Wednesday, March 31, 2010

Squaring two digit numbers in your head

Squaring two digit numbers in your head


[W]hat's 272. Of course, the brute force way to do that is to calculate 27 x 27 which is a bit of a pain because it involves doing something like 27 x 20 + 27 x 7 = 540 + 189 = 729. But there's a much faster way.


Observe that 272 = 30 x 24 + 32. Since you probably know that 32 = 9 this means you have to calculate 30 x 24 + 9 which is relatively easy because the multiplication involves a multiple of ten which means it's really 3 x 24 and then add a zero.



So the rule is that if you want to square number X you first round it to the nearest multiple of 10, called that X + r, and then calculate X - r (i.e. round the same amount in the opposite direction). You calculate (X + r) x (X - r) and add back the square of the amount you rounded by, r2, which will be 1, 4, 9, 16 or 25.


This works because ( X + r ) x ( X - r ) + r2 = X2 - rX + rX - r2 + r2 = X2.





Squaring two digit numbers in your head

Wednesday, March 24, 2010

NYTimes.com: Reading Scores Lagging Compared With Math



The nation’s schoolchildren have made little or no progress in reading proficiency in recent years, according to results released Wednesday from the largest nationwide reading test. The scores continue a 17-year trend of sluggish achievement in reading that contrasts with substantial gains in mathematics during roughly the same period.

“The nation has done a really good job improving math skills,” said Mark Schneider, a vice president at the American Institutes for Research and a former official at the Education Department, which oversees the test, known as the National Assessment of Educational Progress. “In contrast, we have made only marginal improvements in reading.”

Why math scores have improved so much faster than reading scores is much debated; the federal officials who produce the test say it is intended to identify changes in student achievement over time, not to identify causes.

In seeking to explain the lagging reading scores, some experts point to declines in the amount of reading children do for pleasure as they devote more free time to surfing the Internet, texting on cellphones or watching television. Others blame undemanding curriculums.

For example, Susan Pimentel, an expert on English and reading standards who is a member of the governing board that oversees the test, said that American schools were fairly efficient at teaching basic reading skills in the early grades, but that as students matured they need to be consistently challenged to broaden those skills by reading not only complex literature but also sophisticated nonfiction in subjects like history and science.

“We’re not asking them to read nearly enough,” Ms. Pimentel said.

One group of students, though, has made significant gains in reading over the last decade: the nation’s worst readers. The average scores of fourth graders in the bottom 10 percent for reading increased by 16 points from 2000 to 2009. In contrast, the average scores of the nation’s best fourth-grade readers, those in the top 10 percent, rose by only 2 points during the same period.

“All the progress in reading is being made at the bottom,” said Tom Loveless, a senior fellow at the Brookings Institution. “Our worst readers are getting better, but our best readers are staying about the same.”

Sheila W. Valencia, an education professor at the University of Washington, said the Bush administration’s $1-billion-a-year reading initiative, Reading First, focused instruction in thousands of public schools on building lower-level reading skills.

“We have evidence that Reading First helped young students increase their ability to read words, but not their capacity for comprehension, and the national assessment especially measures reading comprehension,” Professor Valencia said. “So that’s one hypothesis for why scores have stayed pretty constant.”

The reading test, mandated by Congress, was given to 338,000 fourth- and eighth-grade students last spring. Results of the math test, also administered last spring, were released in October.

On average, eighth graders scored 264 on a 500-point scale in reading, compared with 263 in 2007, when the test was last given. Fourth graders scored 221 on the 2009 test, the same average as two years earlier.

Read more

Friday, March 5, 2010

Paper Rater Analyzes and Improves Your Writing



If you like to write but lack confidence in your skills, Paper Rater is a a free, web-based service that analyzes your writing and offers feedback on your grammar, spelling, and more.

Paper Rater couldn't be easier to use. Just paste in the text you want analyzed, choose what type of content it is—essay, research paper, speech, etc.—and submit it for review. Within seconds, Paper Rater generates a report that analyzes several aspects of your submission.

Naturally, the app takes a look at grammar and spelling, but it also gives feedback on your writing style and choice of words. To get suggestions on word or phrasing replacement, just right click on the highlighted words.

Paper Rater also detects plagiarism by comparing the content you submit with published online content to see if there are any similarities. This feature can be overridden by simply flagging passages with the proper citations.

Paper Rater is a solid tool for double-checking your work as you prepare your next speech or presentation. What tools do you rely on to hone your writing skills? Share in the comments.

Paper Rater

Sunday, January 3, 2010

Get a preview of PACE Learning Center on Judah

Opening Monday, January 4th, 2010. Our newest location at 2436 Judah Street, between 29th and 30th Avenue, in San Francisco, CA 94122, will offer small group academic tutoring for students grades K-8 and starting on Saturday, January 16th, 2010 Test Preparation classes will begin for grade 2-8.

Hours of operation:
Small Group Tutoring
Monday through Thursday 2:30pm-6pm
Test Prep Classes
Saturday & Sundays 9:30am-4pm

For questions, call us 415-681-7223.
Or email us at learn@pacekids.com

Look at a few of the Judah Street PACE Learning Center's location photos. Starting from the first day.