Division with Fractions 1 and 3/4 divided by 1/2

This is an example from Liping Ma's book:

Using Decimals
How much is 1.75 divided by .5?
1.75/.5 = 3.5


Using Fractions
1 and 3/4 divided by 1/2
1 and 3/4 = 7/4
7/4 divided by 1/2
How many half cups are in 7/4 cups?
1 half cup = 1/2
2 half cups = 2/2 = 1
3 half cups = 3/2
4 half cups = 4/2 = 2 -- this is too much

7/4 divided by 1/2
multiply 7/4 by the reciprocal of 1/2
7/4 x 2/1 = 14/4 = 7/2 = 3 and 1/2

Division with Fractions is "a topic at the summit of arithmetic". In the introduction, she asks a division with fractions question: 13/4 divided by 1/2 and offers three additional problem-solving methodologies (besides Keep, Change, Flip) -- Dividing Using Decimals, Applying the Distributive Law and You Don't Have to Multiply.

Checking Multiplication with Casting Out Nines

Multiplication can be checked using Casting Out Nines. (rather than long division)

By studying the digits in the problem and comparing them to the digits in the answer, we can gain confidence that we have done the problem correctly.

Here are some examples:
12 x 12 = 144
The digits in 12 add up to 3 (1+2)
The digits in the other 12 add up to 3 (1+ 2)
3 x 3 = 9 (144 adds up to 9)

13 x 13 = 169
The digits in 13 add up to 4 (1+3)
The digits in the other 13 add up to 4 (1+ 3)
4 x 4 = 16 (169 adds up to 16)
We could also add up the digits in the 16 of 4 x 4 and get 7
and get 7 in the answer by casting out the 9 in the 169 so we are left with a 16 that add up to 7.

125 x 4 = 500
The digits in 125 add up to 8 (1+2+5)
The 4 is just a 4
8 x 4 = 32 and the digits in 32 add up to 5
The answer 500 also adds up to 5.

What You Know About Math?

Great and enthusiastic fun video about the TI-84
http://www.youtube.com/watch?v=Ooa8nHKPZ5k

Learning Math Takes Patience

Feature on an award-winning Calc teacher in North Carolina who emphasizes practice for improvement and likens the process to bettering athletic ability. The article also talks about how Math attitude affects students and performance.

Personal Finance Classes in High School

This is such a needed app for Math and Life!!

Economics is also terrific but can be theoretical rather than practical.

Math provides the foundation for processing and understanding personal finance and economic terms to increase savviness and savings while reducing debt.

Singapore Math Success

Singapore Math in Focus is hailed by students and teachers.
http://www.kentucky.com/142/story/1109176.html

ACCUPLACER: College Placement Exam

The ACCUPLACER is used by many colleges for placement into Math and English.
Passing these tests is important in order to avoid non-credit remediation classes.
The title link goes to a page with a pdf of sample questions for both Math and English.

Tips for the ACCUPLACER:
http://www.collegeboard.com/student/testing/accuplacer/accuplacer-tips.html

Where is the GED?

While states are spending money and resources on exit exams, it would be interesting to think about using the GED as a standard. According to this document, only 60% of graduating high school seniors would pass the GED Tests on their first attempt:
http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_FactSheet_20092.pdf

GED sample questions:
http://www.acenet.edu/Content/NavigationMenu/ged/test/prep/sample_questions.htm

Math Show for Preschoolers

This new Nickelodeon preschool show will debut on January 25th.
Web site of show
http://www.nickjr.com/team-umizoomi/


http://www.nickjr.com/family-entertainment/kids-books/nickjr-quick-picks/best-math-books-for-kids.html

Math Quiz by Arthur Benjamin in the NY Times

http://www.nytimes.com/2010/01/03/education/edlife/03quiz-t.html?ref=edlife