##
* *Reflection: Developing a Conceptual Understanding
Collections of Equal Groups - Section 2: Creating Equal Groups

I know that students need time to explore concepts using their hands and their voices. Many times, we as educators, forget that what we deem simple, such as the idea of "equal groups", may not be conceptually developed in our students.

This activity was necessary in order for the children to work together in creating an understanding of what that *equal groups* means, what it looks like to create equal groups, and to build strategies in order to do so.

*Exploring a Concept With Manipulatives*

*Developing a Conceptual Understanding: Exploring a Concept With Manipulatives*

# Collections of Equal Groups

Lesson 8 of 15

## Objective: Students will be able to create equal groups of a collection of items and write the correct expression for their work.

## Big Idea: Students begin to understand and use strategies to find the factors of a given collection of items. They will act out division in order to express the multiplication concept.

*50 minutes*

#### Warm Up

*10 min*

*Girls and boys, we have been talking for the past few days about groups of items and working to solve story problems with an understanding of the group size. Today we are going to work on grouping and dividing in order to recognize a group of items as a whole thing. This is what I mean...*

At this point, I put a small collection of items, like pennies, on my document camera to display on the board. You could do this on the floor in front of the kids as well. I tell them to watch what I do and listen to my "thinking out loud".

*Okay, I want to create groups of these pennies and make sure that each group is equal, or fair. The first thing I think I will do is count them up and see how many I have altogether. I have 15. Now, how can I make equal groups, like I am sharing these with my friends? I guess I could start by pretending I am passing them out to one friend and myself. * Begin sorting...

It is important to do interactive modeling for a few examples to show the students how you would write the expressions to show your work.

*expand content*

#### Creating Equal Groups

*25 min*

I went to the K-5 Math Teaching Resources page for ideas of activities to help students work with the concept of a group of items being one unit. The following activity proved to be just right. You may want to make sure the collections in your bags/cups are not too large, as the students need time to create as many equal groups as possible. You won't want them burdened with too many in the collection to deal with.

I post Counting Collections (K-5 Math Teaching Resources) on the document camera enlarged, to project it on the board. You could also make a copy of these directions for each partnership to have at their work space.

I had my children choose a cup of items. When they felt they had exhausted the groupings for that cup, they simply returned it to the table and chose another so that everyone had work to do the entire time.

As the students work, prompt them to find some strategies in their efforts with guiding questions such as:

- How many items are in your collection in total?
- Do you know a multiplication fact with that number as a product?
- What do you know about the number 2 and the number 24, which is your total?
- What are you planning to try to create equal groups? Why?
- Why can you make only 2 equal groups for this one? (Prime numbers)

This video shows students working to "name" their equal groups with an equation.

The following video is of a partnership dealing with a prime number.

#### Resources

*expand content*

#### Discourse

*10 min*

In this part of the lesson, instead of having the students share out to the whole class, I choose to give them an opportunity to explain their thinking to a smaller group, as well as critique the work of others (MP3).

I ask the student partnerships to group with another partnership that had the same number of items in their collection cups. Each partnership shares the equal groups they were able to make and compares with the other partnership if anyone had a different strategy or number of groups.

As students work, I once again tour the room, listening so that I can make adjustments (if needed) to my lesson.

*expand content*

#### Homework

*5 min*

In order to provide more practice with this concept, I send a copy of the activity home with each student with a note for them to grab a handful of objects from home like coins, legos, macaroni noodles, etc. and work on this concept with someone at home.

*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: It's As Basic As That
- LESSON 2: Naming Arrays
- LESSON 3: Variables
- LESSON 4: X Represents Groups Of
- LESSON 5: Each Orange Had 8 Slices
- LESSON 6: Creating a Word Problem Book
- LESSON 7: Equal Groups on a Number Line
- LESSON 8: Collections of Equal Groups
- LESSON 9: Explaining Multiplication
- LESSON 10: The Story Of Multiplication Day 1
- LESSON 11: The Story of Multiplication Day 2
- LESSON 12: Making Equal Groups Part 1
- LESSON 13: Making Equal Groups Part 2
- LESSON 14: Associative Property
- LESSON 15: Associative Property With Manipulatives