Two New Math Apps

Both of these apps will help your kids master addition, subtraction, multiplication and division. They do not teach but provide fun rigorous practice for elementary school kids.

Bubbling Math for iPad and Mac by Tappy Taps.

This type of graphics will probably be most attractive to the girls (age 5-9) . The interface is very intuitive for novel as well as experienced players. Parents or kids can select level of complexity for each kind of the operation. Parents can review the day-to-day progress and wrong answers. As child progresses new lands and places are unlocked. I wish there would be more to the story that would push your child keep going or alter the plot based on the child's responses.  Still, it is a great beautiful alternative to simple math sheets. iPad app is $1.99, Mac version is $3.99 but now if FREE.

Operation Math Pocket by Spinlight.

Terrific comics-style graphics for older kids (9-12), especially boys. Kids need to be comfortable with reading and comprehension to understand the overall plot. I wish there would be a woman agent to attract girls as well. As you solve +,-,*,/ exercises you unlock some spy gear and accomplish spy missions all around the world. Nice, fast-paced, engaging. As with the Bubble Math app, it could be great to get to the next level of interactivity where the story is feasibly affected by child's responses. However for the price of $2.99 on iPad and $1.99 for iPhone/iPod (during the limited offer-launch sale) this beauty is a bargain.

Can you trust the mirrors?

If one of your New Year's resolutions was to shape up, I have good news for you: You look much thinner than what you think you are. Don't believe me? Take an old lipstick or washable markers, stand in front of a home mirror and carefully draw your outline on a mirror. Now measure the size of the face you just drew. It would be about half of what you expected. Viva-la-mirror!

How can it be that you on a surface of a mirror is about half the size of the real you? Here is the math:

Take a look at the triangles ABC and DEC.
Your face and its virtual image in the mirror have a size AB. The projection of your face on the mirror surface is the red line DE. AB is twice the size of DE because CH is twice the size from you to the mirror.

Are you really half the size? No, I was just kidding.
Our brain focuses on what is reflected in the mirror, rather than on the surface of the mirror. AB and not DE.

This peculiar trick is from a great book by John D. Barrow "One Hundred Essential Things You Didn't Know You Didn't Know. Math Explains Your World."

Top image by Dru!, distributed under CCL.

Baby Feeding Math

We have a new baby in the house and with her arrival came various logical riddles that appear very simple, yet the solutions are not trivial although can mean quiet, health and happiness of the whole household.

What time did I last feed her?
What breast did I last feed her from?
How much did she drink?

While I have been trying to remember the last feeding times, I have not always been able to keep track of the "last breast." In many cases you can feel the pressure of the milk, however not always - just recollect the sleepless zombie state new parents find themselves in. I mentioned this problem in my newsletter and many of you wrote suggesting placing a sticker on a bra, writing L or R on a notepad, moving a ring from one hand to another. Someone proposed this as a great idea for a startup.

Today another creative solution arrived by mail from the Similac baby formula company. A present or an advertising trick, depending on how you look at it.  An elegant hand bracelet:

Instructions advise to put the bracelet on the hand corresponding to the side of the last feeding (when breastfeeding) and slide the heart-shaped window to the mark corresponding to the time of the last feeding. Two riddles are solved with one bracelet! Very neat - I am already using it.

Another puzzling and usually annoying question that is frequently asked by nurses, doctors or grandmothers is: "How much milk does your baby consume in one feeding?" When baby is on a formula - it is easy to answer. When breastfeeding - the only way to answer this would be to pump, measure, then feed.  Too much work just to satisfy the curiosity. Feeding time may give a clue to the answer, but as experience shows milk sucking speed depends on the baby's age, temper and hunger state. What other optios are there? You may weigh the baby before and after the feeding or weigh the mom, but the 100-200mg consumed will likely get lost in the noise of the weighting scale or a burp.

Undoubtedly various creative solutions to these questions are in the works.  Have your own ideas - rush to patent it; use someone else's idea - share it with us.

Multiplication Song

Like many of you, I have memorized the order of the letters in the English alphabet thanks to the "ABC" song. In my case it happened at the age of 30, from my kids' Sesame street DVD (with Billy Joel). Yes, I learned the alphabet before in school but it never settled so naturally inside my brain until I heard it fused with music (and over and over again). No matter that I am practically tone deaf.

