Each team gets six integers 1-100. These could be randomly given by rolling dice or by playing cards or non-randomly by having students pick the 6 integers.  

One team or the teacher chooses two integers to make a fraction. Here the green students are thinking of making the fraction 48/17 or 17/48.

The other teams now have 20 seconds to make their own fraction that is less than or equal to the target fraction. The closest fraction will win. Of course, if we give students enough time the top ones will figure out the best possible answer from their set of cards, but we're not going to give them enough time to do that 😉 All students will have a chance to win.  

The teams have all chosen their fractions and now each team starts calculating to see if they've won. Which is closest without going over? 

It turns out we don't even need to calculate the first decimal to find that orange is the closest without going over. Students should be encouraged to be lazy. "Don't calculate any more than you have to! Relax ;-)" 

The teacher now asks two children to say any 1-100 integer for the numerator and denominator of a new target fraction. She might alternatively roll a 100 sided dice or select cards. It is best she does not just choose the numbers herself so the game looks fair.

Which team got closest without going over?

Orange won - and look - the yellow team did too much work. They calculated with too much accuracy 😉 They already knew they had lost after calculating their fraction was about 1.5

Sometimes - instead of getting two new integers - the teacher will just flip the fraction. Are you ready? You have 20 seconds to try to get as close as possible to 44/60 for one of the teams. The twenty seconds starts when you go to the next slide.

20 seconds to get as close to 42/60 with one team...

Did you do better? Let's let the students calculate who won.

Well it looks like yellow or orange won, but your kids will need to keep calculating because now more precision is needed to determine the winner. Be as lazy as you can, but here you have to go to three significant figures.

After you play the game ask students to select numbers so as to maximize their chance of winning. My first incorrect thought about choosing numbers was to choose numbers belonging to the Fibonacci sequence: 8, 13, 21, 34, 55, 89. That's so wrong it's funny! Enjoy puzzling! Gord!

Venus Flytrap – dangerous decimals

(MathPickle, 2013)

Here is a pdf to print the cards and rules of the game. Enjoy 😉

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

 
MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

 
MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.

(http://www.corestandards.org/Math/Practice/)

Please use MathPickle in your classrooms. If you have improvements to make, please contact us. We'll give you credit 😉

Gordon Hamilton

(MMath, PhD)

 

Lora Saarnio

(CEO)