Additional Math Pages & Resources

Tuesday, February 28, 2012

It's a Pain in the Neck

Have you ever had one of those aggravating cricks in your neck that just won't go away? Neck pain can make it difficult and even downright painful to turn your head, comb your hair, get dressed, and complete everyday tasks.

Excel Math is designed to help students learn skills they can apply to their lives so they can grow into adults who are not pains in the neck (but who have higher-level thinking skills and are proficient in elementary math concepts). 

Here's a Student Lesson Sheet from the Fifth Grade Excel Math Lessons. You can try a few problems and confirm your work by adding the the answers for the problems in each box. If the sum of those answers matches the Checkanswer in the corner, you are correct. For the first box you would add the three answers together (one word problem and two division problems) to get $28.60 (shown in box A). This page is designed as Guided Practice—problems the students can do in class, guided by the teacher, after the lesson is presented:
Fifth Grade Excel Math Student Sheet

These Guided Practice sheets give the teacher a chance to move around the room and give students individual help, as needed. While the other students work through the problems on their own, the teacher can see at a glance which students are having trouble getting the correct Checkanswer (in the lettered sections) and can be available to instruct those students one on one.
Some students (and teachers and office workers) may get occasional neck pain from poor posture, sitting slumped over their desks or computers. In fact, neck pain is a common condition that affects an estimated 70% of persons at some point in their lives. Studies estimate that 10.4% to 21.3% of people will develop neck pain in a one-year period, with a higher incidence noted in office and computer workers. (No surprise there.)

The prevalence of neck pain is generally higher in women than in men, higher in high-income countries than in low- or middle-income countries, and higher in urban areas than in rural areas. Many factors influence the onset and course of neck pain, including risk factors outside our control such as age, sex, and genetics. 

If you have neck pain (or any other kind of pain), your doctor may ask you to rate the pain on a scale of one to ten. This is the Wong-Baker Facial Grimace scale:

Click this image for a more elaborate version.

Clinicians offer various therapies to patients who are looking for relief from neck pain: 
  • medication
  • manipulation and mobilization 
  • massage 
  • acupuncture
  • electrotherapy 
  • exercises
  • traction
  • patient education
  • biopsychosocial rehabilitation
The first federally-funded studies on neck pain examined which treatments of three treatments were most effective. As reported in the Annals of Internal Medicine, researchers in Minnesota tested 272 people between the ages of 18 and 65 who had nonspecific neck pain for 2 to 12 weeks. They wanted to determine whether spinal manipulation therapy, medication, or home exercise with advice  worked best for acute and subacute neck pain in both the short and long term.

The studies found that for participants with neck pain, spinal manipulation by chiropractors was more effective than medication in both the short and long term. However, a few instructional sessions of home exercise (such as gentle stretching) resulted in similar outcomes at most points in time. One measure showed about 80% of patients in the spinal-manipulation group and the home exercise groups reported a reduction of at least 50% in pain levels after 12 weeks compared with about 70% of people in the medication group. 

About 30% of patients in the exercise and manipulation groups reported a 100% reduction in pain levels during the same time period compared with about 13% of patients in the medication group. "It's good news for patients that there's something they can do themselves," says Gert Bronfort, vice president of research at Northwestern Health Sciences University in Bloomington, Minnesota, and the study's lead author.

Online Graphing
Source: Annals of Internal Medicine

On the other hand, according to the authors of the editorial, Pain in the Neck: Many (Marginally Different Treatment Choices) from the Annals of Internal Medicine, the findings of available studies do not give us one single, optimally effective treatment for neck pain. Overall, most therapies had low to moderate effectiveness. And even the Minnesota study mentioned above did not include a placebo group and did not track whether patients actually adhered to home exercise or medication. They were free to add additional therapies to their treatments as they wished. In other words, everyone's situation has to be evaluated on a case by case basis, in consultation with a professional, to determine the best treatment or treatments for their particular needs.

