cheesemonkey wonders

cheesemonkey wonders

Monday, August 13, 2012

Life on the Number Line - board game for real numbers #made4math

UPDATE: Here is a working link to the zip file: https://drive.google.com/open?id=0B8XS5HkHe5eNNy10MWZVSDNKNnc

Last year I blogged about my work on a Number Sense Boot Camp, so I won't rehash all of that here. This year I want to give the follow-up on how I used it last year, what I learned, and how I'm going to use it this year in Algebra 1.

This was my breakthrough unit last year with my students. It anchored our entire Chapter 2 - Real Numbers unit and really solidified both conceptual understanding and procedural fluency in working with real numbers, the real number line, operations on real numbers, and both talking and writing about working with real numbers. We named it Life on the Number Line.

Here's how the actual gameboards, cards, and blank worksheets looks in action (sans students):


I sure hope I didn't make a bonehead mistake in my example problem!

The most effective thing about this activity was that it compressed a great deal of different dimensions of learning into the same activity, requiring learners to work simultaneously with the same material in multiple dimensions. So for example, they had to think about positive and negative numbers directionally in addition to using them computationally. They had to translate from words into math and then calculate (and sometimes reason) their way to a conclusion. They had to represent ideas in visual, verbal, and oral ways. And they had to check their own work to confirm whether or not they could move on, as no external answer key was provided.

Since they played Life on the Number Line for multiple days in groups of three or four players comprising a team who were "competing" in our class standings, learners felt that the game gave them an enormous amount of practice in a very short amount of time. Students also said afterwards that they had liked this activity because it helped them feel very confident about working with the number line and with negative numbers in different contexts.

I also introduced the idea of working toward extra credit as a form of "self-investment" with this game. For each team that completed and checked some large number of problems, I allowed them to earn five extra-credit points that they could "bank" toward the upcoming chapter test. Everyone had to work every problem, and I collected worksheets each day to confirm the work done and the class standings.

What I loved about this idea was that students won either way — either they had the security blanket of knowing they could screw up a test question without it signifying the end of the world, or they got so much practice during class activities that they didn't end up actually needing the five extra credit points!

Students reported that they felt this system gave them an added incentive to find their own intrinsic motivation in playing the game at each new level because it gave them feelings of autonomy, mastery, and purpose in their practice work.

The game boards were beautifully laminated by our fabulous office aide but do not have to be mounted or laminated. The generic/blank worksheets gave students (and me) a clear way of tracking and analyzing their work. And the game cards progressed each day to present a new set of tasks and challenges.

All of these materials are now also posted on the Math Teacher Wiki.

Let me know how these work for you!

UPDATE 10/27/2016: Here is a working link to a zip file of all the components for this: https://drive.google.com/open?id=0B8XS5HkHe5eNNy10MWZVSDNKNnc

11 comments:

  1. Am I missing something? I don't see what the rules of the game are. Maybe I have it. They roll one number die and two +- dice. They record the +- rolls first and then the number, so that they get (as in the worksheet shown) something like 0 (old position) + -5. Then they take a card (in this case an 'odd # task'), figure it out, and do what?

    This sounds great. I'd like to ask kids at my son's school if they'd like to play test it.
    Reply
  2. I just just discovered the msmathwiki and in turn your blog. I love everything you have written. I have been teaching for 14 years, but this is the first time I've taught Algebra. I love playing games and am so excited I don't have to create them all from scratch. I will excitedly be checking your blog daily to see what other awesome activities you post. Thank you!!!! 
    Reply

    Replies




    1. Thank you! I'm glad these are helpful to you.
  3. Thanks for the feedback! In answer to Sue's question, the rules are, everyone works every problem. Each player starts at the origin, rolls the three dice, and moves where they indicate. Choose an even, odd, or zero problem card. Everybody works the problem and checks answers, then the next player rolls.

    It's only a game structure. I keep "score" by confirming how many problems each team has completed and checked each day.

    Hope this helps.
    Reply
  4. I'll tell you how this goes when you send me a beautifully LAMINATED class set of these made by the lovely office ladies, okay?! C'mon now, sharing is caring. I wanna do this, but it's too much work to make. #cryingwahwah #stopthewhining
    Reply
  5. Hi, I loved your idea. I am trying it over the summer. I have a question about some of the answers to the cards. On the 2-1 green and yellow cards, you have a few fill in the blank cards. What was your answer for them? For instance, one of the cards says "To avoid getting confused, we read the expression -w as _" The one that has been stumping me is, "The absolute value of ANY number is always _, which means that it is always also_"
    I know it is positive but what is the other blank?

    Thanks!
    Reply

    Replies




    1. Sorry about that! I forgot that you weren't there in class when I was drumming these ideas into our collective consciousness.

      With regard to the first card, when we start out in Algebra 1, I always have students read "–w" as "the opposite of w" or as "opposite w" rather than as "negative w." This helps ground them in what a signed VARIABLE means, as opposed to a signed NUMBER. If the value of w happens to be (–2), then –w is opposite-w which is –(–2) which is going to be a positive. Because they ground themselves in thinking about the opposite sign of the VARIABLE (rather than as a negative number), they get less confused as they evaluate expressions using different values for "w."

      With regard to the second card you mentioned, I also have students actively use the definitions of positive and negative — i.e., a positive number is defined as being greater than zero while a negative number is defined as being less than zero. So in the case of that card, I would hope they would say that "The absolute value of ANY number is always positive, which means that it is always greater than zero."

