##
* *Reflection: Perseverance
Equal Groups - Section 3: Try It Yourself

Shortly after sending the students out to work on this task, I had four students come to me and ask how many groups should they have. I responded with a question, *How many counters do you have? *They told me had 36 counters and one group had 40 counters. I said, *I don't know how many groups, that is what I need you to find out. Remember, every group has to be equal.*

Another student came to me and asked me for two more counters because he had 48 counters and he wanted to put them into five groups of ten. I explained there were no extras, and I asked him how would he write a multiplication sentence if he didn't have equal groups? He stared at me and was thinking, and then he said, "Nevermind, I guess I have to keep trying."

This perseverance, expected in the Common Core Math Practices, is exactly what I was hoping to see from the students. However, while the students persevered through the first grouping structure, only a few students continued to regroup their counters into second and third models of equal groups. I knew that I would need to teach additional lessons on equal groups.

*Perseverance*

*Perseverance: Perseverance*

# Equal Groups

Lesson 5 of 6

## Objective: SWBAT show equal groups to explain multiplication.

#### Warm Up

*5 min*

During the warm up of this lesson, I create groups, each with dots inside, to model multiplication. This is a review of the process that was used for the lesson Multiplication Models and Structure, where I taught students to draw sets of equal groups to model multiplication.

During the previous lesson, I demonstrated using circles with dots on the inside to show equal groups, and I modeled the format to write number sentences in the format of *groups x objects in a group = whole amount*. Students also wrote the repeated addition sentence for the number of objects inside of each group.

For example, if there are three groups, each with four dots inside, the number sentences are written as:

3 x 4 = 12 and 4 + 4 + 4 = 12

Today I am not using repeated addition because the focus is on multiplication.

First, I draw a few examples for products less than 36 including 3 x 6, 7 x 5, and 4 x 8. I remind students about the importance of using dice patterns (as this allows students to subitize). Additional exposure to subitizing not only assists students in being more accurate in their computations, it develops pattern recognition. For students still struggling with developing their number sense, subitizing helps to develop strategies such as compensation and counting on, because it gives students structure for composing and decomposing numbers. In my class, using dot patterns is is an expectation aligned with MP6 - attend to precision. When children draw the dots randomly, I remind them that this is not a mathematical representation. I also know it interferes with the development of the equal groups concept.

Then, I have students draw equal groups on their individual whiteboards and write the matching multiplication sentence on their board. I provided number sentences for the students to draw including:

2 x 3, 5 x 6, and 2 x 9.

*expand content*

#### Guided

*5 min*

After students put away their whiteboards, I call them back to the carpet and describe the scenario of having a container of pencils that need to be passed out and shared by the students. Since there are six teams in our class, we need to figure out how many pencils each team receives. We don't have much time, and we need to distribute them quickly.

I show students a group of pencils. I ask them to help me come up with a quick plan to solve sharing them out fairly. I have the students share their thinking with a partner sitting next to them. At this point in the lesson, I chose not to have a share out and demonstration of their plans and solutions because I want them to try different ideas in the next section of the lesson. In circulating, I record their plans on a sheet of paper and these plans will be tried in the wrap up of the lesson.

*expand content*

#### Try It Yourself

*15 min*

Students get to chose their partner to work with in this section of the lesson. I give each set of partners an even number of linking cubes to put into equal groups.

Prior to the lesson, I separated groups of cubes into even quantities. Students were given either 36 or 48 counters each. These numbers are specifically chosen because many different models of equal groups can be derived using the same number of counters.

I provide white copy paper for the students to draw their equal groups. As students display one equal grouping, I instruct them to continue on to find other ways to group the counters equally.

*expand content*

#### Wrap Up

*10 min*

Using some of the suggestions from the students earlier in the lesson, I demonstrate some of their strategies. One is to draw two groups and check to see if the number of counters was even. Another suggestion is to pick 25 groups because that is the number of students we had in the classroom. We discuss how easy or difficult it would it be to draw 25 groups and agree that choosing two groups is easier than 25, but they couldn't come up with another option.

Next, I ask the students to draw two equal groups on their whiteboards. Two students ask for help with their number of cubes, and I model four equal groups for them. The number of cubes this show how they had sort the groups into two groups of eighteen.

When I ask for their thinking, this group says they just guessed and tried four groups and explained it worked. The boy that had asked for two more counters explains he used skip counting to help him set up equal groups. Many students still want to put their counters into benchmark groups of five and ten, but cannot come up with a strategy to create equal groups unless it was groups of two.

*expand content*

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