Great article on the impact of cultural conditioning on the negative perceptive of maths amongst students.

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Fibonacci numbers are the sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. (Add two numbers in the sequence to get the next one.)

Take two neighboring numbers in the sequence, such as 5 and 8. Turns out, 5 miles is approximately 8 km. Take 34 and 55: 34 miles is about 55 km.

If your number is not in the sequence, write it as a sum of numbers that are:

Convert 10 miles into kilometers. 10 = 5 + 5, and 5 miles is about 8 km. So, 10 miles is about 16 km.

OR

Convert 25 kilometers into miles. 25 = 21 + 2 + 2.

21 km = 13 miles (about)

2 km = 1 mile (about)

2 km = 1 mile (about)

25 km = about 13 + 1 + 1 miles = about 15 miles.

The reason has to do with the fact that the conversion factor, (0.621371192 mi/km) is pretty close to the ratio to which sequential Fibonacci numbers converge (0.61803)

More details here http://riebecca.blogspot.co.uk/2012/07/adventures-in-fibonacci-numbers.html

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**Message boards/forums**

**Ask Dr. Math**

Browse old math questions or ask your own. Expert answers. The archives have thousands of answered questions covering all math topics from elementary to college level.

mathforum.org/dr.math

**S.O.S. Mathematics CyberBoard**

Active discussion board where you can ask math questions about algebra, calculus, geometry, trigonometry, probability, college math, computer science, physics, and more.

www.sosmath.com/CBB

**Mrs. Glosser’s Math Goodies Forums**

For students, teachers & parents. Homework help, Teacher Talk, Parents place.

www.mathgoodies.com/forums

**Math Help Boards**

From pre-algebra on through university-level math. It has experienced staff, is completely free, and as a policy does not give answers away without the asker showing some effort.

www.mathhelpboards.com

**FreeMathHelp.com**

A math homework help forum.

www.freemathhelp.com/forum

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It tells about two teachers who frequently employ open-ended problem-solving sessions in their teaching – and the students (almost all) like it well and are very motivated.

In math education, **OPEN-ENDED** problem usually means it doesn’t have a specific step-by-step solution. You can solve it in many different ways. Or, it may have more than one solution.

The problems these teachers use are often from real life, and not quick to solve. Instead it can take some time and struggling to get anywhere. (Hey, that’s how problems in real life often are, too!)

But, struggling can be valuable. One of the teachers featured in the article, Heidi Ewer, says:

“Struggling helps them see this as an investment of their own time and energy. It makes them more willing to learn,” Ewer says. “Struggling to solve problems requires students to use their intuitive skills to investigate concepts, she explains,

and, in this way, they gain a deeper and more lasting understanding of the mathematics.”

There’s even some value in trying impossible problems! Douglas Twitchell says in The Value of ‘Impossible’ Problems, “*…if you have students who are interested in trying, think of the mathematics they might learn in the process of attempting these!* [some very difficult problems]”

I realize dealing with open-ended problems is not easy to do if you’re not an experienced math teacher – and not even then. Like the other teacher from the article, Judith Carter, says, a problem-solving activity is not something she can fit into every day, or even every week.

But,maybe an occasional session dedicated to a challenging open-ended math problem can be fitted into a scheme of work.

If you’re ready to give some challenging problems for your student(s), check out these:

Open-Ended Math Problems from The Franklin Institute Online (middle school level).

Here are some more

**Problem Solving Decks **

Includes a deck of problem cards for grades 1-8, student sheets, and solutions. Many of these problems are best solved with calculators. All of these problems lend themselves to students telling and writing about their thinking.

mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5856325

**Math Stars Problem Solving Newsletter (grades 1-8)**

These newsletters are a fantastic, printable resource for problesm solve and their solutions.

mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5856332

**Virtual Math Club**

Problem sets & puzzles similar to those found on math contests such as the AMC 8, AMC 10, MATHCOUNTS, or the middle school math olympiads, including answers and video solutions posted a week later. For middle school/early high school level.

virtualmathclub.wordpress.com

**Open-Ended Math Problems**

Collection of problems that lend themselves to more than one way of solving.

fi.edu/school/math2/index.html

**Mathematics Enrichment – nrich.maths.org**

Open-ended, investigative math challenges for all levels.

nrich.maths.org/public

**Math Circle Presentations**

Math circle presentations for grades 6-12 from University of Waterloo and their related student exercises, available as PDF files. These can be used as enrichment, as challenging word problems or as review of certain topics.

cemc.math.uwaterloo.ca/events/mathcircle_presentations.html

**Figure This! Math Challenges for Families**

Word problems related to real life. They don’t always have all the information but you have to estimate and think. For each problem, there is a hint, other related problems, and interesting trivia. Website supported by National Council of Teachers of Mathematics.

www.figurethis.org

**MathsChallenge.net**

Search for number, geometry, probability etc. word problems and challenges. Includes solutions.

mathschallenge.net

**Massachusetts Tests for Educator Licensure, Mathematics Subtest**

This is a downloadable math practice test for prospective elementary school teachers, and it contains a lot of good problems for problem solving practice, mostly in the middle school, some in the high school level.

www.mtel.nesinc.com/PDFs/MA_FLD003_SubtestII_PRACTICE_TEST.pdf

See also:

**Word Problems Solving Strategies**

Gives one example of each strategy: Find a pattern, Make a table, Work backwards, Guess and check, Draw a picture, Make a list, Write a number sentence, Use logical reasoning.

www.mathstories.com/strategies.htm**Math Word Problems Worksheets**

Free worksheets from About.com for various grades in PDF form.

math.about.com/od/wordproblem1/Worksheets_for_Word_Problems_Various_grades.htm

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Fred and Frank are two fitness fanatics on a run from A to B. Fred runs half the way and walks the other half. Frank runs for half the time and walks for the other half. They both run and walk at the same speeds. Who finishes first?

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- Exploring Lesson Study (connectededucoach.wordpress.com)

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