Features of the Problem Sequences
Use of Technology
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- Search You can search for mathematics problems by category in topics, habits of mind (problem solving method), duration (the amount of time available for an activity), technology, and mathematical background required. Learn more about each of these ways of searching by clicking on them (above). You can also search for keywords in the title, synopsis, and topics of a problem, and you can even search by date to see what is new.
- List of problems Once youve chosen your search criteria, you can click the List Selected Problems button to display the synopsis for each relevant problem and the information about problem attributes: habit of mind, use of technology or other materials, mathematical background, duration, mathematical ways of thinking it develops, and so on. This information will help you judge whether the problem is at your students level of knowledge, how much of your classroom time it will take, and whether it will fit your goals. From the list, you can select and print particular problems.
- Synopsis Each synopsis provides a brief overview of the problem sequence, letting you quickly judge the fit of a problem set for your lesson. The synopsis often mentions both a concept organizationthat is being introduced or developed, and a set of skills that are practiced at the same time. Be aware that sometimes these are in different areas of mathematics, building connections for students. The synopsis may also list prerequisite student knowledge for solving the problems, and it may list other problem sequences that it relies upon and that must be solved first. Any contexts such as sports, weather, science, art, and so on, are mentioned in the synopsis so that you may search (by keywords) for contexts. Finally, the synopsis mentions related problem sequences, if any.
Each link to a problem sequence contains Problems and Answers; most also contain Hints and Solutions. These components, on separate pages, are downloadable as a single file in PDF format, to allow high-quality viewing and printing with Adobe Acrobat Reader®. (All four parts are written to be readable by both teachers and students; you decide how you want to use the hints and solutions. A few problems also display problems in HTML format, for fast online browsing. In the future, all problems will be available in both PDF and HTML formats.
You may create (by printing or photocopying) multiple copies for use with your students. Because hints, answers, and solutions are on separate pages from the problems, you can choose whether or not to distribute these as well. You may also give your students the Web address (URL) for this Web site and titles of the problem sequences youd like them to work on. In that case, of course, students have access to all parts of the problem sequence.
- Problems The problems themselves are, of course, the intended for the students to read and work through. You can give these to students for work in class or, in some cases, as homework.
- Hints Hints provide a bit of extra help for those students who need it. The hints might include additional questions to help students work through a problem, point out an important detail that could be overlooked, or remind students of a useful mathematical fact or concept. You may pass out the entire hints page, or give single hints to particular students or groups. If you give problems for homework, feel free to post hints on your own Web page.
- Answers Answers without full solutions can be used as a quick check of student work. Students who answer a problem incorrectly can go back to their work to find mistakes and reevaluate their thinking.
- Solutions Solutions can be read either by you or by students. Solutions clearly describe all steps in solving a problem, and highlight important mathematical ideas that are developed in the problem. They are written so that students can read them, understand them, and learn from them. Solutions may include teacher notes on the margins with suggestions about using these problems and possible student misconceptions.
Sometimes various technologies, from non-electronic manipulatives to computer software, make it possible to develop mathematical ideas that are otherwise hard to explore. Problem sets that depend on particular technologies are clearly marked, and you can search for sequences by the technology they use.