DEFEND your ideas with a Journal

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Students will be able to express their thinking using concrete examples, such as writing, which includes drawing.

Big Idea

Students need practice in representing their mathematical thinking in order to share it with others and assess their own understanding. This lesson engages them to work out a problem from a story read to them in more than one way.

One Hundred Hungry Ants-Lesson Introduction

15 minutes

I find literature a wonderful way to engage students in a new math concept.  Today I will read the book "One Hundred Hungry Ants" by Elinor J. Pinczes.  It is a fun and charming book about ants trying several formations in order to race to a picnic before the food is gone. It can be used to illustrate arrays and an addition/subtraction problem.  My goal is to create an opportunity for the students to begin "seeing" math in all areas and to  use their journals to draw representations of their thinking.  

Mathematicians, will you please join me at the community area for a story?  I am so pleased to see you pushing in your chairs and walking safely to the area.  

I am going to start today's lesson with a really fun story called "One Hundred Hungry Ants" by Elinor J. Pinczes.  All of these ants are trying to solve a problem on their way to some picnic food.  While you listen, see if you can decide if the ant's solutions were helpful or not.

Read the story and allow plenty of time for the students to view the illustrations.  They may notice the configurations (arrays) changing and the number sentences change.  In order for the students to easily interact with the illustrations and see the math forming, I put my book up on the document camera.  You may want to consider ways you can display the illustrations for the students to pay attention to while you read.

Mathematicians, please turn and talk to your partner about what math you noticed in this book. Don't forget to face each other, listen carefully, and give me the thumbs up signal when you are finished.  Okay, turn and talk.

Listen in for comments about the time the ants wasted, the formations they created that equaled 100, and the subtraction problem at the end.  Highlight these comments.

Wow, I heard some smart thinking!  Someone said that if the ants hadn't stopped at all to reorganize, they would have made it to the food before the other animals got there.  One person said that all of the ways were unfair because some of the ants would always be at the back.  I heard another person say this reminds them of division!  What deep thinking.  

Though I did not use this video in my lesson, it may work for your class.  I love that it is set to a tune and that the vocalist puts the words "Now let's divide" into the song.



Defend with a Journal

20 minutes

In this section, I want to guide the students to take a stand, or create an idea of how math can help solve a real problem.  This type of work is crucial for the math practice of  constructing viable arguments and critiquing the reasoning of others.  In the story, 100 ants need to get to the food before it is gone.  I will ask the students to think about how they would organize the ants to accomplish this and to draw a picture or sketch to prove that it is a good idea.  

Boys and girls, I would like for you to think about what you shared with your partner and what you learned from listening  In a moment I am going to ask you to return to your seat and work in your reflection journal about this topic on the board:

What is the best way for the 100 ants to get to the food?

You will need to draw a picture showing your idea and you will also need to write sentences or label.  When we share these later, it will be helpful to the reader to have an illustration of your thinking.  Be creative in how you do this.  I am not going to do mine today, because I want to see what you are thinking!  Are there any questions?  Okay, then, off you go!

At this point, confer with the students at the tables.  Ask questions like, "What is your thinking behind having the ants go in rows of 2's?"  "I see you wrote a few sentences.  What is your plan for your drawing?'


After about 10 minutes, have the students return to the community gathering area with their journals.  I share my journals using the document camera.  

Talking Moves and Sharing

15 minutes

At this point in the school year, I begin working with the students on what we call Talking Moves.  I have taught these strategies for several years, because I believe it is important for students to develop the language of expressing their thinking through concrete and verbal expressions.  However, this is the first time I have paid attention to the aspect of this strategy as a mathematical practice. 

Giving these sentence starters helps organize thought, keeps a conversation positive and risk free, and maintains the topic of discussion.  Today I will introduce:

  • I agree with you because...
  • I would like to add...
  • I disagree because...


I don't do a great deal of modeling (yet), other than showing the students these starters on the wall.  Later, in other lessons, we will fishbowl and practice using them.  Today is just about putting it out there for them to try.  

I am so excited about what I saw you working on in your journals and I bet you are excited to share!  Boys and girls, when we share in our classroom, we must remember how hard everyone is working.  We will give a speaker just as much respect as we do when we turn and talk.  I would like you to look at the sentence starters I put up on the board today.  They are ways we can respectfully respond when someone is done sharing their thinking.   This way, our comments can help everyone learn and feel good about sharing.  Please read them to yourself. If you want to try using one of them today, that would be fantastic.

Call students to share at the front of the room.  Allow them at the end to ask for 2-3 questions or comments.  Be watching for reasoning behind the drawing and call attention to labels and or sentences that are the in depth.  Also, encourage students in the audience to try the sentence starters.  Share as many as time permits. 


5 minutes

Mathematicians, this has been a fabulous math session!  I am so excited that you were able to listen to our story and begin using math to solve a problem.  You also remembered very well how to share your ideas in a turn and talk move and you drew wonderful representations in your journals to share.  Well done!  

What did you like about today's lesson?  Is there anything that stumped you?

Tomorrow we are going to talk about the math vocabulary for what those ants were doing when they got into groups.  I am going to talk to you about what we call "arrays".  We are also going to work with partners in our journals again.  Smart work today!