BTC in my 7th grade math classroom

Thornton – math teacher

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Julie Thornton
7th grade math teacher
Denver, CO
jthornt5@gmail.com

  • Hello World!

    Hello!  My name is Julie Thornton, and I started this blog to document how I am using Building Thinking Classrooms (BTC) in my 7th grade math classroom.  Over the past few years, I’ve been experimenting with some of the ideas from Peter Liljedahl’s Building Thinking Classrooms into my classroom.  This past summer, I attended a Building Thinking Classrooms (BTC) Institute in Sacramento, which I loved and highly recommend, and decided that it was time to try this model for a full year in my classroom and see how my students fared.  This blog documents my first official year of implementing BTC’s concepts into my math classroom, which consists of 7th grade students.

    Please note that what I was doing while students are working and my comments about the lesson are listed in bold italics for clarity purposes.  The parentheses indicate student responses.

    Day 1: First day of school and first day of introducing BTC.

    Materials needed – deck of cards; whiteboard markers that are all the same color; one different color for me; one white board erasers per group.

    Part I. Introduction to the problem.

    So, in this class, we are going to do things differently.  I am going to present you with a question or a situation, and then you will work in a random group with a few of your classmates to answer my questions.  Then we will come back together and debrief our learning.  

    Today we are going to start with a shape.  What shape has four lines that are the same length?  (Get answers.)  Okay, now let me tell you more.  These four lines are used to create 90 degree angles.  There are four 90 degree angles in this shape.  What is my shape?  Raise your hands, please. (Students say it’s a square)

    Okay, I will draw this shape on the board.  How many squares do we have here?  (I got a variety of answers including 17. Not sure how that came about.) How do you know?  

    Okay, so now I want to make a bigger square composed of more squares. Now I will make a grid with four squares on it.  

    You are going to start with this grid today in your small groups and determine how many squares you have with your group.  Don’t yell out the answer!

    Before we start with the group work, we need to divide into groups.  Each of you will draw a card and then go to the white board that has the number of your card on it.  Once you get in your group, you will take turns doing the following 

    • one person will ask another what their name is and write it at the bottom of the white board, then you rotate the marker and repeat until everyone has their name on the board.  Does that make sense?  

    Other important things:

    • Rotate the marker as you work – there is one marker per group 
    • The goal is to work together while sharing your ideas NOT to have one person dominate the discussion
    • What can you do if you are someone who likes to talk a lot?  How can you engage the quieter group member?

    A couple of other things – at the top of your whiteboard, you will write down the problem you are working on. In this case, you will write 2 x 2 because that is the grid you are starting with. – like this – at the top of the banner, you will write down the problem you are working on – in this case, your banner will look like this:  2×2

    Don’t forget to draw a picture of the square you are working on.  

    So, who can tell us what we are doing when we get into groups?  (Student responses.)

    Okay, and there’s one last thing – you will answer a this or that question – here is your question for today – mountains or beach?  

    Part II. Work time (about 20 minutes)

    Let’s get going.  

    While students were working on this problem, I was actively monitoring the room, making sure everyone has their names written on the board along with their answer to the this or that question, seeing who needed help getting started, who needed a hint, and who was ready for the next problem. I also monitored the rotating of the marker and who was actually talking to each other.

    Answers:

    • 2 x 2 has one 2 x 2 square and four 1 x 1 squares for a total of 5 squares
    •  3 x 3 has one 3 x 3 square, four 2 x 2 squares and nine 1 x 1 squares for a total of 14 squares
    • 4 x 4 has one 4 x 4 square, four 3 x 3 squares, nine 2 x 2 squares, and 16 1 x 1 squares for a total of 30 squares
    • 5 x 5 has one 5 x 5 square, four 4 x 4 squares, nine 3 x 3 squares, 16 2 x 2 squares, and 25 1 x 1 squares for a total of 55 squares

    Hint question: do the squares all have to be the same size? 

    Part III. Consolidation (about 20 minutes)

    Get everyone back to one white board for debrief.

    Turn-n-talk (explain how to do this) with your neighbor about these questions:

    • What made this task easy or difficult?  
    • How did you complete this challenge?
    • Discuss how many squares there were in each grid

    Listened to student ideas and gave them more question:

    • Is there a pattern to how many squares there are in each grid?  
    • What else did you notice about this class or the work we are doing in this class?
    • What questions do you have?

    Part IV. Work time (remaining time in class)

    I explained homework, a handout to get to know students better. I also included the following two challenge problems for students.

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    Reflection: Students worked better in groups that I though they would. Once they got going, they got into the problems. I would do this again day 1.