My daughter quickly mastered the Hebrew alphabet also from  a song - "Alef, Beth" by Naomi Shemer.
My late grandma surprised us all starting to sing some childhood songs in Yiddish at the late stages of her Alzheimer, when she no longer recognized any of us.  This all is not a coincidence.We are more likely to remember a poem that was put to music than "bare" rhymes.  Scientists have shown that music facilitates quick memorization, long-term memory retention and efficient retrieval of information. So, shouldn't we be singing more at school and work?

In the past few months, a large amount of readers and friends consulted with me on how to help their 3rd graders memorize the multiplication table. Well, I have been struggling with this with my own daughter and nothing seems to do the magic. We tried memorizing the diagonal, or starting from the upper-left corner and slowly increasing the square size, we practiced on windows of buildings that we passed by, we tried online games and iPhone games. She got better and better at it but was easily forgetting complex parts after a few days without practice. Plus, it was not fun at all.  Perhaps we should put the multiplication table to music.

I checked on YouTube and found a few attempts by various artists. If you are aware and like some other clips - please add the link below or email me.
Share this with your kids. Better yet, write your own!  There are few professional musicians among our readers and I challenge you all to try - contribute a rhyme, or music or both.

The Multiplying Multiplication Song !!!


Mrs. D's Multiplication Rap Remix™

How to make a festive paper decoration

My daughter convinced me to share with you the tips and tricks on making this wonderful paper decoration for Christmas,  Sukkot, birthday or any other celebration.

She made it in school and I noticed how every math-curious person who came into our house in the past week (including my father and cleaning lady) carefully folded it and tried to reverse-engineer the creation process. We did it as well and after a few failed attempts finally managed to figure it out.


You will need: two pieces of regular (A4 size, white or better colorful) paper, scissors, ruler, pen, eraser and stapler.

Start with a full sheet of paper.

fold it in half and again in half:

Hold on from the folded corner and cut the open corners of the sheet diagonally:

You are left with a folded piece in the shape of a triangle. Use ruler and pen to make the following lines on this triangle.  Note that lines are parallel to the triangle's base. They start at the opposite sides of the triangle and neither line goes all the way to the other side:

Cut along the lines:

Unfold the triangle:

and unfold again very carefully:

Gently tilt the middle part so that you can hang the decoration from it:

You got it!

Now you can make another one of those and staple them together:

Enjoy:

And now when you mastered this try reverse-engineering this Escher's drawing:

Online Math Games: Bad or Good for your kids?

You get a link from your child's teacher. You load the page and easily interest your 8-year-old in the selection of colorful and innocent math games. Alien addition, sailboat subtraction, penguin multiplication, drag race division and tens of others. You point her to multiplication that you both have spent the entire August practicing. You patiently wait while she spends 5 minutes on choosing the color for her penguin and then leave her in front of the naive penguins jumping from iceberg to iceberg. You go to fill the dryer with laundry or check your email with a cup of coffee. When you return, you are most likely to find your darling in front of youtube, pbskids, frustrated and certain that she is bad at math. How did this good turned bad so quickly?

I have always been ambivalent about recommending online math games. CD-ROMs - yes. We have a few excellent ones in my household and both kids enjoy playing them for hours. They are grade-based, start you on the Easy level, and do not rush or humiliate you. With online games it is a different story. Many of them, such as recommended at my kids' school Academic Skill Builder Games take into account the speed of answering along with the correctness of results. Every game is a race where for starters you are guaranteed to come last unless you are choosing a game way below your skill level.
Ready, set, go.
The timer is rushing you.
You notice the red, blue and green penguins are getting ahead while your pink cutie is sinking in the water each time you confuse 6 x 1 and 6 + 1. No time to recover. You press the wrong button again, you squeak in frustration, you lick your tear. Game is over. Your name is last in the results list alongside the naive little pink penguin. Math is fun, isn't it?

A perfect five minute scenario for a quick bloom of serious math-phobia. Beware of online math games. Never ever let your kids start them alone. Instead - demonstrate and test the game on yourself first. Let kids see you struggle with the keyboard, the rules of the game, the penguin sinking disaster, let them see you lose and not give up. It may take a few trials. When you finally manage to finish first, play it together with your kid with one of you answering and another pressing the buttons. Finished in the first three? This is fun. Now you both are ready for the full transfer of the game power to the kid. The level is right, the rules are clear, kid has warmed up and ready for an exciting math practice.

If you are away at work and have to instruct your kid to play such games remotely - recommend to them to start on a very easy level way below their grade skills, carefully reading the instructions and slowly raising higher as they get more comfortable and confident with the speed and rules of the game.

