# The Big Competition

The kids guessed the weight of this acorn squash at Palo Alto’s Mathnasium.

This week, Palo Alto’s Mathnasium decided to have a fun competition. We asked all of the kids to hold an acorn squash and guess how

much it weighs. The kids were allowed to use other objects, whose weights were known, to compare its

weight. The acorn squash

weighed a total of  2 pounds and 7.1 ounces. After all of the kids voted, four winners were announced. These winners were the closest to the squash’s true weight.

# Weight Fun in Palo Alto

The competition we did is a great way to teach your child about weights. Take any fruit or vegetable found in your home, like pumpkins or sweet potatoes, and ask your child to guess how much it weighs. Let them compare the foods’ weight to other weights (like a gallon of milk or a candy bar). After they guess, weigh it and see if they came close to the food’s true weight. After, you can ask them to calculate how close they were (subtracting the food’s true weight from their guess). You can also ask your child to convert their answer from pounds to ounces, or from pounds to kilograms.

1 pound = .45 kilograms              1 pound = 16 ounces

Weighing different foods is fun and can help teach your child about weights!

# Pumpkin Pi(e) and Other Fall Math Facts for Palo Alto

Fall is here again, and that means it’s time for warm clothes, red and gold leaves, and costumed children walking around the Palo Alto streets. But when it comes to fall flavors, there’s only one food that stands apart: pumpkin. Whether it’s in a pie, a bread, or even Starbucks’ now famous Pumpkin Spice Latte, this big orange squash is the hallmark of the season. But how much do you really know about the pumpkin? Here’s some mathy pumpkin facts to show off this fall in Palo Alto.

## Many Shapes and Sizes

Pumkins are one of the most diverse fruits (yes, it’s a fruit!) in the world, with over 100 varieties growing across the world. They originally grew in North America, and were brought to Europe in 1584 by Jacques Cartier, almost 430 years ago. Pumpkins range in shape from fairly flat and squat to almost perfectly spherical, and in size from only about 5 inches across to a whopping 2,009 pounds, the world record holder grown last year by Ron Wallace in Rhode Island. Pumpkins for baking and eating tend to be smaller than Jack-O-Lanterns, such as the Sugar Pie and Cinderella pumpkins, and sometimes they’re even hollowed out and used as their own baking dish.

## Pumpkin Math Fun around Palo Alto!

Besides being used for eating and carving, pumpkins can be a fun way to learn math in the fall! Since they’re close to circular, pumpkins

Math-themed pumpkins decorated by one of our Palo Alto-Menlo Park Mathnasium students.

can be a good way to practice your geometric formulas for circles and spheres. For example, if a large spherical pumpkin has a diameter of 1.5 feet, what is its circumference, it’s surface area, and its volume? The circumference would be 4 feet 8.5 inches, the surface area would be 7.07 square feet, and the volume would be 1.77 cubic feet. For those that are a little rusty on their formulas, remember that

c=?d, SA=4?r^2, and V=(4/3)?r^3.

Regular pumpkins take around 100-120 days to grow, and are usually planted in late May or early June. If a pumpkin is planted on June 1st, when would it be ready to pick? 100 days after June 1st would be  September 8, and 120 days would be September 28.

Pumpkins are delicious, fun, and full of mathy potential. There are pumpkin patches in Redwood City, Mountain View, and Half Moon Bay, all just a short drive from Palo Alto, so head out and practice your geometry with your kids soon!

# Bay Area Transportation and The Math of the Morning Commute

The Bay Bridge during light traffic. Millions of people commute across the Bay Area every day.

We’ve always known that getting around the Bay Area at rush hour is a mess. Freeways and surface streets from Palo Alto to Vallejo grind to a standstill, and buses and trains are packed like sardine cans. But recent events such as BART strikes and bridge upgrades have revealed just how complex the transportation network in the Bay Area can be.

## A Lot of People, a Big Bay

The Bay Area, including the counties of San Francisco, San Mateo (home of our Mathnasium of Palo Alto-Menlo Park), Santa Clara, Alameda, Contra Costa, Marin, Napa, and Sonoma, and Solano, has a total population of about 7.2 million people. However, unlike other large metropolitan areas, which typically have one primary employment hub, the Bay Area has many different commuter hubs, including the Financial District of San Francisco, downtown San Jose, the tech centers of Silicon Valley and the peninsula, downtown Oakland, and more. For this reason, people are travelling both ways every morning and night, meaning that there’s no street or freeway that’s safe.

In addition, the Bay Area’s geography makes the commute even more complicated. The huge San Francisco bay is traversed by only five bridges: the Bay Bridge from San Francisco to Oakland, the Golden Gate Bridge from San Francisco to Marin County, the San Mateo Bridge from San Mateo to Hayward, the Dumbarton Bridge from Menlo Park to Newark on the East Bay, and the San Rafael bridge from Richmond on the north bay to San Rafael on the Marin peninsula. Mountains also make road-building hard, resulting in features such as the congested Caldecott Tunnel through the Berkeley Hills.

The Bay Area recently became the metropolitan area with the highest percentage of “mega-commuters,” people drive at least 50 miles and spend 90 minutes on their morning commute; the rate for the Bay Area was 4 times that of the United States overall!

## The Options for Bay Area Commuters, and the Results

Besides taking the congested freeways such as US 101 from San Jose to San Francisco through Palo Alto or Interstate 80 through Berkeley and Emeryville, many residents take public transportation such as BART, Caltrain, or the myriad bus systems on their daily commute.

