Mike's Math Corner

          Getting ready to take the MCAS or SAT? Do some of those math questions leave you scratching your head wondering where to even begin? Each week I'll be solving a sample MCAS or SAT question. I will start out with ways to eliminate wrong answer choices, or if possible, solve the problem outright without using complicated mathematics. I will then solve the problem 'the hard way', using the tricks from those higher-level math classes.

         This week's problem is a SAT math question involving geometry that I found on analyzemath.com:
 
AC is a diameter of the circle shown below and B is a point on the circle such that triangle ABC is isosceles. If the circle has a circumference of 8 Pi, what is the area of the shaded region?

.

A) 16 - 8Pi
B) 64
C) 8Pi - 2
D) 4Pi -8
E) 4(2 - Pi) 


           This is definitely a 'hard' question. Circles, areas, and not even a radius to work off of. Lets say for a moment you forget how to work with circles completely. Start with the answer choices and USE YOUR CALCULATOR! Answers A and E are both negative numbers.  Areas are never negative, so these are out. Also, if you remember that the formula for the area of a circle has pi in it, any piece of that area has to involve pi as well. Answer B is wrong because it does not have pi, and because its WAY too large. Get this far, and you have a 50-50 shot, and we havn't even done anything yet. Answer C is around 23, and D is around 5. Looks like a pretty small portion of the circle, so I'd guess D if I had to.
        Now for some math. Luckily, they tell you the circumference, and the formula for that is provided on your reference sheet: C=2*pi*r-->8*pi=2*pi*r--->4=r At this point, since the answer choices vary by a large ammount, I would approximate BC as being a bit longer than the radius (say 5), and make a rectangle with height of ~1 (about a quarter of the radius) to approximate the shaded region. This gives you an area of ~5 square units which, yet again, points to answer D. 

        If you're still curious on how to get an exact answer: Because angle B lies on the arc of a circle, and intercepts a diameter, it must measure 90* (this is a geometry theorem). Therefore, the isosceles triangle is a 45-45-90.  Drawing a radius from the center of the circle (call it point O) to point B will make 45-45-90 triangle BOC (altitudes of isosceles triangles drawn from the vertex angle are also angle bisectors). Angle BOC, being 90*, represents a quarter of the whole circle. We can find that area with the formula (1/4)(pi*r^2)=(1/4)(pi*4^2)=4*pi. We can then subtract the area of triangle BOC, to leave us with the exact area of the shaded region. For triangle BOC: A=1/2*B*H=(1/2)(4*4)=8. The shaded region is then: A=4*pi-8, or roughly 5 square units. Answer D

           OK, so in review, on this hard SAT question, it was possible to make an educated guess after doing VERY little math and come up with the correct answer. Using only the formula for circumference, and approximating the shaded region as a simple rectangle also gave us the correct answer. Actually doing the math out was far from easy and, I imagine, time consuming (although congratulations are in order if you did manage to solve it!). Remember that the SAT is a timed test! It is designed around logic and challenges you to come up with simple solutions to complex problems. As such, solving this completely would be considered a waste of valuable time on the real test, and could leave you struggling to finish the section in time.

Local Children's Author Releases Book

Children’s author, a Taunton native, paints with words

Millie Hull swaps poetry for pastels

The book is illustrated by Linda L. Tillson of Raynham.

By Frank Mulligan

Lakeville Call

 

Lakeville —

The beauty of Millie Hull’s paintings portrays her love of the art.

Particularly her work in her beloved pastels.

But several years ago, Hull developed an asthmatic-like reaction to the presence of pastels and oil paints. She suffered severe headaches, as well.

She continued working in pencil, watercolor and acrylics but it just didn’t provide the same feeling of fulfillment.

So, as Hull tells it, she began “painting with words.”

She added, “I just love to write. When I couldn’t paint, I decided to write.”

She joined the Lakeville Council on Aging Writers Group, which was founded by Jane Rando, “a wonderful teacher,” and compared notes - literally - with a group of “very nice,” people.

In fact, her new children’s book, “Why? Why? Why?” is dedicated in part to Rando and classmates George Orall and Rollene Krim.

The book is illustrated by Linda L. Tillson of Raynham, and poses children’s questions in verse.

The musings include,

“Why do we have mosquitos,

fleas, hornets, ticks and flies?

We could live well without these things

I’m sure you realize.”

Hull, who is a Christian writer and has taught Sunday school for 34 years, finds the answer in her faith, which is shown in her own approach to art. When she was unable to paint, she didn’t grow bitter. She found another way to express herself.

And her faith is indicated in another verse, toward the book’s close.

“So someday I will ask Him for

I know that God will know.

But the first thing that I’ll ask Him

Is why He loves us so.”

“That’s the most important question,” Hull says.

Each of the children’s light-hearted questions, like why dogs run to greet while cats tend to shy away, why fish have scales and turtles a shell, rendered in verse is illustrated by Tillson. Hull, the former painter, raves about Tillson’s skill. “She does beautiful work and is a very humble person.”