These are my thoughts. Teachers and parents - what is your experience, strategies, trials, errors and successes in the online math gaming world?

It depends on how you measure it

I always thought that cooking is simple as long as you have a reliable recipe. Over the years I learned to trust some of the newspaper food columnists, while taking with a grain of salt my kids’ class cookbooks because some words fade during the kids’ mail transit and Xeroxing.

Once you have a good recipe there is usually no one to blame for a bad outcome other than yourself. Well, occasionally you can tell that the eggs were too big or the stove is new. My eccentric grandaunt used to prohibit us from entering the kitchen during baking and blame us for disturbing the cake’s gestation period if it didn’t rise. But there is really not much more. One cup of flour is one cup of flour anywhere in the world, one tablespoon of butter is one tablespoon of butter. Or is it?

This week’s article in the New York Times surprises us by suggesting that it is not. It refers to an experiment when ten different people were asked to scoop 1 cup of flour and pour it into a bowl. The weight of flour in the individual bowls varied between 4 and 6 ounces depending on the strength and technique of scooping used by each participant. This meant that some of these people may be making a cake with 1.5 times as much flour as others.

What else can we use instead of the traditional and universal cup and spoon volume measures? The weight (mass), says the article advocating for simple kitchen scales. Note that weight is equal mass as long as we cook on earth.

Image by jamieanne, distributed under CCL.

Let’s recollect some math and physics:

Mass = Volume x Density

If the mass of 1 cup of flour in the bowls varied from 4 to 6 ounces, it means that the density is to blame. Faster scooping, scooping up vs down techniques, different storage, type of flour, shape of the cup – all of them can influence the density of the flour. To get the same amount in your recipe rely on mass.


The difference may be even more drastic when dealing with grated cheese. According to the article “the heavier shavings of a box grater can fill a cup with twice as much cheese as” “billowy ribbons of machine-shaved cheese.”


So, get yourself a kitchen scale for the next holidays. Use mass-based recipe source and you will:

1. Get consistent recipe-matching results every time.
2. Easily double or halve the recipe.
3. Have less stuff to clean. You can use only one mixing bowl by slowly adding ingredients into it directly from the containers and zeroing weight on the scale after each addition.

What about your old favorite volume-based recipes? One cup of oil in mom's sweet corn bread, one cup of honey in the Rosh haShana cake. Should you just convert them to mass?  This Pyrex measuring cup clearly marks 1 cup volume as 8 oz mass.

Remember the formula:

Mass = Volume x Density

For water measurements: 8 oz = 1 cup x Water Density
Oil, melted chocolate and honey are obviously denser than water. Higher density gives higher mass: around 10 oz for one cup of oil, and 12 oz for one cup of honey. So, beware of the Pyrex' cup.


It is just you now in the kitchen with your scale and math.

Amazon links to buy kitchen scale:

Presenting Math as an Art

I was disconnected from the internet for most of the August and got a luxury of time to read a few deep-hidden non-fiction books from our library. One of these books was a shocker - a light, eloquent, captivating and constructive critique of the ways mathematics is percieved and presented at schools, universities and most of our households. It is a very refreshing and convincing analysis from a former scientist and experienced math teacher and I am going to recommend it to every teacher, parent and high school student. The book is: "A Mathematical Lament" by Paul Lockhart. It is subtitled: "How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form."

Dr Lockhart suggests that math is an art and should be treated exactly like music and painting. We should not be learning math because it is applicable to our daily lives or essential in our future occupations, but rather because the process and the result bring joy to our soul like listening to or producing music does. Forget all the bad math associations you have nurtured and think of a pleasure that discovery of any pattern brings to us. And the sweet mental game of attempting to explain this pattern.

Take for example this curiosity:

1 = 1

1+3 = 4

1+3+5=9

1+3+5+7=16

1+3+5+7+9=25

Fascinating! Sum of the subsequent odd numbers produce results that are all square numbers.

But why?

Can any square number be represented as a sum of subsequent odd numbers?

If we let our mind wonder about this for a while we may be able to come with an explanation, perhaps even as thrilling as this one:

Any square number can be drawn as a square, such as this big and colorful 5x5. Any square can be split into such colorful parts.

Count the number of little pieces in these parts. They are 1 (purple), 3(green), 5(yellow), 7(blue) etc. These are our subsequent odd numbers. Looks like any square can be split into such pattern.

