Every week, you're going to get access to a fresh Problem, and each Problem of the Week comes with extensive supports. So where are all of these resources, and what should you do with them? Good question! All of the resources related to each Problem of the Week are found in the blue Resources menu, found to the right of the Problem. All of our Resources are built to help you work through the Problem, in the way that best suits your needs. Here, we outline what each Resource is, why it has been included, and how it might be used.
First, there is the Math Category. This will give you a very brief overview of what mathematical topic (or topics) the problem deals with. This might be a brief word or two, or a few sentences; some problems are easy to pigeonhole, and some aren’t! The Math Category will give you a bird’s eye view of what you’ll be dealing with in the Problem.
Next, there are the Thinking Skills. This is a more detailed, but conversational, discussion of the kinds of thinking that will be applied in the problem. Some of the skills will be specific to the mathematics of the Problem, like visualization. Other skills deal more with the proper mindset for the Problem, like perseverance. You can read this section in detail, or you can just skim to get an idea of what you’re in for. You might want to go back to this as you do the Problem, especially if you are mentoring someone, to inform your own ways of thinking, and the habits of mind you might want to instill in your learner. You could also simply read this section after the Problem is done, to get our take on what your brain might (or should!) have been doing as you solved the Problem, and inform your thinking for future problem-solving.
The Math Category and Thinking Skills are always accessible with the Problem, as is the Solution, which you can also find in the Resource Menu. Unlike our suggestions for the Math Category and Thinking Skills, we would ask you, even plead with you, NOT to read the Solution immediately. To get the most out of what we offer, it’s worth taking the time to struggle with the Problem, at least for a little while, before you begin to read the Solution. The Solution typically will come broken up into sections, where each section corresponds to a particular step in the solution. If you are stuck on how to begin the Problem, or just need a little push forward somewhere, you might use the Solution, but only focus on the section you need, rather than read the Solution in its entirety. (Other than the very first section, the sections will not open until you click on their titles, so you don’t accidentally read something too far along in the Solution that will spoil your thinking fun!) Whatever happens, the Solution is here to help you move forward in your problem-solving; we think that the Solution might sometimes be useful as a hint guide. You, and your learner, can go back and forth between your own problem-solving and the Solution as needed. Our Problems are involved enough that you can read much of the Solution and still have plenty of thinking left over to be done!
Of course, you may solve the Problem and not even need to access our Solution for help. After you are finished, we would still ask that you read the Solution. First, it’s always nice to see if your solution matches ours, and if it doesn’t, then maybe there’s something more to learn by seeing how we did it, or by comparing the two approaches. Keep in mind, also, the rest of your experience will often depend on your understanding of how we approached the Solution, as we explain below.
There is also an additional tool found inside of the Solution. Some sections of the Solution will have an orange icon that looks like a book, appearing in the lower right corner of that section. If you click on it, you will see the Supporting Questions that go with that section. Sometimes it’s difficult to help someone move forward in her thinking without giving away key parts of the Solution. If you or your learner is struggling and needs a push, these Questions are here to help encourage thinking along a productive path. These Questions will provide little nudges that you can give to your learner to help him advance through the Problem. You will also see Supporting Q’s in the Resource Menu, but there you will see all of them collected into one list, section by section.
Once you’re satisfied that you’ve solved the Problem, click the toggle at the top right to mark it SOLVED. Doing this will unlock the “extension problem”, i.e. the Exstemsion. It’s best to only tackle this extra problem after you are satisfied that the main Problem is finished, since the Exstemsion problem will often build upon ideas from the main Problem’s Solution. Then you can treat the Solution to this Exstemsion just like you did for the main Problem; the Exstemsion Solution is accessible immediately, and you can use it for hints if you get stuck, or just read it for your own pleasure, as suits you best.
When you are finished with the Exstemsion, use the toggle at the top right to mark it SOLVED. This will unveil the last components of your experience: the Big Ideas. This is where we look back at what you did and give you some further insight into the mathematics. We might give you some interesting history about the Problem and/or Exstemsion, highlight connections to current mathematical trends and research, or explore some of the deeper ideas and theorems that underlie your work that you might not expect. The Big Ideas should definitely be read after you are comfortable with the Solutions to both the Problem and Exstemsion; the Big Ideas rely on these solutions as their core.
If you have questions or feedback related to any of the Resources that come with our Problems, please don't hesitate to contact us at firstname.lastname@example.org.
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