By Natalya St. Clair
Quick! What are the first fifty digits of π? On March 14 (3/14), math students around Champaign-Urbana will be celebrating π Day , if not in the classroom then definitely at home. Young mathematicians typically recite as many digits of π as they can, measure the circumference to diameter ratio for round objects, sing πTunes like “American π”—and of course, eat pie at 1:59 (3/14:1:59).
I can remember the first time I taught a series of mental math tricks on π Day to middle school students. Sharing the joys of arithmetic to a child is truly a gift. Often, students reach for their calculators to solve math problems for homework, but mental arithmetic contains its own delights. The following activities can be taught for π Day, or any math occasion.
Memorizing Digits of π
Attempts to memorize the value of π have lead to records of over 60,000 digits, although most of this relates to technique than genius. In Secrets of Mental Math, mental mathemagician Art Benjamin describes using a phonetic code to associate one-digit numbers with consonant sounds:
1 is the t or d sound.
2 is the n sound.
3 is the m sound.
4 is the r sound.
5 is the l sound.
6 is the j, ch, or sh sound.
7 is the k or hard g sound.
8 is the f or v sound.
9 is the p or b sound.
0 is the z or s sound.
Once this list is memorized, you can use this system to memorize the sentences: “My turtle Pancho will, my love, pick up my new mover, Ginger. My movie plays in a favorite bucket. Ship my puppy Michael to Sullivan’s backrubber.” Translating this sentence into digits will result in the first sixty digits of π. Neat!
Some math students will enjoy learning mental math tricks in adding and subtracting digits of π as well.
Adding and Subtracting Numbers From Left to Right
On pencil and paper, students are encouraged to add and subtract numbers from right to left. However, in mental mathematics, it is easier to add and subtract numbers from left to right. For example, to add 31 + 41, first add 40, then add 1, to get 72. Let’s try another.14 + 31 is simply 44 + 1 = 45.
For numbers with carries, we can still simplify the problem by adding from left to right. For example, 41 + 59 is 91 + 9, which is 100. The same is true for three-digit numbers: 314 + 159 = 414 + 59 = 464 + 9 = 473.
For subtraction, students can simplify the problem by computing from left to right. For example, 59 – 26 = 39 – 6 = 33. Some subtraction problems involve borrowing, but the strategy is the same. For example, 31 – 15 = 21 – 5 = 16.
Another method is to turn the subtraction problem into addition. For example, 31 – 15 = 31 – (20 + 5) = 11 + 5 = 16. Students from grades 1-7 can have fun adding and subtracting two-digit numbers, then eventually moving to three-digit mental addition and subtraction, too.
Natalya St. Clair double majored in studio art and mathematics at Scripps College. She combined her passions for both subjects to illustrate The Art of Mental Calculation. She has taught middle school math for seven years at Countryside School and has been an award-winning MATHCOUNTS coach in Illinois. She has served as a contributing member of numerous outreach programs, including the Machine Project, Illinois Geometry Laboratory, MATHCOUNTS, and the Independent Schools Association of the Central States.