Being a Christian writer of children’s books is a perfect mix for her, Hull says.

“It’s a mixture of my love of the Lord, love of writing, and mostly my love of children,” says the mother of two daughters and grandmother of four who lives in Taunton with her husband, Paul.

Hull adds with a laugh, “It’s a three-way combo.”

Hull and Tillson have a website at forward-light-publications.com and the book is available at Readmore Books in Taunton, Maria’s Card and Gift Shop in Middleboro, Bev Loves Books in Rochester and Heritage House Christian Bookstore in Brockton.

Copyright 2011 The Taunton Gazette. Some rights reserved

Read more: Children’s author, a Taunton native, paints with words - Taunton, MA - The Taunton Gazette http://www.tauntongazette.com/archive/x1705409606/Children-s-author-a-Taunton-native-paints-with-words#ixzz1F0FWaAPV

Beth's Book Corner

Hungry for a Good Read?

Here at Learning Magic, the buzz around the building is building about a brave new book. We’re all hooked on Suzanne Collins’ The Hunger Games series. Students and tutors alike are all talking about this series non-stop. This post-apocalyptic thriller popped up on Taunton High’s summer reading list this year, and caught us all by surprise. I picked it up a whim, and passed my copy on to MaryEllen. Since then several other tutors and students have all read the same copy, and we’re all in agreement: this is one of the most exciting books we’ve ever read.

Now, a book that centers on a reality television competition that pits teenagers against each other in a wild fight to the death in a post-apocalyptic futuristic society may not be everyone’s cup of tea. I know I was very hesitant, given the subject matter. But I was instantly drawn to Katniss’ heroic journey and her selflessness.

Now, this book might be a little intense for some young readers. However, anyone above the age of 13 should appreciate what this series has to offer. The language is easy to read, but chock-full of rich symbolism, similes, and metaphors. Action lovers will be on-edge during the battle scenes, and those with a romantic streak will be enthralled by the love triangle subplot. With parallels to Romeo and Juliet alongside gritty violence, there’s something for everyone.

If you’re like us, and cannot put down the first Hunger Games book, be sure to check out the next two in the series: Catching Fire, and Mockingjay. You won’t be disappointed.  Also, be on the lookout for the Hunger Games movie to be released in 2012!

http://www.suzannecollinsbooks.com/

Snow days for Taunton schools piling up - Taunton, MA - The Taunton Gazette

Snow days for Taunton schools piling up - Taunton, MA - The Taunton Gazette

Taunton —

After calling off school on Wednesday for the sixth time this year, Taunton is searching for ways to make up the canceled school days.

“Every option has pros and cons,” Superintendent Julie Hackett said.

Options on the table include going to school during vacations or on Saturdays. The School Committee plans to hold a meeting at 5:30 p.m. Monday at Pole School to discuss the issue.

Whichever decision is made, committee chairman Joseph Martin said he doubts it will please all parties involved.

“Everyone’s not going to be happy,” he said.

As things currently stand, Taunton schools would let out on June 28 if there are no more cancellations. With inclement weather becoming commonplace this winter, however, additional snow days are a real possibility.

Taunton is in a particularly precarious situation because it didn’t start school until Sept. 7, due to a request from the contractors performing renovation work at Taunton High School.

Many school districts across the region face the prospect of making up snow days to ensure that students had 180 days of classes. The current fiscal year ends June 30, so going to school into July is not a likely option.

The fiscal calendar not withstanding, Hackett said she does not believe in sending students to school during the summer break.

“We wouldn’t want to go to school beyond July 1,” Hackett said.

Martin suggested a potential way to make up snow days without having to cut into vacation time or weekends. The idea would be to lengthen some school days in order to make up the time. Depending on how many hours are added to a school day, two or three extended days could potentially make up time from one snow day.

Hackett said she asked the state Department of Elementary and Secondary Education whether such a plan would be allowed. She expects an answer in the coming days.
“I think extending the school day makes a lot of sense,” Hackett said. “The transportation’s already there, the students are already there, the teachers already there.”

Such a plan could potentially cause scheduling conflicts with after-school sports and other activities.

“Anything you come up with, you’re going to come up with issues,” Martin said. “There’s not going to be any easy solution to this.”

He and Hackett noted that many high school students work on Saturdays, and many families have already made plans during school vacation weeks.

Hackett said several parents have emailed her with suggestions of going to school on vacation days. She said she plans on sending a notice on the matter to parents and staff members.

“I’m interested in hearing what staff and families have to say,” she said.

Taunton Education Association president Janet Anderson said the teachers union plans to meet with members to discuss the options for making up snow days. She said she has also discussed the issue with Hackett.

“We’re going to work on it,” Anderson said. “We’re going to see if we can come up with a solution that works with minimal disruption.”

Contact Gerry Tuoti at gtuoti@tauntongazette.com

Snow!

Learning Magic will be open again today, February 3rd after the winter weather kept us closed for the past two days! How did you spend your snow days?