Probability: Independent vs. Dependent Probability mass function of sum of two regular dice. (Photo credit: Wikipedia) Materials: Paper bag that you cannot see through 10 things of three colors, such as M&Ms, jelly beans, suckers, buttons, tiles Paper Pen or pencil Optional: change the number of colors or items Instructions: Draw a line across the paper. Above the line, write the name of each color Count the number of items of each color Just below the line, write down the number of items of that color Draw 10 lines below the color names and number them 1 through 10 Put all the items in... (Read More ...)

If a piece of cake is to be added to another piece of cake, the pieces need to be converted into comparable quantities, such as cake-eighths or cake-quarters. (Photo credit: Wikipedia) Unit fractions Materials 5 donuts Optional: loaf of bread, small pizzas, bagels, cups of milk Instructions Divide the five donuts evenly among 8 people Optional: divide 5 pizzas, bagels, bread loaves or cups of milk among 8 people What Should Happen? If you divide each donut in half and give each of the 8 people one half of a donut, then divide the remaining donut evenly into 8 pieces and give each one a piece,... (Read More ...)

Distribution – 80/20 rule Pareto chart (Photo credit: Wikipedia Vilfredo Pareto was an Italian economist who noticed in 1906 that 80% of the land in Italy belonged to 20 percent of the people and that 80% of his pea pods came from 20% of his peas. An American engineer, Joseph Juran, popularized these observations, named them the Pareto principle, also called the 80/20 rule, and applied them to quality improvement techniques in business in the 1940s. The 80/20 rule means that in many cases, 80% of the effect comes from 20% of the causes. Juran, for example, found several applications for the... (Read More ...)

Sorites Paradox or the Paradox of the Heap Something new to do when you are building summer sand castles. Tuning fork by John Walker stamped with note (E) and frequency in hertz (659) (Photo credit: Wikipedia) If you remove one grain of sand at a time, when does a heap of sand stop being a heap? Though this is a philosophy question, not strictly a math activity, my son, who double-majored in math and philosophy, tells me that eventually the two disciplines come together. Sorites, for Sorites paradox, is named for the Greek word for heap, soros. The Sorites paradoxes are attributed to a Greek philosopher... (Read More ...)

Fibonacci spiral Fibonacci spiral with square sizes up to 34 (Photo credit: Wikipedia The Fibonacci sequence starts out 1, 1, 2, 3, 5, 8, 13, 21, continuing indefinitely by adding the last two numbers to get the next number. Fibonacci found it in travels with his father, studying Indian mathematics. He described it in his 1202 book about calculations, after which the number series was named for him. It was originally described as a way to determine how many rabbits you would have if they had a pair of rabbits every month. But, it turns out this sequence can also be seen in spiral form in many natural... (Read More ...)

Fibonacci Sequence. The Fibonacci sequence in terms of rabbits (Photo credit: Wikipedia) The Fibonacci sequence is a series of numbers in which each number in the series equals the sum of the two numbers before it. It was described by Leonardo Fibonacci, an Italian mathematician, in his 1202 Book of Calculations. He also introduced and popularized Hindu-Arabic numerals, which he learned when he traveled with his merchant father to North Africa. They eventually replaced Roman numerals for calculations and that’s what we use today, the numbers 1, 2, 3, instead of I, II and III. The problem... (Read More ...)

Animated fractal mountain (Photo credit: Wikipedia) Fractals If you try to measure something irregular, like the coastline along a creek, you will find that the shorter the measuring unit you use, a one-foot long stick instead of a three-foot-long yardstick, for example, the longer the thing will be, infinitely. Normally, in geometry, you measure something that is curved, by setting a straight line against the curve and using more and more straight lines around the curve until you can approximate the length of the curve. With something that is shaped irregularly, though, this doesn’t work. This... (Read More ...)

How to Use an Abacus A Chinese abacus (Photo credit: Wikipedia) Although I studied Chinese in college and have been to China three times, most recently this summer, I had never learned how to use an abacus until researching this activity. If you understand simple addition and subtraction, you can use an abacus. With summer upon us, you probably have all the materials at hand. This activity would take 10 minutes to assemble if you didn’t have to wait for the glue to dry. As it is, it will take about an hour. If you and your grandchild both make one, you can have races to see who can solve... (Read More ...)

Coming up next week: Fireworks on the Fourth of July (Photo credit: Wikipedia) When Was the First Episode of Seinfeld? Monday, July 1, 2013 Do you remember where you were for the last episode of Seinfeld? Sunny Tuesday, July 2, 2013 What inspired the singer/songwriter to write this song? How Does Your Husband Keep You Happy? Wednesday, July 3, 2013 Does your husband pay attention? The Very Hungry Caterpillar Book Thursday, July 4, 2013 (Happy Fourth of July!) How does the artist make those distinctive, colorful images? Make Your Own Abacus Fun with Grandchildren,... (Read More ...)

Graph theory. The problem of the Seven Bridges of Königsberg. (Photo credit: Wikipedia) I used to think that there was no point in giving someone a math problem that was unsolvable. What could you learn from that except your tolerance for frustration? It turns out, though, that mathematicians, even when they suspect a problem has no answer, are not happy until they can prove it. That is the case with the famous Seven Bridges of Königsburg problem. Leonhard Euler, a Swiss mathematician and physicist, proved this problem had no solution in 1735, and in the process, invented graph theory, structures... (Read More ...)