Lesson Overview & Objectives:
This interactive lesson involves teaching young students how to evaluate a mathematical argument and practice writing and revising their own mathematical argument.
Students learn to evaluate arguments for validity and form their own arguments to a math problem while focusing on estimation.
Common Core Mathematical Practices:
 Construct viable arguments and critique the reasoning of others.
 Students distinguish correct logic or reasoning from that which is flawed, and explain the flaw.
 Students make conjectures and use stated assumptions, definitions, and previously established results in constructing arguments.
 Use appropriate tools strategically.
 Students consider the available tools when solving a mathematical problem.
 Make sense of problems and persevere in solving them.
 Students use concrete objects or pictures to help conceptualize and solve a problem.
 Students can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Writing skills to stress while teaching this lesson:

Idea Development (Writing with a clear, central idea or theme in mind; putting researched ideas into one’s own words)

Organization (Beginning the writing with a strong introduction; ending the writing with a satisfying conclusion by linking the conclusion back to the introduction)
Materials List:
Holly's StepbyStep Teacher Instructions:
Before starting this lesson, students
should have had some exposure to the concept of even and odd and measurement.
 Introduce the essential question: What is a good argument and how can I write a good argument in math? Ask students to give ideas on what an argument means (reason why). Make sure to talk about the meaning of an argument being like a fight and how that might tie into the mathematical meaning of argument.
 Frame the story – Don’t Let the Pigeon Drive the Bus by asking students to listen to the pigeon and see if you can hear what reasons that pigeon gives for driving the bus. Read the book. Ask students to discuss with partners if they can remember 2 reasons that the pigeon gives for driving the bus. Put up a piece of chart paper divided vertically in half. Reread the story, stopping after each page to see if there is a reason that is given by the pigeon to drive the bus. Note the reason and put it on the chart.
 After finishing the book, have the students look at each reason and decide if that is a good argument. Note student impressions on the validity of the argument on the right hand side of the chart paper. Have a discussion on what is a good argument.
 Brainstorm ideas on what would have been a good argument that the pigeon could have used to get to drive the bus. Possible idea – There is an emergency one town over and we need to move people away from the disaster, so I need to take the bus there. Click on the chart image at right to see it in larger form.
 ***Listening to someone else’s argument/reason and summarizing**** Show the question: How do you know if a number is odd or even? Explain your thinking. Ask students to discuss an answer to the question in partners. Next ask students to give their idea for an answer and ask another student to summarize what they heard another student say. Try to come up with 3 or more different complete answers using different methods. If a student hasn’t explained their thinking thoroughly, coach the student to add to his/her explanation until it is complete.
 Everyone looks at student work on the answer to the even/odd question worksheet. Evaluate the student work in groups or as a class. Have each group (or the class) decide if it is a good argument. Each piece of work has ways that it can improve. As a class how could we form a good argument to answer the question, how do you know if a number is odd or even? Explain your thinking.
 Frame a discussion on estimation. I would tell the students that I want to estimate how many hand lengths it would take if I were measuring the height of the wall in the classroom. I would talk students through my thinking of measuring my height and make it a reasonable amount more. As a class do a guided group write on what a reasonable estimate for the height of the wall in hands would be making sure to focus on good, solid arguments.
 Hand the students out 3 x 3 Postit® Notesized templates. Ask them to determine a reasonable estimate for how many Postit® Notesized templates wide the classroom wall would be. Have them talk to a partner first to come up with an idea and check for good arguments. (In my lesson sample, I asked students to guess about the width of two whiteboards instead of a whole wall, as seen in the picture below)
 Students write a response to the estimation task on this answer sheet: Give an estimate to how many Postit® Notesized templates it would take to measure the width of our classroom wall. Explain or show how you got your number.
 Teacher looks at the student writing samples and groups students by what strategy they used to answer the question. Conference with the student groups to discuss their writing and how it can be improved. (I made posters naming their strategies and providing guiding questions to make sure that students provided good arguments and explanations. I used the posters in the student conferences, as seen in the photo below.) Ask students to put some ideas down for improvement, then have them write a second draft.
 I mentioned to the students how many different strategies there were to solve this one problem on estimation; our class had five: guess and check, use a pattern, use a similar problem, make a model, and draw a picture. I introduced each strategy from my poster and invited the students who used that strategy to come up to author’s chair and read their work. I asked to students to focus on one question from the poster to answer about the author’s work.
Second Grade Student Samples
Prompt: Give an estimate for how many Postit® Notesized templates it would take to measure the width of one of our classroom's whiteboards . Explain or show how you got your estimate.
Estimation Technique #1: Guess and check 
My guess is 13. I held the bookmark in the air and looked at it. I used my bookmark to count from the front to the back and it took 13 to fill the whole white board.
Sonia 
Estimation Technique #2: Draw a picture 
My model was using four desks. It takes 8 Postit® Notesized templates to go across my desk. It takes 8 desks to go across the whiteboard. I counted 8 Postit® Notesized templates 8 times to get 64. (Click here to see Elizabeth's entire writing process).
Elizabeth 
Estimation Technique #3: Make a model 
Hannah, Elizabeth and I were using a very good strategy. We were using Postit® Notesized templates, desks and a pencil. Our model was using 4 desks and we counted them 2 times. We put the Postit® Notesized templates on our desk and it took 8 Postit® Notesized templates to measure our desk. We counted the Postit® Notesized templates eight times and we ended up with sixtyfour. Our model was using our desks.
Aria 
Estimation Technique #4: Find a pattern 
First I had 8 Postit® Notesized templates covered my desk. I counted the desks and I got 7 desks. Then I counted and I got 16. Then I counted again and I got 24. I counted again and I got 32. I counted again and I got 40. I counted 8 again so I got 56. I used the number grid to get 56 Postit® Notesized templates.
Fox 
It took 8 Postit® Notesized templates to cover my desk. I think it will take 12 desks to fill my class whiteboard. It took 96 Postit® Notesized templates to cover the whiteboard. I used my number grid to count 8 twelve times.
Keith 
It took 8 Postit® Notesized templates to cover my desk. I thought there were 8 desks so I added 8, 8 times = 64. I used the number grid.
A.J.

Estimation Technique #5: Use a similar problem 
I got the answer by using my desk which was 8 Postit® Notesized templates long. I think it would take 9 desks to go across the white board. 32+32+8=72. One of the walls was 72 Postit® Notesized templates long too. I think my idea was the best with my surroundings.
Carson

