More Summer Math for Palo Alto Kids!

Summer has come to an end for students in Palo Alto, Menlo Park, and other local schools. Here are some summer themed problems to commemorate for your Palo Alto, Menlo Park student!

Palo Alto vacation math help

The Twelve Apostles in Victoria, Australia
Photo from

  1. You’re going to spend 3 weeks in Europe! You want to visit one city per week, which means that you get to visit 3 cities. Your choices are Paris, Barcelona, Rome, Munich, and Athens. How many different combinations of cities can you visit? (Hint: the order doesn’t matter!)
  2. You’re flying to Australia! Your flight leaves at 10:30 am in the morning (Palo Alto time), and lasts for 11 hours and 20 minutes. In Australia, your watch is set 19 hours FORWARD. What time is it in Australia when you arrive?
  3. You’re eating dim sum in Hong Kong and buy $50.25 worth of food. You pay a tax of 5.2%, and then you pay a tip of 15% (15% of the food and tax combined). How much money did you spend for lunch?
  4. Plane tickets to Argentina cost $1,620 and your family buys 12 tickets (for your grandparents and cousins too!) How much did they spend on plane tickets?

These summer math problems will keep you entertained for a little bit! Be sure to keep practicing your summer math skills, and to take advantage of this summer for some math tutoring and learning! For more information and recommendations for math practice, check out the Mathnasium of Palo Alto – Menlo Park’s website.


Math on the Beach near Palo Alto

It’s almost summer in the Bay Area! Local schools in Palo Alto, Menlo Park, Redwood City, Stanford, and other neighboring areas will be out soon! However, while summer’s a great time to have fun, it’s also an opportunity to practice your math! Here are some beach-themed math problems to celebrate summer, and to help hone your math skills!

Beach math palo alto

Photo by Teinesavaii, via Wikimedia

  1. When you get to the beach in the afternoon, it’s 83 degrees Fahrenheit, but after sunset, it’s only 68 degrees! By how much did the temperature decrease?
  2. You go to the beach with 7 friends. At the boardwalk, everybody each buys 2 cotton candies at $1.30 each, and 3 funnel cakes each for $3.50. How much did everyone spend altogether?
  3. After a game of volleyball, your opponents scored 12 less than 3 times of the points that you scored. Your team scored 7 points. Who won the game?
  4. The distance between Palo Alto and the beach is 20 miles, and you complete the drive in 30 minutes. What speed did you drive at (in miles per hour)?

We hope that practicing your math skills on these problems will keep your math abilities strong for the next school year at your Palo Alto, Menlo Park, Redwood City local school! For more information and recommendations for math practice, check out the Mathnasium of Palo Alto – Menlo Park’s website.

Hey Palo Alto, here’s a cool math trick: .999… equals 1

Math trick for Palo Alto math lovers: Why .999… equals 1

We’re all smart in Palo Alto. We’re probably smarter than most other people. But some things, we just haven’t thought of before. Or maybe, you thought about them back when you took Calculus in college, but it’s been a while. Well don’t you worry, those of us who still use math in our daily lives love sharing fun mathy facts to the rest of our intelligent Palo Alto friends!

You’ve probably heard before that the repeating decimal .999… equals 1. And with a little long division, we can see that this is so. Or if you like, we can split it up into 1/3 and 2/3, two things that add to 3/3, which we know is 1.

2/3 is equal to .666… and 1/3 equals .333…

If we add these, we can see that

2/3 = .666…

 + 1/3 = .333… 

3/3 = .999…

There we go! 1 = .999… – done! How easy was that? Most of us are satisfied with that as proof! So we must be correct.

What’s that? A select few sceptics are still in disbelief? How could .999… equal 1, you say? Isn’t it always .0…01 away from equalling 1?

Hmm… Well maybe we can try something else. Let’s break this up into what we really mean. How about a (geometric) series of numbers that add up to .999…, like this one:

.999… = .9 + .09 + .009 + .0009 + .00009  …

Okay, cool. Let’s rewrite these as fractions:

.999… = 9/10 + 9/100 + 9/1,000 + 9/10,000 …

Now, we’ll think about what defines a geometric series like this. These things take a sequence of numbers and add them all up. This sum that we have heads in some direction. Sometimes, it can lead toward infinity, like when adding a sequence like 1, 2, 4, 8, 16 … – we call this a diverging series. Other times, though, the sum of the numbers in a sequence head towards a particular number as you add each next term. For example, if we try to add the terms in the sequence 1/2, 1/4, 1/8, 1/16, 1/32 … Our first two terms add up to 3/4 (.75), the first three add to 7/8 (.875), the first four add to 15/16 (.9375), and the first five add to 32/33 (.9696…). Every term we add will bring us closer and closer to a fraction which equals one.
Because of this, we say that the series converges at 1, or that the sum of the infinite terms in the sequence is 1.

