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.
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
This sounds great. I'd like to ask kids at my son's school if they'd like to play test it.
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.
I know it is positive but what is the other blank?
Thanks!
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
Thanks again!
Hope this helps!
Elizabeth (@cheesemonkeysf)
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?