      Since definitions are our bedrock for the axiomatic aspects of algebra, this practice grounds them in thinking about whether a number lives to the left of zero (in the world of negative values) or to the right of zero (in positive territory).

      Hope this is helpful. Let me know if there are any blanks I can fill in!

      - Elizabeth
    2. Thanks! This helps a lot! I came up with numerous possible answers but I couldn't sleep without knowing your right answer! lol

      Thanks again!
  6. In the example you showed, did they just chose whether to go to positive or negative 5?
    Reply

    Replies




    1. Chelsea — They rolled three dice: two + / – dice and one six-sided number die. If they roll + — 5, they move 5 in the NEGATIVE direction (i.e., to the LEFT of zero). If they were to roll a + + 5, then they would move 5 spaces in the positive direction.

      Hope this helps!

      Elizabeth (@cheesemonkeysf)
  7. Greetings everyone,
    Enjoy the shared learning and knowledge.
    I am interested in using this to model rational addition and subtraction - i.e. -2.45 + 3.6 or -3 and 1/4 + 2 and 7/10
    How would you incorporate this in to the game?
    Reply

16 comments:

  1. Am I missing something? I don't see what the rules of the game are. Maybe I have it. They roll one number die and two +- dice. They record the +- rolls first and then the number, so that they get (as in the worksheet shown) something like 0 (old position) + -5. Then they take a card (in this case an 'odd # task'), figure it out, and do what?

    This sounds great. I'd like to ask kids at my son's school if they'd like to play test it.

    ReplyDelete
  2. I just just discovered the msmathwiki and in turn your blog. I love everything you have written. I have been teaching for 14 years, but this is the first time I've taught Algebra. I love playing games and am so excited I don't have to create them all from scratch. I will excitedly be checking your blog daily to see what other awesome activities you post. Thank you!!!!

    ReplyDelete
    Replies
    1. Thank you! I'm glad these are helpful to you.

      Delete
  3. Thanks for the feedback! In answer to Sue's question, the rules are, everyone works every problem. Each player starts at the origin, rolls the three dice, and moves where they indicate. Choose an even, odd, or zero problem card. Everybody works the problem and checks answers, then the next player rolls.

    It's only a game structure. I keep "score" by confirming how many problems each team has completed and checked each day.

    Hope this helps.

    ReplyDelete
  4. I'll tell you how this goes when you send me a beautifully LAMINATED class set of these made by the lovely office ladies, okay?! C'mon now, sharing is caring. I wanna do this, but it's too much work to make. #cryingwahwah #stopthewhining

    ReplyDelete
  5. Hi, I loved your idea. I am trying it over the summer. I have a question about some of the answers to the cards. On the 2-1 green and yellow cards, you have a few fill in the blank cards. What was your answer for them? For instance, one of the cards says "To avoid getting confused, we read the expression -w as _" The one that has been stumping me is, "The absolute value of ANY number is always _, which means that it is always also_"
    I know it is positive but what is the other blank?

    Thanks!

    ReplyDelete
    Replies
    1. Sorry about that! I forgot that you weren't there in class when I was drumming these ideas into our collective consciousness.

      With regard to the first card, when we start out in Algebra 1, I always have students read "–w" as "the opposite of w" or as "opposite w" rather than as "negative w." This helps ground them in what a signed VARIABLE means, as opposed to a signed NUMBER. If the value of w happens to be (–2), then –w is opposite-w which is –(–2) which is going to be a positive. Because they ground themselves in thinking about the opposite sign of the VARIABLE (rather than as a negative number), they get less confused as they evaluate expressions using different values for "w."

      With regard to the second card you mentioned, I also have students actively use the definitions of positive and negative — i.e., a positive number is defined as being greater than zero while a negative number is defined as being less than zero. So in the case of that card, I would hope they would say that "The absolute value of ANY number is always positive, which means that it is always greater than zero."

      Since definitions are our bedrock for the axiomatic aspects of algebra, this practice grounds them in thinking about whether a number lives to the left of zero (in the world of negative values) or to the right of zero (in positive territory).

      Hope this is helpful. Let me know if there are any blanks I can fill in!

      - Elizabeth

      Delete
    2. Thanks! This helps a lot! I came up with numerous possible answers but I couldn't sleep without knowing your right answer! lol

      Thanks again!

      Delete
  6. In the example you showed, did they just chose whether to go to positive or negative 5?

    ReplyDelete
    Replies
    1. Chelsea — They rolled three dice: two + / – dice and one six-sided number die. If they roll + — 5, they move 5 in the NEGATIVE direction (i.e., to the LEFT of zero). If they were to roll a + + 5, then they would move 5 spaces in the positive direction.

      Hope this helps!

      Elizabeth (@cheesemonkeysf)

      Delete
  7. Greetings everyone,
    Enjoy the shared learning and knowledge.
    I am interested in using this to model rational addition and subtraction - i.e. -2.45 + 3.6 or -3 and 1/4 + 2 and 7/10
    How would you incorporate this in to the game?

    ReplyDelete
  8. I'm having trouble getting on your wiki site. Is it not available anymore?

    ReplyDelete
  9. I am in the same boat as Hannah (above). I am hoping to use your game with my 7th graders this week!

    ReplyDelete
  10. I am in the same boat as Hannah (above). I am hoping to use your game with my 7th graders this week!

    ReplyDelete
  11. I am in the same boat as Hannah (above). I am hoping to use your game with my 7th graders this week!

    ReplyDelete
  12. I was looking for something like this…I found it quiet interesting, hopefully, you will keep posting such blogs….Keep sharing .
    Run 4 Cat Ninja Ludo Star

    ReplyDelete