When we start adding the terms in our series here, we’ll get that our first two equal 99/100, our first three equal 999/1,000, our first four equal 9,999/10,000, and our first five equal 99,999/100,000. Here we can see that the more terms we add, the closer we get to equaling 1!

Though we may never reach one by adding the terms of this sequence, as we head toward infinite terms, we can show that the limit of the sum is 1.

So, call it crazy, or wizardry, or a flaw in the decimal system, but .999… and 1 are two different ways to represent the idea of the same real number!

For more math tricks in the Palo Alto area:

Check out Mathnasium of Palo Alto-Menlo Park alto math trick

Hey, math and Stanford Fans! Try some football word problems

Here in Palo Alto, there are a lot of Stanford fans.  Stanford has one of the best college football teams in the country, coming in at  #5 in the rankings this week.  They have a flawless record of 3-0 after beating San Jose State, Army and Arizona State.  However, 19 of the top 25 teams have not lost a game this year, and all of them have 3 or more wins.

Stanford math word problems

Stanford math word problems

So why is Stanford number 5 and not number 25 like Fresno State, who is also 3-0?  Here at Mathnasium, because we are near Stanford, we are working to figure out how these rankings work.  Many different variables go into deciding who will be ranked, and what they will be ranked.  These include points scored, points allowed, strength of schedule, yards gained, yard allowed, and many more.  We will try to begin figuring these rankings with a few word problems. Can you help us by solving these word problems?

Here are the fun Stanford math word problems:

1. Stanford scored 34 points in their first game, 34 points in their second game and 42 points in their most recent game.  How many total points have they scored so far this season?

2.  Stanford’s opponents have scored 13, 20 and 28 points.  How many total points has Stanford allowed?  How many more points have they scored than they have allowed?

3.  Oregon has scored 66, 59, and 59 points, respectively in their first 3 games. They are ranked #2 in the country.  How many total points has Oregon scored?  How many more points has Oregon scored than Stanford?

4.  Find the average number of points that both Stanford and Oregon score per game.  To do this, take the total number of points that you already calculated, then divide by the number of games, 3.

Challenge Word Problem for extra smart Stanford kids:

5.  Pretend the rankings are based completely on points scored.  If Oregon scores 27 points in their 4th game against Cal, how many points would Stanford need to score in their game in order to overtake Oregon in the rankings?

At Mathnasium, we are more focused on math than football.  But, if we did have a football team, we would know exactly how to be #1!

Learn more about Math Tutoring and Mathnasium of Palo Alto-Menlo Park (and find more fun word problems) —


Saving Menlo Park with Math

The weather in the Bay Area is some of the best in the world.  You could go to Menlo Park at any time of year and you probably wouldn’t be able to guess the season.

Unfortunately, environmental issues like global warming and climate change might ruin that.  So we decided that instead of just helping kids with math, we would help the world too! Now, Mathnasium is going green and printing on both sides of pages.  You can thank us later.



Fortunately, we are not only doing this for the weather.  There is plenty of math involved as well.  Here are few word problems you can try to help us save the planet.

  • At Mathnasium, the hard-working kids use up 1,200 sheets of paper every day.  Well, they used to, before we switched to double-sided pages.  Now, if they use both sides of every page, how many sheets of paper will they use per day?


  •   If we use the same number of sheets per day, 5 days a week, then how many sheets of paper are we saving every week?


  • Challenge: Last week, 348 double-sided sheets of paper were used up by diligent Menlo Park students.  This week, the printer malfunctioned and only 3/4 of the pages printed on both sides.  If the students do exactly the same amount of work this week, how many sheets of paper will be used up?

Mathnasium loves saving the world and Menlo Park, but we ran into some problems.  Because we used to use the back side of the sheets as scratch paper, we are now running out of scratch paper. Thankfully, it is nothing that math can’t solve.  A few word problems should do the trick.

