Reflection: Real World Applications Division by Sharing Vs. Grouping (Day 2)  Section 1: MiniLesson
The students have worked on a lesson where they pretended to be Grandma's Famous Cookie Production Company. While they worked on that lesson very well, I realized they needed more specific work discriminating between the two types of division. Critical Area #1 in 3rd grade is "Developing understanding of multiplication and division and strategies for multiplication and division within 100." In the description of this understanding, the following points are made:

Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equalsized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations.

For equalsized group situations, division can require finding the unknown number of groups or the unknown group size.
Therefore, I decided to spend another day or two having them "act out" situations and recording the outcomes.
If you try this lesson, I suggest you do it for at least two days so the concepts become habit for the students before they begin reading word problems.
Division by Sharing Vs. Grouping (Day 2)
Lesson 6 of 13
Objective: Students will be able to share objects equally to find quotients, or use known quotients to find missing factors.
Big Idea: Children need to understand that there are two different contexts for division. This 3 day lesson path will engage them in activities that act out the different types.
MiniLesson
When the students arrive at the community area, I ask them to form a circle. I then ask a student to be my partner to help me act out some stories about cookie orders for our Production Company (yesterday's lesson). This modeling strategy is called Fishbowl and works well when you are using manipulatives.
I have cubes and cups to represent our cookies and packages. I have a chart on the board already with 3 columns: Total, Cookies Per Package, Number of Packages. I ordered the columns in this way to model a division equation, but I am not using the symbol yet.
If you use this mini lesson, tell different stories to the students and ask them to help you fill in the chart with your known information and then act out what needs to be done to find the missing factor or the missing quotient. Possible stories may be:
We have 27 cookies baked. We can put 3 cookies into each package. How many packages can we fill?
We have 27 cookies baked. We have 7 packages to fill. How many cookies can we put in each?
Active Engagement
When you are ready to send the students off to work on their own, you may want to consider having them work with partners. The conversations and teamwork is always helpful in concept development. It also helps me assess understanding when I can eavesdrop!
When I have the students move into the active phase of the lesson, I hand them baggies with cubes and cups. I also fill in different parts of our chart on the board and ask them to copy it into their math journals. These will be the situations they work to solve. I usually have all work done in the journals, instead of a worksheet, as it acts as a glossary for the students as we go through the year.
As the students work, I typically stand by and listen in. Many times I ask them to explain what they are doing, why they are doing it, or prompt them to dig deeper. This is a perfect time to do some oneonone or small group work as well.
These boys did not have a strategy when they began. I prompt them to consider the chart more and talk with me about what "per" means. Then the lightbulb lit!
This group is also working on a grouping task and were not in agreement of the outcome.
In this clip, the student explains that they "passed out" the cubes in to the nine packages.
Share
To close each of these two sessions, I have students come up and share how they solve the problems on our chart. As each partnership completes explaining, I ask if anyone did it differently. This is a great time to stretch your students' thinking. You never know what the responses will be here, but the debates and different ways of thinking are always valuable. Don't skip this part.
Hi Michelle,
I am reading your lessons to help some of the 3rd grade teachers I coach unpack the standards. Understanding the scope of the division standard is tripping me up and I wanted to ask a fellow MT.
Do 3rd graders need to understand remainders in division?
How do you handle quotients with remainders?
Thanks so much for your help.
Julie Kelley (5th grade math MT)
 2 years ago  ReplyPatricia, I am very pleased that this lesson was helpful for you. My students enjoyed it as well:) I think that student explanation, either verbally or written, is crucial to their growth as real learners in a community. If I can ever help with strategies to build "talk", let me know. Enjoy your summer.
 2 years ago  ReplyI really liked the strategies you used to show students different ways to divide. They are simple and easy for students to do, at the same time they are understanding the concept of division. Your lesson plans are clear and show exactly what to do, thanks. I like how your students can explain their thinking process using the lesson content vocabulary. I can replicate the lesson with my students, thanks.
 2 years ago  ReplySimilar Lessons
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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