Exotic Arithmetic

Instructor: Harold Reiter, Ph.D.

Intended for: Grades 6-8

Dates: June 26-30 (9AM-NOON)

To be prepared for algebra, students need both fluency and deep understanding of arithmetic.  This course is designed to facilitate that deep understanding through challenging problems beyond the standard middle school curriculum. Students working through this material, even with the help of a teacher, should expect to experience some confusion. Indeed, learning to 'tolerate confusion’ is an important step in learning mathematics. The problems are intended to be just within reach, or perhaps just out of reach, of individual students. It’s a little like the weight lifter who adds a few pounds to the bar at each session. That’s the way to build strong muscles. Working problems individually or as a group that are close to your limit similarly builds brain strength.

Students attending should... enjoy doing mathematics and be thoroughly comfortable with the standard K-6 mathematics curriculum, including arithmetic with fractions and divisibility of integers.  

Sample problems:  

1) Notice that 1089 × 9 = 9801. Is there a four-digit number abcd which reverses when multiplied by 4?

2) Find a fraction between one half and two thirds and explain why your fraction works.

3) Consider 13×62 = 26×31. This is called a multiplication palindrome. Your challenge is to find all of these. (The four two-digit numbers must all be different.)