Hi All,
Today's problem/activity is called WHO'S LEFT STANDING? It's based on playing a simple game, but has lots of intriguing patterns to investigate. You can use this activity with Grades 2 -12. Young kids will see the mathematical patterns emerge as they play while older kids will see the same and may even be able to express what they find algebraically.
The game is simple. Kind of a "Duck, Duck, Goose." If you were to have a few people get in a line and then start with the first person on the left and say, "in," and the next person, "out," the first person stays standing and the second sits down in place.
You continue down the line alternating each person as "in" or "out." When you reach the end of the line, you go back to the beginning to the first person still standing and continue till only one person is left standing. Played with two players, #1 would be left standing. In the photos here, you can see when played with four, #1 is left standing. How about with 12 players? or 53? Who would be left standing?
Depending on the number of people playing, could you always predict who would be left standing? It helps to keep track of the numbers and how they relate to each other.
Since you probably don't have a bunch of people to play this, you can use any physical thing to replace people like plastic cups, cans, or dominoes. When numbers get too big you can just draw rows of circles and cross them out.
But even drawing circles gets tedious when you try to work with numbers like 125. Is there a mathematical way to predict the outcome? Patterns help us predict. In this problem, the pattern at first seems very predictable, but then it changes. Looking for the overall pattern is the challenge. We find there are often patterns within patterns.
I'm attaching some pdf's here with a basic lesson plan and some charts you might want to use as you collect data to help you look for patterns in the numbers that will guide your predictions.
Here's the link to pdf: https://drive.google.com/file/d/1_55YxwMyGFFT8FKgbLVN85RKDHNIiSkj/view?usp=sharing
Have fun! Take your time with this one.
All the best,
Bob
This activity is based on an idea originally published in Teaching Children Mathematics, a publication of the National Council of Teachers of Mathematics (NCTM).
Today's problem/activity is called WHO'S LEFT STANDING? It's based on playing a simple game, but has lots of intriguing patterns to investigate. You can use this activity with Grades 2 -12. Young kids will see the mathematical patterns emerge as they play while older kids will see the same and may even be able to express what they find algebraically.
The game is simple. Kind of a "Duck, Duck, Goose." If you were to have a few people get in a line and then start with the first person on the left and say, "in," and the next person, "out," the first person stays standing and the second sits down in place.
You continue down the line alternating each person as "in" or "out." When you reach the end of the line, you go back to the beginning to the first person still standing and continue till only one person is left standing. Played with two players, #1 would be left standing. In the photos here, you can see when played with four, #1 is left standing. How about with 12 players? or 53? Who would be left standing?
Depending on the number of people playing, could you always predict who would be left standing? It helps to keep track of the numbers and how they relate to each other.
Since you probably don't have a bunch of people to play this, you can use any physical thing to replace people like plastic cups, cans, or dominoes. When numbers get too big you can just draw rows of circles and cross them out.
I'm attaching some pdf's here with a basic lesson plan and some charts you might want to use as you collect data to help you look for patterns in the numbers that will guide your predictions.
Here's the link to pdf: https://drive.google.com/file/d/1_55YxwMyGFFT8FKgbLVN85RKDHNIiSkj/view?usp=sharing
Have fun! Take your time with this one.
All the best,
Bob
This activity is based on an idea originally published in Teaching Children Mathematics, a publication of the National Council of Teachers of Mathematics (NCTM).
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