Using Least 1s
(Conway & Guy, 1962)
Using multiplication and addition try to create the target number using the least number of ones. For example… to get to the number 12, you could do (1+1+1+1)*(1+1+1) or (1+1+1+1+1)*(1+1)+1+1 but the first solution is better since it uses only seven ones. This is good for elementary school.
Now we’ll try it using addition and exponents, but not multiplication. Which pair of operators is fastest? This is good for older students.
We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.
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!
Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.
MP2 Think abstractly!
Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.
MP3 Work together!
Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.
MP4 Model reality!
Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.
MP5 Know the tools.
Students master the tools at their fingertips - whether it's a pencil or an online app.
MP6 Be precise!
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!
Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉
MP8 Be lazy!?!
Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?
Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 If you are using MathPickle with adults, please mention the website. If you are from a private school, please ask parents or administrators to donate.