Lockhart writes that in school "the rich and fascinating adventure of the imagination has been reduced to a sterile set of facts to be memorized and procedures to be followed." Being math expert, math lover and experienced math teacher he suggests a number of directions to improve such math education:

• "Mathematics is an art of explanation." This means that students should be allowed to pose their own problems, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble togather their own explanations and proofs."
  
• Math history is fascinating and provides a great base for captivating storytelling. Instead of handing kids formulas to memorize retell them stories of ancient and contemporary mathematicians and their search for solutions to the fascinating problems that are wrapped in these formulas today.
• Like other arts math should be subject to debate and critisize in schools. "Is this argument sound? Does it make sense? Is it simple and elegant?"
  
  
• Forget proper notations that are frequently a source of frustration. "Math is not a language, it is an adventure." DaVinci, Pollock,and Warhol each created art in their own way.

The author also cleverly warns that although math is and should be presented as an "art" subject, such shelving may be dangerous as "useless" art disciplines are frequently the first to be cut off from the curriculum in time of budget cuts.

This book will definitely change the way you think about math.

It may boil your blood from anger with the author or on opposite, the current math curriculum against which he convincingly stands.

It may explain you why you always hated math classes but liked riddles and puzzles.

It surely will inspire you and teach you a few tricks that you will rush to share with your kids as I did.

Daily Roadside Math

Walking around Vancouver today I noticed this stretched bicycle sign:



Why is it so distorted? Was it painted by a machine that accidentally accelerated shortening the bicycle at the top?

There must be a reason for this distortion. Probably something facilitating our perception. Similarly to the Ambulance sign painted with a horizontal flip on the ambulance truck to allow the sign be correctly read in a rear view mirror.

Let's see. Who is it for? A warning for approaching cars and bicycles that this road is bicycle only. They should be able to see it from 20-50 feet away. Let's check how the sign looks from such distance:

Just perfect!
What exactly is happening with this visual illusion?
The drawing of the bicycle is cleverly made to account for the perspective projection distortion in our eyes (and brain) and allows for the bicycle to be perceived clearly from the average height and far distance. Note how the bicycle wheels appear perfectly round on the second picture.

This is simplified demonstration of our eye perceiving bicycle wheel as perfectly round from a distance and as an oval from close up.

Now, how about an explanation to this signage?

From Magic Squares to Sudoku

In 1415, the German renaissance painter and mathematician Albrecht Dürer created this busy copperplate engraving of a woman melancholically contemplating amongst a clutter that includes an hour glass, a balance scale, a sphere, a polyhedron (aka philosopher’s stone), a purse, and keys. Like his contemporary’s Mona Lisa, this mysterious painting has been extensively studied, speculated upon and written about. It is believed that it was planned to be the first in a series of paintings describing various temperaments: melancholic, phlegmatic, choleric, and sanguine. It is titled: “Melencolia I”




Among the peculiar geometrical tool in this painting, in the upper right corner, one can find … a magic square!



Wait; weren’t magic squares invented by Ben Franklin three centuries after?

Magic squares are tables of numbers where sums of every row, every column and both diagonals produce the same number. In Drurer’s square the sum is 34:








Magic squares have been around for thousands of years. Magic squares of size 3x3 are mentioned in the Chinese literature dating 650 BC. Magic squares of size 5x5 and 6x6 are found in an encyclopedia from Baghdad written in the ten’s century. They were engraved in stone and metal, worn as talismans, their usage believed to ensure longevity and prevention of diseases (from Wikipedia). Magic squares can be spotted in art all around the globe. The Indian Parshva temple still contains a 4x4 magic square carved in the 10th century. The Passion facade of Gaudi’s Sagrada Família church in Barcelona, designed by sculptor Josep Subirachs, features a 4×4 magic square with a sum of 33 that is the age of Jesus at the time of Passion.



What has fascinated people about Dürer’s square is that in addition to the regular magic properties, it contained more mathematical patterns and messages:

1) Numbers in each of the following five quadrants add up to 34.



2) Any pair of numbers symmetrically placed about the center of the square (such as these) sums to 17:



3) The two numbers in the middle of the bottom row give the date of the engraving: 1514



4) The numbers 1 and 4 at either side of the date correspond to, in English, the letters 'A' and 'D' which are the initials of the artist.

What about Ben Franklin? As a child and an adult he amused himself with creating large size magic squares such as this 8x8:



While his squares are not truly magic squares because sum of each of the diagonals is not equal to the sum of numbers in every row or column, they are still pretty cool. To compensate for a lack of the diagonal property Franklin defined a broken diagonal or “bended rows” properties where the sum of numbers in each highlighted bended rows is the same.



