##
* *Reflection: Developing a Conceptual Understanding
Making Equal Groups Part 1 - Section 1: Mini Lesson

The idea of equal groups is so critical to the deep understanding of multiplication and division, that I have decided to spend more time than I have in the past on making sure the students are secure in using them and identifying them.

This lesson is a simple one. Simple to design, execute, and prepare for. However, the time for students to manipulate, construct, make meaning, and communicate not only helps create our math community, it sets the stage for deep thinking.

Give yourself permission to spend time on what may seem simple and watch the depth of understanding in your students increase.

*Simple Lesson, Big Idea*

*Developing a Conceptual Understanding: Simple Lesson, Big Idea*

# Making Equal Groups Part 1

Lesson 12 of 15

## Objective: Students will be able to create equal groups given guidelines.

## Big Idea: Third grade students will be using equal groups the entire school year. It is imperative that they understand how to create and manipulate them. This lesson will help them explore various ways of working with equal groups.

*45 minutes*

#### Mini Lesson

*10 min*

As the students gather at our community center, I ask them to think about things that come in equal groups. After a short time, they turn and share with their partner in a turn-and-talk. As I listen, I pick out a few good examples as well as some that don't make sense, and write them on the board.

I give the students my thumb's up, indicating they should complete their conversations, turn towards me and listen. I direct their attention to the list I create from what I've heard:

pop tarts

packs of gum

yugioh cards

candy

We discuss if each of these items really do come in equal groups, and what that term means. I guide the students to the idea of candy. Do we really know each bag or box has the same amount? No. They are most likely close, but not always equal.

I then ask if we can create equal groups of 2, if we use everyone in our math class (we have 18). I suggest they try. Then I ask them to see if they can stand in equal groups of 3? Of 5? Of 4?

*expand content*

#### Active Engagement

*25 min*

I give the students directions for an activity. The materials are simple - several cups filled with small objects (pennies, colored chips, cubes, etc.) with a plastic spoon.

**Student Instructions:**

Get two scoops of objects and count the total.

Roll a die to determine the group size and organize their objects accordingly.

Count how many equal groups they could make and write any left overs.

As the students work, I visit with each partnership and discuss what they are doing and why. This is my time to see if they notice any patterns, prompt/model vocabulary to help build their math vocabulary, and help with any misconceptions. The following clips are examples of how I "intervene", and show students at different levels of understanding.

These girls work through the activity properly, so I talk with them about "why" they are using the number 6. I want my students to become very skilled at recognizing what number names the group size.

The boys in this clip are excited to see that they can "do it", meaning there are no remainders in their first model. I will make sure to visit them again and see if they have remainders in their chart. I want them to be able to explain why there might be remainders.

This student is still working to understand what an equal group is. He is simply moving the objects apart and not organizing at all. This is a time that I would do a one-on-one mini lesson reviewing how to create an equal group and help him learn exactly what it is.

*expand content*

#### Wrap up and Sharing

*10 min*

As a wrap up, I put two spoonfuls of cubes under the projector and have partnerships come up to roll the die and then do the grouping. I do this 9 times, as I have 18 students.

During the work, I ask the audience to "predict" how many groups the presenter might have and if there will be any left overs. They share this information with their partner in the community area. This type of review is always motivating, as the audience is engaged in trying to figure out the solution before the presenters. Now the entire class is working, not just the two at the board.

*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