. They were asked to begin their work by rolling the dice to create their equations and to be sure to show their understanding with word problems and drawings.

You may choose to have them illustrate or write more than one story. I like to have them create one of each and then have a choice. The posters do not need to be "decorative", though some of the students will want to add their decorative elements.

During the work time, visit with the partnerships, asking them to explain what they are doing and why. This conversation is the most important part of the active engagement, as it pushes students to identify their understanding and communicate it to you in a way a paper product can not.

This student shares a story she wrote for 12 ÷ 2 = 6, which is a skill we have worked hard on. I am pleased she was able to quickly write one that is correct.

#### Resources

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#### Sharing

*10 min*

Students do a poster tour to view each other's work, and then add or revise their own work. I find this an easy, yet powerful way to share work without it getting too boring, which can happen when we are presenting at the board. Students get to move their bodies, yet keep their minds engaged in the lesson.

I'd urge you to plan the tour so that there is time for revision. This is a practice that cements the transfer of learning from short term, to long term, memory.

If you choose to do a poster tour, be sure to remind your students to look at the math, not the "art" or even the spelling!

*expand content*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities

- LESSON 1: Using Journaling to Create Lessons
- LESSON 2: What is Division
- LESSON 3: Grandma's Cookie Production Company
- LESSON 4: Is It Multiplication or Division?
- LESSON 5: Grouping or Sharing?
- LESSON 6: Division by Sharing Vs. Grouping (Day 2)
- LESSON 7: Sharing vs. Grouping Engagement Lesson 1
- LESSON 8: Sharing vs. Grouping Engagement Lesson 2
- LESSON 9: Sharing Maybe?
- LESSON 10: ÷ Represents "Put Into Groups of"
- LESSON 11: Explaining Thinking in a Journal
- LESSON 12: Using Multiplication to Solve Division Stories
- LESSON 13: The Multiplication - Division Relationship