Table of Contents
Looking at Cubes
Teaching Aids and Resources
This is just a fun activity, not relating directly to math, but perhaps relating peripherally to problem solving. Any one of these three pages will take most students a half hour or more. Students may find it fun to do this in small groups. Good activity for a day where only a few students show up and you want to challenge them with something they will enjoy.
This problem relates to math. Easy to understand, but with a little catch where some insight will help. A 10–15 minute activity. Can be done in groups.
For the a short class period before the holiday or as a 10 to 15 minute filler. It should be done individually IN PENCIL. Be sure to have extras available.
A matching test. The vocabulary is all mathematical, but the matching definitions aren’t. Can be done in groups. A 15 – 20 minute activity.
A fill-in-the-blanks test. The vocabulary is all mathematical, but the matching definitions aren’t. Can be done in groups. A 10 – 15 minute activity.
These are easy little “problems” or thought-provokers. Allow a half hour.
Looking at Cubes
This is a problem that involves spatial relationships and may be difficult for students to do in their heads. It will be easier if blocks (1 inch cubes) are available for students to use in trying to solve the problem.
Looking at Cubes - Problem
This is the original problem as stated. It is not as obvious or as easy as the problem statement makes it seem. Try it before you look at the solutions.
Looking at Cubes - Grid
This is the original problem with a grid drawn as a visual reference.
These are more difficult problems that will usually require some time and thought to get the correct answer or the best answer.
Think outside the box on both of these. I recommend giving them separately. Easy to understand.
This may have to be taught. I suggest doing one or even two of them together as a whole class before having students work on their own. These are easy enough that it is OK to give a whole sheet of them. Note there are two separate pages so they can be used on different days.
This puzzle has many solutions. There is an underlying principle for this problem which leads to any or all solutions quickly and easily. This problem can be used as a springboard to further discussion of the principle.
All of these problems are easy to understand. The level of difficulty is intermediate. They don’t require high level math skills, just problem-solving skills such as finding a pattern or working backward or something as simple as trying the problem to see what happens. Problem #2 may be difficult.
These are simple to intermediate in difficulty. Working backward, making a list, or simply guessing and checking will solve these.
These are easy. Insight would make them easier.
Problems for Topics
These problems relate to topics in algebra (distance problems, exponents) or in geometry (circles, triangles, Pythagorean Theorem, polygons), and the calendar. They are interesting and some have counterintuitive answers. I suggest using these when your students are studying the topics of which these are examples.
Problems in Reasoning 1
These are all easy - if you reason them out. No math skills are involved. Problem 4 looks difficult or perhaps tricky, but is easy to solve if you don’t try to do it in your head.
Problems in Reasoning 2
The third problem is easy. The first has a simple solution, but does require insight. The second problem will require some thought to reach the best solution.
Looking at Cubes Max - The maximum solution to the problem.
Looking at Cubes Min - The minimum solution to the problem.
IQ Test Answers
Mathematical Romance Answers
Solution to Calendar Cubes
Solution to Help Santa
Solutions Prob Topics
Solutions to 5 Problems
Solutions to 8 Problems
Solutions to Chain
Solutions to Cryptarithms
Solutions to Reasoning 1
Solutions to Reasoning 2
Stories and Tidbits
Every Fifth Man - This appeared as a mystery short story and has some mathematical content.
Humor in Mathematics
Questions to God - This is just for fun.
Smullyan - This is an article about Raymond Smullyan, who authored several books of unusual problems and puzzles. Several of them are included with this article.
The Fun They Had - A single page Isaac Asimov short story of the future when machines did the teaching.
World According to STUDENT Bloopers - This is just for fun. Try to read it without laughing. I dare you!
The cartoons below all appeared in newspapers and relate to teaching or math.
Cartoon 04 - Peanuts
Cartoon 05 - Peanuts
Cartoon 06 - Funky
Cartoon 07 - Funky
Cartoon 11 - Peanuts
Cartoon 13 - Sally Forth
Arthur Gask - A cartoon story in the style of Jules Pfeiffer.
Teaching Aids and Ideas
All of these items may be helpful or interesting to teachers. At the very least they should stimulate some thought.
13 Sins of Teaching
This was written by a teacher for teachers. In addition to listing the “sins,” there is an extremely brief discussion and a Corresponding Virtue for each of the “sins.”
Class Management Aids
Some classroom teacher tools made up by teachers. They are included to provide some ideas. Included are: class rules, a holistic general scoring guide, a grade sheet for group grades for oral presentations, a homework grading guide, some possible questions you could use for students to write (3 minute essays) about their experience working in a group, a guide that an outside evaluator might use to rate your instruction, and a self-evaluation of your instruction.
This is here primarily because it lists 75 suggestions for classroom management. If you read through these suggestions and even 2 or 3 strike you as being helpful, this will be worth reading. Of course, it won’t hurt much if you glance at the rest of the article, also.
This recounts the experience of a teacher trying for the first time to implement constructivist learning in the classroom. It contrasts it with a more traditional approach used by another teacher.
Far and away the best short discussion (8 pages) on implementing group learning. The other 12 pages are lists that my be helpful. All lists and tables relate directly to the article.
Memo from a Child
This could go with the 13 Sins and the management suggestions in that it succinctly lays out some do’s and don’ts in interacting with students.
An online discussion of what to do if students don’t do their homework. Several teachers contributed their ideas or methods for dealing with this problem. Diverse ideas. Very thought-provoking.
Parents Can Make A Difference
A handout that you can consider sharing with parents.
Teach Math to Sp.Ed. Stdnts
A short list of suggestions for working with special education students.