Pi Day is March 14

Saturday March 1, 2025

On March 14 at 1:59pm, folks from all over the world celebrate “Pi Day” with games, activities, and pie-eating contests. Here are my best resources for showing kids how pi shows up in the real world and also how to learn about pi in a way that not only makes sense but isn’t flat boring.


Pi (p) is a number slightly greater than 3 that shows up when you divide the circumference of a circle by its diameter, no matter what size the circle is. It also shows up in other shapes like spheres, ellipses, cylinders, and cones as well as unusual places like summation series, number theory, probability, bell curves, and the Fibonacci series.


I’ve prepared two different versions that you can access, and each comes with its own video. If this is your first time encountering “pi”, then start with the first one. Otherwise, jump in to the full version and have fun!


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Pi: Simple Version

Pi is an irrational number, which means that its digits never end and that it doesn’t contain repeating sequences of any length. Mathematicians can’t say with absolute certainty that pi contains every possible finite number sequence—but they strongly suspect that this is the case.


Materials:


  • This worksheet (all pages)
  • 3 tennis balls in a can
  • Box of toothpicks
  • Chalk (optional)

Pi: Full Version

After you watch this video, you can download the Pi Day activities n a PDF workbook packet. There are 10 stations, each with a specific hands-on activity about pi. Each station also has a couple of materials you will need to have along with the printed instructions, so gather these together also. (There’s a master list on the second page of the download.)


Materials:


  • This worksheet
  • 3 tennis balls (still in the can)
  • string
  • scissors
  • tape
  • measuring tape
  • ruler
  • circular objects
  • toothpicks
  • poster board with parallel lines
  • six-sided die
  • question cards cut out
  • pile of pennies and tokens
  • calculator
  • pencil
  • access to internet on three different computers for three different stations
  • Pies for no-hands pie eating contest for the treasure. I like to use small aluminum tart pans with a graham cracker on the bottom, then a dollop of jam, finished by whipped cream. Yum!

Be sure print out a couple pages of “pi tickets” on page 18. The students get one “pi ticket” for each answer correct on the answer sheet they turn in.
The Final “Pi Station” has graham crackers, assorted jams, and whipped cream that students can “build their own pies” – one for every ticket they’ve earned!



The video below will walk you through the handout and give you even more ideas and show you cool images you can create for your decor!



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Over the years, I’ve collected quite a stash of activity sheets and games for kids from other sources. I don’t know where they all came from, so please respect their copyright information on the sheet itself when you share with others.


Logic Numbers

Friday July 31, 2020

This is a neat logic trick which allows you to flip over a stack of cards numbered 1-10. When you flip the back upright, they are in numerical order. There is a special way to make it work, so pay close attention to the video. I’ll show you exactly how it works.


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Download Student Worksheet & Exercises


Does this make sense? What order do you think the cards need to go in so that the trick works? Use your logic skills to work it out.


Exercises


Your exercise for this lesson is to not only challenge someone else with this problem, but be able to explain it to them in a way that they understand the solution.
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Multiplication Tables

Monday July 27, 2020

If you haven’t memorized your multiplication table yet, I am going to show you how to you need to memorize only three of the 400 numbers on a 20 times table in order to know your table.

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Download the student worksheet that goes with this lesson.

Math isn’t about solving problems on any one particular way, but rather it’s about puzzling the solution out multiple ways! The times table is essential to doing math in your head, but you don’t need to know every cell on the table by heart. With a couple of quick tips and tricks, you’ll be able to know your table up to 20 without a lot of memorization simply by being clever about the way you go about it
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Pen & Paper Math Games

Monday May 4, 2020


Imagine you’re in the car with the kids, excited to see your extended family (or at least, specific members of your extended family), and you’re not quite there yet.


And the kids been glued to their video games, cell phones, and electronic devices the whole time. You know it’s not good for them, but at least you have some peace during the car ride. You shrug it off, not too worried about it, thinking about all the running around with cousins they’ll do once they get there.


And then you hear…


“Are we there yet?”
“I’m bored.”
“I’m hungry.”


…and whining.


Now what do you do?


It seems impossible for kids to entertain themselves these days without the use of batteries.


That’s what spurred me to create this “Pen & Paper Games” packet that I want to share with you. It’s full of my very best on-the-go, play-anywhere games that you don’t need any equipment (other than a brain) to play! These games I’ve played with my kids over the years, even standing in lines at Disnleyland.


Click here to download the packet and enjoy with your family!

 
 
By the way, Bagels is still our favorite line-waiting game, because it’s so fun to play and easy to teach the on-lookers who are wondering why we keep shouting “PICO!” and “FERMI!” followed by uproarious laughter. Bagels is good for the car too, only maybe without the shouting. It’s basically a mental version of the old Mastermind game, but don’t tell them that! Just enjoy the game and have fun learning and exploring our wonderful world.


Solving a Rubik’s Cube

Wednesday September 16, 2015

Everyone old enough to remember the Rubik’s Cube craze of the 1980s in the USA also remembers how it was near impossible to solve the thing! Originally created by a professor of architecture Erno Rubik, it was sold to a toy company in 1980 as the “Magic Cube”.


To date, over 350 million cubes have been sold worldwide, making it the world’s top selling puzzle game, and most people think of it as the best-selling toy of all time as well.


