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.

Happy New Year!

Lesley's Center for Mathematics Achievement has some exciting offerings in the upcoming year.  These include monthly Saturday workshops, a Dine and Discuss focusing on the CCSS and PARCC, graduate level math courses in Brockton, Quincy, and Springfield, collaborations with UEI and MoS, and a Summer Institute.  We are excited for the upcoming new year and continuing our work with mathematics teachers and education.  We hope that you can join us for some of these events.  If you want more information, you can find all of it at: CMA Homepage!

And to start of the new year...
How many factors does 2013 have?  How many of the factors are prime factors?

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

 

 

Common Core State Standards, MA Frameworks and the Work of the Center

Since it became evident that Massachusetts, as well as 45 other states, was adopting the Common Core State Standards (CCSS) we have struggled with how best to serve the needs of the teachers with whom we work. The staff of the Center for Math Achievement (CMA) at Lesley University is committed to supporting the mathematical needs of teachers in any way possible. We will continue to offer courses on site in districts and weekend workshops, participate in dine-and-discuss meetings with the Association of Teachers of Mathematics in Massachusetts (ATMIM), mentor/coach teachers, and publish materials that will promote effective teaching and learning.

Sol Garfunkel, mathematician, author, and professional development provider, in an email delivered through Jerry Becker’s list serve describes himself as “schizophrenic” when it comes time to deal with the CCSS. His dilemma, as with many mathematics educators, is how to reconcile an untested set of standards which he does not support with his commitment to best support teachers who have to implement them. I am in agreement with Sol, who went on to articulate how well-written the 1989 National Council of Teachers of Mathematics (NCTM) standards were and how we, as a nation, never truly implemented those standards as articulated. I would add that the revision of those standards as articulated in Principles and Standards for School Mathematics 2000 have also been largely ignored. Yet, after spending time at the International Congress of Mathematics Educators-12 (ICME-12) in Korea, I heard from many educators from around the world how much they value the work of NCTM and use their standards and publications religiously. In fact, many presenters from countries which out-perform the US on international assessments stated that the reason their students do so well is because their curriculum is based on the NCTM standards.

More information on the PARCC assessment will be released in the coming weeks and we will pass on that updated information as soon as it becomes available. Until then, feel free to ask any questions you might have, or to provide us with information you may have that we are missing.

Anne