To prevent neck pain, try doing moderate exercise on a regular basis. Swimming, walking, stretching, and biking can all help strengthen your body and keep you in shape. (Consult your doctor before beginning any exercise program.) When seated in front of a computer, take frequent breaks. Get up, walk around the room, stretch, and change your position. Once you begin to feel discomfort in your neck, check with your healthcare provider, and then ease some of the pain with this simple exercise: Gently retract your neck, pulling your head back like a chicken, and then tilt your chin slightly downward. Do you think a relaxed version of the chicken dance would work just as well?

Wednesday, February 22, 2012

Whose Head Is on That Coin?

Can you name the presidents on the dollar bills? How about on coins?

In Excel Math, we teach students how to add dollars and coins and make sense of monetary calculations. Pictured below is a Guided Practice page from the Excel Math Second Grade Teacher's Edition. See if you can solve these problems without looking at the answers. Section E uses coins of various values. Can you recognize them? (We've provided the answers so you can check your work.)

Excel Math Grade 2 Student Lesson Sheet

Excel Math Lesson Sheets contain problems supporting the Daily Lesson, short Basic Fact Practice (when appropriate), in-class Guided Practice, and Homework. The Lesson Sheet above is a good example of the in-class Guided Practice led by the teacher.

Now back to coins. In 1900 George Washington was first commemorated on a U.S. Mint dollar coin along with the Marquis de Lafayette (all of the United States coin and currency images pictured here are from the United States Mint):
Born in 1757 to wealth and privilege, at the age of twenty the Marquis de Lafayette sacrificed everything to support the American revolutionary cause. Lafayette’s Revolutionary War heroism and his efforts to get the French government to sign a treaty of alliance with the colonies in 1778 earned him fame and respect on both sides of the Atlantic. In 1784, the State of Maryland bestowed citizenship upon Lafayette and his descendants.

In 1824, while on a tour of the United States accompanied by his son George Washington Lafayette, Congress awarded LaFayette land in Florida and $200,000 in cash. The next year, LaFayette returned to Virginia and presented the Masonic Lodge in Alexandria with a 10-inch long key to the Bastille. In 1790, LaFayette sent George Washington a second key to the Bastille, which is on display at Mt. Vernon. Here is the reverse of the coin pictured above. It depicts a statue of LaFayette on horseback. The inscription reads, Erected by the Youth of the United States in Honor of Gen Lafayette Paris 1900:

The Mint Act of 1792, which created the United States Mint, specified that certain design features appear on legal tender coins, including the quarter. One side of the coin had to include the year in which it was minted, an image that symbolized liberty and the inscription LIBERTY. The reverse (tails) of the quarter featured an eagle and the inscription UNITED STATES OF AMERICA.

In 1932, the 200th anniversary of Washington's birthday, a profile of President George Washington's head replaced Lady Liberty. To celebrate the Bicentennial in 1976, a colonial drummer replaced the eagle on the reverse. In 1999 the quarter's reverse underwent its first of 50 changes under the 50 State Quarters® Program to honor each state. Here are some of those state quarters. George Washington's profile appears on the obverse or heads side:
Arkansas Quarter from the
50 State Quarters® Program
Kansas Quarter
Louisiana Quarter
Arizona Quarter

Washington Dollar

And the Washington dollar with George Washington's face on the obverse side:
In 2010, the United States Mint launched the United States Mint America the Beautiful™ Quarters Program. This is the El Yunque National Forest coin depicting a Coqui tree frog and a parrot from Puerto Rico. Each coin in the series features a common obverse with the 1932 portrait of George Washington by John Flanagan:

Laura Gardin Fraser (1899-1966) became the first woman to have her design appear on a commemorative coin when she designed the obverse of the 1921 Alabama Centennial Half Dollar picturing William Wyatt Bibb, the first governor of Alabama, and Thomas E. Kilby, the then-current governor:
In 1931, Congress held a competition for a coin to honor the 200th anniversary of George Washington's birth. Ms. Gardin Fraser submitted a design that, though popular, was not chosen. Her design, however, was revived for the five dollar gold coin 68 years later, in 1999:

