Developing Number Sense

As our students enter middle school and beyond, too often they lose opportunities to continue developing their number sense. Students at this age tend to appreciate more and more the beauty behind numbers, our number system, and the patterns and relationships among them. For this month’s blog I am resurrecting some fun number questions from the Mathematical Digest, Term 1, 1994, Number 105. This mathematical digest has a wealth of information and challenges to be solved. Enjoy!

Anne

Match the clues with the numbers in the box.

Clues

1. An odd cube
2. The first prime 
3. The fourth triangular number
4. Srinivasa Ramanujan* said that this number was equal to (9²  + 19² ÷ 22)²⁵
5. The second perfect number
6. The smallest odd abundant number
7. 6! + 5! + 4! + 3! + 2! + 1!
8. The first number after 1 to be both a square and a triangular number
9. The ninth highly composite number
10. A three digit palindromic square number
11. G. H. Hardy’s taxi cab’s number 

There are twelve numbers in the box for the eleven clues.  Which number does not have a clue written for it?  This number is featured in a very well-known book written in 1726. What is the name of the book? 

*Srinivasa Ramanujan (1887-1920) has been described as the greatest mathematician India has produced in the last 1000 years. His work has only just started to be appreciated and understood. His formulae are being used in areas such as polymer chemistry, statistical mechanics, computers and even cancer research.

Problem of the Week

A number of children are standing equally spaced around the edge of a large circle and are numbered consecutively.  Abby is 14^th and Emma is 32^nd and are standing directly across from each other.  How many children are there?

In a week, we will post solutions for this problem.  At that time we will also choose one commenter who gave the correct answer to get a copy of Zeroing in on Number and Operations (the commenter who wins can choose from PreK-K, 1-2, 3-4, 5-6, or 7-8).  If you want to be entered into the drawing please comment with your solution, and leave your first name last initial.

We look forward to seeing your responses!

Katie