Magic squares could be considered the ancient relatives of the modern Sudoku game. In the late 19th century, French newspapers started publishing matrix puzzles – 9x9 magic squares with some numbers removed. Then the puzzle slowly evolved taking away the sum requirements and instead requiring that each row, column and diagonal have all the numbers from 1 to 9. And finally, the 3x3 sub-division was added producing the modern day Sudoku (you can click to play):



Thousands of Sudoku are published in the world daily. You have likely seen someone doing Sudoku on his way to work, at the playground, laundromat or in the coffee shop. A good story attesting to Sudoku’s popularity was published in the Sydney Morning Herald. In June 2008 an Australian drug-related jury trial costing over Australian $1,000,000 was aborted when it was discovered that five of the twelve jurors had been playing Sudoku instead of listening to the evidence.

When to expect when you are expecting

They were expecting their third child – a daughter – a week after Labor Day. Perfect timing: their older kids will be out of the house and back to school, and the doctors back in town. All was well except that a few months before he realized that the September 12th due date fell inconveniently close to a professional conference in Europe, which he organized. “To go or not to go?” was pulsating daily in his brain. Will she manage here with 2.5 kids on her 9th month of pregnancy without me? What are her chances of delivering 3 weeks earlier? Shall I bring my mother to help here instead of me? If I stay – something will surely be messed up at the conference. Who will do my part? What would my colleagues say about me abandoning them? It is an honorable responsibility and I want to see it through.

***

Due date is calculated based on the empirical observations that it takes an average of 38 weeks from the moment of conception to the moment of delivery. But no one knows when exactly conception took place and how fast the sperm moved and fertilized the egg, plus it may be embarrassing to admit that you did it while at your in-laws or on a friend’s couch. So we look around for the closest related landmark – the menstrual period. Its first day usually is 10-18 days before the conception. So, your due date is approximately:
38 weeks + [10-18] before conception days =roughly 40 weeks from the first day of your last menstrual period
And ironically enough, when you conceive you are already considered 2 weeks pregnant.

The actual birth dates are spread around this 40 week due date in approximately normal distribution (bell curve).

(Graph from Ref 1.)
Graph mark of 24% at the 40th week mean that your chances of delivering on any day of this week are approximately 24%/7=3.4%. You can see that around 90% of babies are born within three weeks of their due date, and 21% are born within 3 days of it. In many geographical places, the right side of this distribution is sharply raised and cut at 42 weeks because the majority of the women that have not delivered by the 42nd week are being induced.

Why does the gestational age vary? Because not everyone ovulates and conceives exactly 14 days after the beginning of the menstrual period; some babies mature faster while some are too comfy inside; second and further babies seems to be more in a rush to come out; mother’s age and weather may influence the dates; and women of some ethnicities tend to give birth a bit earlier than others. (Ref 2, 3, 4)

Back to our expecting couple. He took from Wikipedia the data about probability distribution of actual births with respect to their due date.



He centered the graph on their due date, September 12th. Total area under this bell curve is equal to 1 = accumulated probability of giving birth. The chances of delivery during any interval are equal to the area under this interval. He marked in red the probability of her delivering prior to August 27th while he is away. He added up all the red area under the curve obtaining 0.043. He proudly showed it to her, explaining that her chances of giving birth before he returns are only 4.3%.
She told that this may be true but he is a 100% asshole. She also reminded him that both of their older kids were born two weeks earlier.
He still went abroad and run the conference.
She gave birth a week and a half after his return (on September 8th) to a healthy and beautiful baby girl.
They lived happily ever after, but he was never forgiven.


References:

1. Calculating Due Dates and the Impact of Mistaken Estimates of Gestational Age
2. Gestational Age at Birth, 1994 and 2004
3. American Pregnancy Association
4. Duration of human singleton pregnancy. A population-based study.

iPhone and iPad apps of TheMathMom Stories and Puzzles

New: iPhone and iPad apps of TheMathMom Stories and Puzzles. Get them while they are free. Hundreds have been downloaded in the last week since these apps were released. Read, answer or share from anywhere on the go. Click on the icons to download apps from iTunes. Please share your feedback on iTunes.

Spring IQ Test

Ready to shake up your brain after the long and cold winter?
This IQ Test is easy, fun and playful. No math skills above Kindergarten level are required. Answer quickly, without hesitation.

Puzzle #1: You participate in a race and you are advancing ahead of a racer who is second. What is your place in the race right now?