There are even coins honoring the spouses of Presidents:
Martha Washington Dollar

We may be most familiar with the one dollar bill depicting George Washington in the center:

Thomas Jefferson's image also appears on various coins. Do you recall which ones?
Here are two of them:
Jefferson Nickel
Jefferson Dollar

Monday, February 20, 2012

Counting All Presidents and Their Vices

Today we celebrate Washington's Birthday. George Washington was the first president of our United States. Not many people can name all of the presidents of the United States. And it's quite a bit more difficult to name the Vice-Presidents. A few of them actually became president. Do you recall which ones moved into that office?

In Excel Math, we help students learn elementary math concepts they can apply to their lives as they grow up.

The White House
How many of the United States presidents can you name? In case you need a refresher, we've listed their names along with links to the website with more information about each of them:

18th Century

19th Century

The Washington Monument

The Washington Monument Close-Up

The Jefferson Memorial
20th Century

Lincoln Memorial

21st Century

And here, from the website are the presidents listed with their dates of office and their vice-presidents:

Vice President

If you click on a Vice President’s name who did not also serve as president you will be taken to the page for the President they served. 

Only two U.S. Presidents are buried at Arlington Cemetery. Can you name them?
Arlington Cemetery
Here are their tombstones:
John F. Kennedy's Gravestone
William Howard Taft's Tombstone

Tuesday, February 14, 2012

Going to the Dogs, Part II

Yesterday we met a few of the 78.2 million dogs with owners in the United States. Let's visit a few more today. Here's Bodi, a seven-year-old Great Pyrenees from Lincoln, Nebraska. He is a very spoiled rescue dog:

Bodi's owner spends about $500/year on vet bills and routine treatments for heartworm, tics and fleas. Today we'll discover some additional ways pet owners (and dog and cat owners in particular) spend their money. Learning to compare costs in elementary math can help prepare us for the real world and budgeting for our own expenses as well as for our pet's.

The American Pet Products Association estimates that $50.84 billion dollars was spent on our pets in the United  States in 2011. In 2010 we spent $48.35 billion dollars on our pets. Here are the actual sales of pet products (food, supplies and over-the-counter medicines, veterinarian care, live animal purchases, and grooming and boarding) within the U.S. market in 2010:
2010 Pet Products Sales in the U.S. (in Billions)

Basic annual expenses for dog and cat owners in the United States include surgical vet visits, routine vet visits, food, kennel boarding, travel expenses, vitamins, grooming and grooming aids, and food treats. Comparing the expenses of dogs and cats, dogs turn out to be a bit more costly overall, but cats tend to cost more in surgical vet visits.

Basic Annual Expenses for Dog and Cat Owners (in Dollars)

After taking a look at some of the high costs associated with pet ownership, you might think pet owners would suffer from high blood pressure and depression. Not true. Having a pet can actually help fight depression and loneliness, giving people a reason to take an interest in life. When seniors face adversity or trauma, affection from pets is especially important. The bonding behavior between pets and their owners can give people a sense of security. (Between Pets and People: The Importance of Animal Companionship)

Pets can also help to lower health care costs. People with pets actually make fewer doctor visits, especially for non-serious medical conditions. (National Institute of Health Technology Assessment Workshop: Health Benefits of Pets)

This is a photo of Muffin, an eleven-year-old Cockapoo. Muffin's owner spent about $400 to have her teeth cleaned and a few teeth pulled last year. Here she is helping her family get the house decorated for Christmas:
And here's her neighbor making Valentine's cookies. Muffin is on her way over to check them out. Wishing you and your pet another year of good health and fabulous friendship! Do you have a pet? If so, take our poll on the left sidebar and let us know which one(s) you have.