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

E-Newsletter Brain Teaser December 2009

Ann went from Point A to Point B.

Simultaneously Peter went from B to A.
In six hours they met and in another three hours Peter reached A.
How many hours did Ann travel from A to B?

Peter’s total travel time was 9 hours.
Assume both travel at a constant speed:
Let’s pick a speed for Peter…60 miles per hour so Peter will travel 540 miles altogether (as will Ann). He travelled 360 miles in the first 6 hours and 180 miles in the last 3 hours for a total of 540 miles.

after 6 hours, they were both much closer to A than to B


A----------------X---------------------------------B

If Ann took 6 hours to travel her 180 miles (540-360), she was only travelling 30 mph.
So it will take Ann 18 hours to travel from A to B. (540/30)

If we pick another speed, let’s say 100 mph for Peter
So he travelled 600 miles in the first 6 hours and 300 miles in the last 3 hours for a total of 900 miles.

If Ann took 6 hours to travel her 300 miles, therefore she was only travelling 50 mph.
So it will take Ann 18 hours to travel from A to B. (900/18)

Many apologies for a typo, the original problem in the e-newsletter said:
In six hours they met and in another three hours Peter reached B.

Adding It Up on WNYC

http://blogs.wnyc.org/news/category/education/adding-it-up/

Adding It Up multi-part series from WNYC on remedial Math experiences at LaGuardia Community College

Wired for Math

http://www.nytimes.com/2009/12/21/health/research/21brain.html?_r=1&hp=&pagewanted=all

Brain researchers in cognitive neuroscience are finding that young children can learn Math in preschool. This changes the idea that students need to be at least 5 until their brains are ready for Math.

SAT Skills Insight Pinpoints Strategies

http://www.collegeboard.com/testing/sat/skillsmap/select-interval-mathematics.html

This link connects to SAT Skills Insight that helps students find and developstrategies based on their current score.

COMPASS

http://www.act.org/compass/sample/pdf/numerical.pdf

Elementary Math is Misleading

A retired engineer tutors his 4th grade granddaughter in Math and finds that the standard algorithms have been upstaged by regrouping, estimated and calculator Math.

http://suburbanjournals.stltoday.com/articles/2009/12/19/stcharles/opinion/1220stc-opsh0.txt

This Is Your Brain on a Test

http://blog.newsweek.com/blogs/nurtureshock/archive/2009/12/15/this-is-your-brain-on-a-test.aspx

Carol Dweck, researcher at Stanford (formerly at Columbia), wrote about the Growth and Fixed mindset in her terrific book Mindset http://www.mindsetonline.com./

In the study mentioned on the Nurture Shock blog on Newsweek.com, Po Bronson renames the Growth mindset Knowledge-Hungry and the Fixed mindset Grade-Hungry. The Knowledge-Hungry learners were open to learning from their mistakes. Developing this perspective can help students and their teachers and parents to address the "non-instruction" part of learning and teaching.

The Ten Commandments of Mathematics

http://www.doe.virginia.gov/Div/Winchester/jhhs/math/humor/tencommd.html

The Ten Commandments of Mathematics for Students...LOL

Why Do I Need To Know This?

A great piece on the why question!

http://www.examiner.com/x-29491-Topeka-K12-Examiner~y2009m12d8-Why-do-I-need-to-know-this

Math Scores Do Not Show Much Progress

http://s.wsj.net/public/resources/documents/st_math1208_20091208.html



Based on NAEP

This Wall Street Journal on-line resource includes a sortable table of cities, 4th grade scores, 8th grade scores, etc to compare and contrast results.