BART, the largest system in the Bay Area, consists of five lines and has an average weekday ridership of about 400,000 passengers across the East Bay, San Francisco, and the northern Peninsula. Caltrain, which runs from Gilroy to downtown San Francisco, has an average weekday ridership of about 50,000.  Interestingly, a few single Muni buses in San Francisco have daily ridership of over 30,000, such as the 38 bus from the Richmond District to downtown, which runs every minute during rush hour.

Regardless of one’s mode of transportation, commute times for the Bay Area certainly aren’t short, as the math shows. Santa Clara County residents averaged 25 minutes of commute time, with most people working within the same county. Residents of San Francisco travel 30 minutes every morning on average.

Learn more about Math Tutoring at the Mathnasium of Palo Alto-Menlo Park and how we apply math to the real world at  http://www.mathnasium.com/paloalto-menlopark

# Dinosaur Math for Atherton Kids

The key to making kids interested in math is to apply it to what they already love. For a lot of kids (and some adults as well!), there are few things as cool as the gigantic reptiles that walked the Earth tens of millions ago: dinosaurs. While the science behind them is changing every year (velociraptors are now thought to have had feathers over their entire bodies), the appeal of dinosaurs remains constant, and if parents can link them to math, then the excitement may carry over, inspiring them to succeed in their Atherton-area schools.

A Spinosaurus, as drawn by one of our Palo Alto-Menlo Park Mathnasium 5th graders.

## Digging Up Dinosaur Word Problems

If your kids are anything like some of the students in our Mathnasium center, then they already know almost everything there is to know about dinosaurs. If you want to engage them with fun dinosaur math problems, then a little bit of independent research may be necessary. Anything with numbers is good to know: a dinosaur’s weight, length, or time period can all be put into problems. Additionally, using the standard dinosaurs like Tyrannosaurus Rex or Apatoasaurus won’t cut it anymore; try looking up some more exotic species such as the Pachycephalosaurus or the Microraptor, a 3-foot long, 4-winged bird-like dinosaur that attacked birds, fish from the air. If you can’t find information easily online, take a trip to the Atherton Library on Dinkelspiel Station Lane or the Menlo Park Library on Ravenswood Avenue with your kid, and let them teach you from the books.

## Some First Ideas

Although the best dinosaur word problems will be made at home with help from your kids, here are a few ideas to get you started, as suggested by one of our Mathnasium 5th graders from Atherton.

1) Many large carnivorous dinosaurs would eat, on average, up to 1.5% of their body weight each day. If a spinosaurus, one of the largest carnivores ever, weighted 7 tons, how many pounds of food did it have to eat each day?

Answer: 210 pounds (remember, 1 ton is 2000 pounds)

2) Many scientists think that Spinosaurus ate mostly fish. If a Spinosaurus needed to eat 210 pounds a day and he ate only large Atlantic Salmon, which weight about 30 pounds, how many of these fish would he need to eat each day?

3) If the Giganotosaurus, one of the largest carnivorous dinosaurs ever discovered and one of the only ones suspected to prey on massive herbivores, and the Diplodocus, a huge herbivore that grew up to 120 feet in length including it’s whip-like tail, had lived at the same time, they would have had some incredible fights. However, the last Diplodocuses died about 151 million years ago near the end of the Jurassic, while the first Giganotosaurus lived about 99 million years ago. How many years existed between the times of the Diplodocus and the Giganotosaurus?

# Mathnasium and Fractions: How to Turn a Hard Topic into a Fraction of Cake

Fractions are hard. Many kids come to Mathnasium in Palo Alto to improve their fraction skills, and in turn, we provide our students with tons of practice, until they master the topic both conceptually and practically.

According to a recent Wall Street Journal article, fractions are essential to success in more advanced math, and not all methods of teaching fractions are equal! Rather than memorizing algorithms for addition and multiplication with fractions, students benefit more from understanding fractions in depth, and how they relate to each other, and only then jumping in to complete calculations.

Part of the new Common Core  standards requires mastering certain topics, and you can bet that teaching fractions well is one of the top priorities of this new curriculum! Just how important are fractions? According to the article,

A child’s knowledge of fractions in fifth grade predicts performance in high-school math classes, even after controlling for IQ, reading achievement, working memory, family income and education, and knowledge of whole numbers, according to a 2012 study led by Bob Siegler, a professor of cognitive psychology at Carnegie Mellon University.

The finding is based on long-term studies of a total of 4,276 students in the U.S. and Britain comparing their scores on math tests at ages 10 to 12, and again at ages 16 to 17, then controlling the results for differences in the children’s intelligence-test scores and family background. Researchers believe the reason may be that to master advanced math, students must broaden their understanding of how different kinds of numbers relate to each other, and how they must apply different rules as needed when working with different kinds of numbers.

So how can you help your children in master this challenging but important topic? Here in Palo Alto, we use methods like those of the Augusta, Ga. Mathnasium location highlighted in the article, as well as ideas tested in the research explained in the Wall Street Journal. Here are a few essential points:

• Introduce problem solving only after students understand the meaning of the numerator and denominator of a fraction.
• Use number lines to help students see differences in size.
• Explain that denominators are the “name of a fraction”, rather than just the bottom number.
• And most importantly, make sure that students don’t just learn math, but learn to enjoy it as well!

Learn more about Math Tutoring and Mathnasium of Palo Alto-Menlo Park (and find more fun word problems) —  http://www.mathnasium.com/paloalto-menlopark