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

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

I know you can solve it...but how fast are you?

Challenge your Math Skills

http://www.mathplayground.com/algebra_puzzle.html

Grammar Website

Grammar Website

http://www.grammarnow.com

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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

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.

Improve your writing skills - Don't repeat the same phrases and words

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Design Contest Submissions

Congratulations to Hiroki, $100 Winner, of the New PACE Learning Center Signage Design Contest



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Hiroki's Design








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Jeannette's Design
"Put on the window and layout like a street sign, Yellow and Black."
That's what happens when in my email I say, "You can try to post your design or email it to me and I will post it also. All formats are accepted including scanned cocktail napkins. ;P"
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Here's a quick sketch. My design approach is: Keep it simple. Keep it clean. Don't block up the window as I believe it is your only window?
As for the address & contact info - put it in the upper right block as they have now.
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Hey. Its great to see that PACE is growing. i also have a couple of questions:

where exactly do we upload our designs when finished?

and

are we limited to only the windows? or are we also able to put stuff on the brown marble around the door?

**************Here is my Entry 12/6/09***********************

Here's my design for the new location. While the design isn't very flashy or imaginative, I think its very functional and plausible.

A few notes on what I was thinking regarding my design:



1. On the left side of the doorway is a vertical PACE sign. My idea would be to have block letters that come out from the wall a little (not too much maybe about 2 inches or something). I figure you could probably use the light above it to shine on the name when it is nighttime or dark outside to draw attention.

2. I used the next window to show what PACE has to offer and included pictures that correspond to each area. The pics for Reading and Writing were taken from the PACE website. I put it random math symbols, then used a pic of a backpack from clipart. For small groups, I believe I remember seeing a symbol similar to what I made here on a poster at the DC Pace. It's meant to show one tutor to 4 students, which is what I figured you meant by the small groups. At the bottom is "Come on in...." A little corny, but i think its a way of inviting people who may be looking from the outside to check out PACE. As more incentive to come in, I've also put at the bottom "FREE academic Assessment." People generally have an attraction to the word free, and the whole idea is to get people to come inside so that you can really show what PACE has to offer, and really sell the program to parents/students.

3. The top window shows PACE Learning Center. I thought the name should go on the top, plus I realized that nowhere did I actually say what PACE is, so I thought it was important to show "Learning Center."

4. BIG logo on the front door (also taken from PACE website) for people to see when stopped at the stop sign you mentioned was nearby ( or maybe it was a bus stop). Under the logo is the website and phone number. I put the website first and made it slightly bigger because people might be interested in PACE, and might feel more comfortable checking it out online rather than calling in. Having the web address there makes it easy to see.

5. The bottom half of the door has "A Fun Place to Learn" which is aimed again to attract parents and students to PACE. Again, large font to make it easy to read while people are stopped in their cars/bus. Under that is business hours which I think is always good to have so people know when exactly PACE opens and closes. I remember being somewhere recently, and wanting to know how long the store would be open, but couldn't see a sign showing work hours anywhere.

So that's my design. Hopefully, if nothing else, you can take elements of my design and use it in the new location. Its great to see PACE is expanding, and I wish you nothing but the best.

Sincerely,

Jeremy

New PACE Learning Center's Judah Location-Design Contest

PACE Learning Center, an after-school educational center focused on teaching and inspiring students using small groups, is opening its 3rd location. The new location at 2436 Judah Street, SF CA 94122, is testament to the success of PACE's teaching philosophy and system that was founded 10 years ago in San Francisco.

Following our philosophy of supporting the community through education and innovation, we saw it fit to create a design contest and open entry to anyone and everybody via the Internet.

Winner of the design chosen will be paid a $100 pre-paid Mastercard!

Entries can include digital files, sketches, or other visual media. Clearly explained concepts that don't include exact text but might describe placement, color, or size is also acceptable.

To enter, create an account on this blog, comment on this post, and upload your design.

***Update 12/12/09***** There have been problems uploading designs to the blog. To submit your entry email your design to blog@pacekids.com. *********

Multiple entries are allowed.

Deadline for all entries must be received by December 11, 2009.

Judges for the design will include staff and students of PACE Learning Center.

Winner will be chosen by December 14, 2009.

The winner will be notified on December 15, 2009.

Essential elements that need to be included in the design are:
PACE Learning Center (our name)
415-123-4567 (our phone)
www.pacekids.com (our website)
(what we teach in English & Chinese)
Reading - 阅读
Math - 数学
Writing - 写作
Small Groups - 小班制度
Homework Help - 作业辅导

Examples of types of signage, decals on the windows, banners, fabricated light boxes/neon/flag like signs, again anything your creativity can imagine.

We are open to any questions you may have. Please include them in the comments.

Thank you and we look forward to your entry.

PACEFront-StreetView.JPG

PACEDoorBottomWindow-StreetView.JPG

PACETopWindow-StreetView.JPG

PACEEntry-InsideView.JPG

PACEFront-LeftAngle.JPG

PACEFront-RightAngle.JPG