  • Each student uses 2 pieces of scratch paper in a day’s work.  If 25 students came to the Menlo Park Mathnasium on Thursday, how many pieces of scratch paper will be needed?


  • Assuming the number of students remains constant at 25, how many pieces of scratch paper do we need to buy in order to supply the students for a 30-day month but use as little paper as possible (we still want to keep the weather in Menlo Park perfect)?


  • Challenge: We have 493 sheets of paper left.  We want to make sure we have at least 127 sheets left over for scratch paper.  The math packets we want to print are 8 pages long, and we will print on both sides of the paper.  How many packets can we print and still have enough sheets left over for scratch paper?

Besides what Mathnasium done, there are plenty of ways that math contributes to saving the world.  Everyone could use math to figure out how much they are polluting the atmosphere, and we could use math to figure out how much energy we save, too!

Summer Number Game: Math in Atherton

In Atherton, number games are more fun!

Over summer, practicing math doesn’t have to come hand-in-hand with boring worksheets and times tables. Try this fun number game with your Atherton kids to get them pumped for math over summer and excited for school in fall! And if your kids aren’t the “math-is-so-fun” types, they’ll at least get in some good problem-solving time over the break.

Pico, Fermi, Bagel: The ultimate number game puzzle

Pico, Fermi, Bagel is a super fun game for in the car, at the dinner table, or any old time.

Either two people can play (thinker and guesser), or there can be one thinker and multiple guessers, taking turns to guess the number first.

Here’s how it works:

  1. The thinker begins by thinking of a number with however many digits are decided. The number should have no repeating digits (we’ve never tried with repeating digits, anyway).
  2. The guessers take turns guessing the number; or if there is one guesser, she or he can just continue guessing.
  3. To each guess the guessers make, the thinker will respond with one of the following hints:
  • If the guess has no correct digits, the thinker will call: “Bagel”
  • For each correct digit in the wrong place, the thinker will call: “Pico”
  • For each correct digit in the correct place, the thinker will call: “Fermi”

For example: As the guesser, if you guess the number 562 and you receive the clue “Bagel, Fermi, Fermi,” you know your number contains two digits that are in the number but not in the correct place. The trick is that you won’t know to which numbers the clues apply. (Or the thinker can just say “Fermi, Fermi”– the meaning stays the same, sans “Bagels.”)

For more fun math number games, check out Mathnasium of Palo Alto-Menlo Park:

Atherton number game

Doin’ Math with CREAM Ice Cream Sandwiches in Palo Alto

Ice Cream Sandwich Store

ice cream sandwich

Recently, the new ice cream sandwich place, CREAM (Cookies Rule Everything Around Me), opened on University Avenue in Palo Alto. The place is a huge hit, and there is always a line outside the door. Although the wait may be long, it is definitely worth it! Not only do you get a yummy ice cream sandwich, but it is a great opportunity for your child to do more math.

Math for 2nd – 3rd graders

  • If each ice cream sandwich costs $2.50 and you want to buy 3 ice cream sandwiches, how much  money do you need?
  • There are 20 ice cream flavors at CREAM and 10 different types of cookies. How much more ice cream flavors are there than cookie types?
  • There are 6 people in front of you, waiting in line, and there is only one worker at CREAM. If the worker can make 1 ice cream sandwich per minute and every person in front of you is only planning on ordering one sandwich. How long do you have to wait until it is your turn to order an ice cream sandwich?

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Math ‘n Music in Palo Alto

Can the “Mozart Effect” increase your Palo Alto child with math? 


The term “Mozart Effect”has been used since 1991 when a journalist stated that babies and children who listen to Mozart will become smarter. Since then, scientists were able to prove that Mozart will not making children smarter, but it can help improve a child’s ability to manipulate shapes.

In 2008, a study was done with 8,000 children. The children either listened to ten minutes of Mozart, a discussion of the experiment being held, or three popular pop songs. After, all the children participated in an activity in which they had to predict origami shapes. At the end, the conductor concluded that music did help increase the children’s ability to predict the origami shapes, but to his dismay, the children who listened to the pop songs were able to predict the shapes the best. After analyzing the data, the conductor concluded that listening to any music will not increase a child’s intelligence level, but can help keep the child awake and alert when doing math or any other homework.

