Students will be able to engage in math talk with a partner in order to explain their thinking and to critique another's thinking.

Students always want to share! This lesson allows us to create a routine where everyone is safe in sharing their thinking and comfortable responding to another's presentation of understanding.

10 minutes

To begin today’s lesson, I am going to review the talking moves from yesterday’s activity. They were:

“I agree because….”

“I would like to add…”

“I disagree because…”

In order to model how to use these starters with substance, I will ask for volunteers to put up their journal responses from yesterday. I will then model strong and weak responses.

*Mathematicians, today I would like to review how to use our talking moves on the board. Is there anyone that wouldn’t mind putting their journal responses up on the board so that I can show you really strong comments and weaker ones. *

*Thank you for the volunteering. Okay, let me read over your response. Boys and girls, listen to my two different comments and think of how they are different. ** *

Here is where you will need to make a judgment and use whatever sort of response the student has written. Something like:

*I agree with your idea because when I drew my ants, I had the same shape.”*

* OR*

*“I agree with your idea because I like the way you drew the ants going to the food.”*

*Students, which one did you like more and why? *

Do this type of exercise with one or two more journal entries.

*Okay, that was a great conversation. Today when we comment, we will all try to use our strong statements that will help us all make more meaning.*

Making meaning is our class motto, so I try to use the phrase often throughout the day.

25 minutes

Today’s lesson will help the students begin to work as partners and it will also introduce the concept of arrays and our vocabulary wall.

*Now, let’s review the book One Hundred Hungry Ants. Can someone summarize what the ants did to try and solve their problem? Did it work? What happened at the end to the littlest ant? What math problem represents the end of the book? I agree with you because 100 -1 = 99. When the littlest ant started running away from the other 99 ants, he was “leaving” the group of 100 total ants! Smart thinking!*

*Let’s see if we can draw out the other math that happened today - where the ants kept regrouping themselves differently to try and get to the food faster. Remember, the littlest ant was trying to move them as a whole group more quickly. Let’s write down from each page the different ways they grouped themselves. Right, they went in a single file line of 100, then they changed to 2 lines of 50, then…..*

The teacher should write these groupings on the board or on a piece of chart paper. When all are listed, begin discussing a way to draw the lines of ants. Suggest using an “x” to represent an ant. Do one or two of the combinations. Then begin the discussion of rows.

*Hmm, does anyone notice anything in common with the numbers we lifted from the book and the way these drawings are turning out? Yes! You saw what I saw, the number of lines are like rows and the number in each line is equal to each other. In mathematics, we call these ARRAYS. We can use arrays to help us organize a group into equal rows. Let's give it a try.*

At this point, you should put the students in pairs and ask them to begin working on ways they could put ants into arrays. Watch for them to create equal rows and see if anyone might notice the difference between a 2 by 10 and a 10 by 2.

Remember, this lesson is more about working in partnerships than understanding the arrays. That content will come around in a larger way later in the month. Right now, pay attention to how students communicate with each other, the way they attack a solution, and how they share the work. You might want to suggest certain organization strategies to some, point out patterns you see in their work. Just let them have fun with it and gain all the information you can about them as partners and math thinkers.

15 minutes

After the students have had time to work and draw a few arrays, ask them to gather and begin sharing with the whole group some of their thinking. This is when you will remind them of the talking moves that were reviewed at the beginning of the lesson. When you do this section of the lesson, help guide students to keep the math in mind, not just the “art” or misspellings they see! This is the beginning of setting a risk-free culture in the classroom and a perfect time to gauge the level of thinking the students have in regards to processing another's work.

*Mathematicians, everyone thought really deeply today and I heard and saw wonderful work. I would like for us to share all of this with each other, so will you please gather in our community area? *

*Students, as we share, remember our talking moves should be based on the math thinking and start with one of our statement beginnings. We know we are all wonderful artists and we do our very best with spelling and sentence writing. This part of our day is to help each other focus on our math thinking and celebrate our understandings with one another. *

While the students share, you may want to engage in reminders of keeping the talk about math and off of tangents.