Answer #1: If you answered that you are on the first place - you are absolutely wrong. If you went ahead of the runner who was second, you now took his second place.


Puzzle #2: Two fireman entered a school and one of them claimed to be a father of the other's 2nd grader. Can this be true?

Answer #2: Hopefully, you have answered yes. No complex family relationships are necessary, the other fireman must have been the 2nd grader's mother.

Puzzle #3: A girl entering a library was surprised to see her friend walking toward her. The friend was accompanied by her mother, two grandparents, younger brother and a little puppy. The friend was also holding a doll. How many people in total just came to the library?

Answer #3: Don't even think of answering 5 or 6. They are all leaving the library. Only one girl just came in.

Puzzle #4: How many pairs of animals did Moses take on the Arc?

Answer #4: It was Noah, not Moses.

Puzzle #5: Mary's father has five daughters: 1-Arlene, 2-Darlene, 3-Marlene, 4-Sharlene. What is the name of his fifth daughter?

Answer #5: If you answered anything ending with "lene" - wrong again. Run this puzzle by your toddler kid. She will help you figure out that Mary's father should have at least one daughter named Mary.

Better luck next time. Enjoy sharing this.

Top image of the brain-resembling coral is by boogieswithfish, distributed under CCL.

How to beat Chinese 2nd graders in the frog game

This is a very cool game that is believed to be a 2nd grader computer test in China. Three green frogs, three brown frogs and all you need to do is switch their places over. But wait before you challenge with this your second grader. Click on the image below to try it yourself. Once, twice, ... ten times. Game site allows only small number of simultaneous players and occasionally is unavailable. Bookmark it and reload after a few minutes. It is well worth the wait.

If you start thinking that this is a prank and it is impossible, trust me it is possible. It may take a while, it may be non-intuitive but you can do it. Only if you become absolutely desperate check the solution steps below.

Can you do it now? Challenge your friend or your kid.

Birthday Treasure Hunt

It became a tradition in our family to create birthday treasure hunts for kids. This started back in my childhood when my parents probably wanted to make sure that my brother and I remember to brush out teeth, make beds and dress up among the excitement of opening our presents. So, for each of our birthdays, parents left us a chain of notes that led the kid from his bed to the bathroom, where the greeting poem would be hidden somewhere under the toothbrush holder and a note to search further in his closet. After dressing up and scavenging for the first present in the closet birthday kid would be led to the kitchen for further greetings, presents, riddles and assignments.

These days I am recreating these treasure hunts with my kids and occasionally their friends at the birthday party, adding pirate or mystery flavour and more intellectual challenges (including math). Kids love it, remember these treasure hunts for years and always request it ahead of their birthdays.

I decided to share here one of the recent treasure hunts as it is easily adaptable to any kids' age and any household. To create your own treasure hunt you need a few (I used 6) treasure boxes filled with various presents or candy or goody bags and a chain of notes to search for one such treasure after another.

The first note that I handed my kids said:

Along with this note was a folded piece of paper sealed with a candle wax. On it: After a few minutes of running around the house kids figured out that the note refers to the painting we have that features women picking nuts and the old wooden deer statue on a shelf across from it. The first treasure box was hidden behind the deer. In it among the prizes was a second note leading to the next treasure: Note that the little wavy "x" is a multiplication sign. We have two coded multiplication sentences. Kids needed a bit of guidance, but after some hints quickly realized that: X=3, O=7, Z=9, S=6 Picking up letters 3,6,7 and 9 from the KWGOTARQAV gave them GARA. From this they figured out that it must be "garage" and found the second treasure there. Together with the treasure in the box was another note: Third treasure was hid in the warmer drawer of the STOVE that could be unscrambled from "ETOSV." In it was the next note: After running around the rooms for a while kids discovered the fourth box hidden in my son's closet. In it with the bouncy balls and candy was the next note: Almost there! The fifth box hidden in the bookshelf behind the world atlas contained the final note: I played hangman with the kids and they quickly figured out that the words are: UNDER PRINTER. This is where the last and the best treasure box has been waiting. Exhausted and satisfied after 15-20 minutes of searching around and bending their minds, kids proceeded to start opening the candy and all agreed that this was fun.

I am sure you can use these ideas and come with various versions of such adventure that will be more creative, fun or complex. Please share them! This is quite time consuming but it is joy to make, even more so to participate and it leaves the long lasting childhood memories. Plus it strengthens the association between math, word puzzles and fun.