For more information check out this article:

Is music beneficial for my Palo Alto child?

After much research about the Mozart Effect, studies have shown that although listening to Mozart will not necessarily make one smarter, learning to play an instrument may increase IQ and help develop certain parts of the brain.  If your child ever wants to try something new and fun, they should try learning to play a new instrument. Not only is it fun, but it is also a great way to work their brain.


Learn more about Math Tutoring and Mathnasium of Palo Alto-Menlo Park (and find more fun problems) —


Talking “Math” with your Child’s Palo Alto/Menlo Park Math Teacher

Contrary to what you might think, summer is a great time to get your kid excited about math–especially if they’re not too thrilled about their current math class at school. By encouraging “mathing” in a fun and stress-free environment, you can change your child’s attitude about math over the break! Before school is let out for the summer, you may want to schedule a meeting with your child’s Palo Alto or Menlo Park math teacher to discuss your child’s performance this year and how you can continue their learning over the summer. Below are some tips to make your meeting be as helpful for you as possible!

math tutoring palo alto menlo park math teacher

Tips for a Successful Meeting with your Child’s Math Teacher

  • First thing’s first, set up a meeting! Ask the teacher about what topics were taught during the school year and what specific topics your child struggled with, if any.
  • This is a great opportunity to get some helpful new ideas for math games or activities you and your kid can do together over the summer break, as well as some tips on how to improve your child’s attitude towards math, or “mathitude.”
  • Talk to your child’s math teacher about whether tutoring over the summer break would be a helpful option for preventing “summer brain drain.” Studies show that kids lose about 20% of the information they learned during the school year during the summer, but tutoring centers such as Mathnasium of Palo Alto-Menlo Park can prevent this!

Prevent Summer Brain Drain! 

Don’t let the all the school-year’s learning go to waste during summer break! Check out some of the fun math games you can play with your kid during the summer months, such as the Groups of 10 Dice Game, Math Game Madness, or even “PIG!” Or, try using math in a natural setting, such as calculating the bill at a restaurant, or doubling a recipe you both love to practice measurements and fractions! Talk with your child’s math teacher about more suggestions on how to keep “mathing” over the summer!

~ Mathin’ Catherine, 5/2013

> Learn more about Math Tutoring at Mathnasium of Palo Alto – Menlo Park

Could the Benefits of Math Tutoring Rely on Brain Size & Wiring? Stanford Scientists Have the Answer!

Recently, scientists at Stanford have discovered new and exciting information on exactly how effective math tutoring can be! By tutoring twenty-four 8-9 year olds in math over eight weeks, the children improved on average 67%, the lowest being 8% and the highest being 198%. Why the big difference? Stanford researchers seem to have the answer!

math tutoring brain stanford mathnasium

The Answer’s in the Hippocampus!

“A larger hippocampus, considered one of the brain’s most important memory centers, was the best predictor of improvement with tutoring,” stated Sue Dremann in her article entitled “Benefits of math tutoring depend on brain-region size, wiring” in Palo Alto Weekly.

The scientists used brain scans to look at the kid’s ability to do and learn math, and how their brains functioned and were structured. By analyzing the children’s brain scans, the researchers were able to predict how effective math tutoring would be simply depending on the size of the hippocampus and the wiring of the brain! The type of math tutoring the children received also affected the results. The 24 kids were tutored by doing and repeating speed-problems in order to make the answers automatic. “Once kids are able to pull up answers to basic arithmetic problems automatically from memory, their brains can tackle more complex problems,” explains Dremann.

How Does This Math Tutoring Discovery Affect You?

This discovery is very important for new math tutoring techniques to help children struggling with math everywhere! Says Vinod Menon, a professor at Stanford’s Department of Psychiatry and Behavioral Sciences, “We can actually predict how much a child is going to learn during eight weeks of math tutoring based on measures of brain structure and connectivity.” By studying how tutoring can alter brain wiring, these Stanford scientists plan to tackle how to train the brain to help kids learn math, at all learning levels and ages!

Can’t wait to hear more about new tutoring methods! As a parent, what learning methods worked for you, and what tutoring methods work best for your kids?

~ Mathin’ Catherine, 5/16/2013

> Learn more about Math Tutoring at Mathnasium of Palo Alto – Menlo Park