The original goal of creating this object was to help teach his students how to create something that rotated independently in layers without falling apart. Rubik didn’t realize he had created a puzzle until he scrambled it, and it took him over a month to solve it the first time!


There are eight corners and twelve edges, and when you do the math to figure out the number of possible combinations the puzzle has, it’s about 43 quintillion, or:


43,252,003,274,489,856,000


So what do you do with this thing? How DO you solve it?


It has to do with identifying the different layers, and solving one layer at a time. Here’s how you can do it:


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Download the official solver’s guide here. Or you can build a LEGO machine like JP Brown did to solve it for you!



There’s also a World Cube Association where folks keep track of cube competitions and records. The fastest cube solve was set by Mats Valk in 2013 – he can solve it in under 6 seconds. Some of the more creative competitions include solving the cube while blindfolded (record is 23.8 seconds), with only one hand (record is 12.6 seconds), only using the feet (record is 27.93 seconds), and underwater using a single breath.


Kaleidocycles and Hexaflexagons

Tuesday June 2, 2015

Kaleidocycles are a three-dimensional paper sculpture you can turn around and round! Flexagons were first created by Arthur Stone at Princeton University in 1939, which were later published in 1959 to the general public in Scientific American.


These are simple to make and fun to play with. When I first showed them to my own kids, they immediately made one for each kid in their class, and also stumped the teacher that day when they asked how it worked. [am4show have=’p8;p9;p11;p38;p154;’ guest_error=’Guest error message’ user_error=’User error message’ ]
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Materials:


  • scissors
  • white glue
  • toothpick or paperclip (to spread the glue with)
  • paper or template (use this one or print out one from below)


Click to download the car template or the animal template!


Now that you’ve made a kaliedocycle, let’s take it step further and make a flexagon. Flexagons looks like hexagons, but you can turn them inside out over and over. A hexaflexagon (this is the one we’re going to make in the next video) is made up of 19 triangles folded into six faces from a single strip of paper.  You’ll need a strip of paper and the instructions below. (You can draw images on it when you’re done.)


Materials:


  • scissors
  • white glue
  • paper or template (flexagon and hexaflexagon)


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The video below is made by Vi Hart, a smart and spunky mathemusician who has made amazing videos about the history of hexaflexagons that are fast-paced and fun. 



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Sprouts Math Game

Monday June 2, 2014

This is a really neat game invented in 1967 by two mathematicians that was soon after published in Scientific American, where it caught fire with people all over the world. It’s a very simple game with a lot of interesting mathematics in it, and all you need are two people, a pencil, and paper.

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Download the student worksheet that goes with this lesson.

1. Draw two or three dots on the paper, spaced out a bit. They can really be anywhere you want.
2. The first player draws a line that two of the spots, and makes a new spot in the middle of the line. (You can make a line joining one spot to itself also.)
3. The second player draws her line and spot also, remembering these rules:
a. You can’t make a line that crosses another line.
b. Only three lines per spot, coming to or from it.
4. The winner is the last person to draw a spot!

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Finger Multiplication

Monday May 19, 2014

Having trouble with your 6, 7, 8, and 9 multiplication tables? Sneak a peek at this nifty trick for multiplying single digits together. All you need is a set of hands and about ten minutes, and you'll be a whiz and multiplying with your hands.
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Download the student worksheet that goes with this lesson.
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Cryptarithms

Monday May 5, 2014

Cryptarithms are a puzzle where the digits are replaced by letters or symbols. When the numbers are replaced by letters of the alphabet and it spells something readable, it’s called Alphametics.


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Download the student worksheet that goes with this lesson.


Rules: Each letter represents a unique digit, numbers may not start with zero, and the solution is unique. A few weird things to remember are: stars substitute for any digit, and are not related to each other, dots stand for a decimal point, and lower case ‘x’ means multiplication.
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How Does a Two-Fingered Alien Count? (Binary Counting)

Monday April 21, 2014

One day, my kid asked me how a calculator comes up with its answers. That's a great question, I thought. How does a calculator do math?

After thinking about it, I realized this was a great way to teach him about binary numbers. I am going to show you how to not only count in binary, but also help you understand the basis of all electronic devices by knowing this key element.

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Download the student worksheet that goes with this lesson.

By asking questions, you can discover a lot of what you already know about a subject. In this case, students usually know how to count to 100 or even 1,000, but they don’t consciously know why the numbers change in the sequence that they do. In this activity, we’re going to explore how quantities are represented by numerals (digits 0 through 9), and then learn how you can change the number of numerals and count in different bases. In the instructional video, we’re learning base 2 and 10, but you can use this to represent any base to count in.

Exercises

〖93〗^2
〖193〗^2
〖979〗^2
〖249〗^2
〖415〗^2
〖84〗^2
〖573〗^2
〖333〗^2
〖757〗^2
〖696〗^2
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Guesstimations

Monday February 3, 2014

When it’s too hard to count ’em up and too much time to calculate, it’s time to guesstimate the answer. I use this technique all the time to “ball park” my answer so I know if I’ve made a mistake with my final answer.


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Download the student worksheet that goes with this lesson.


This lesson is useful when you don’t need an exact answer, or if the numbers are way too long to remember. It’s really pretty simple to do: you round up or down, and the closer to the ones digit you can handle, the more exact your answer will be.
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Division

Monday January 6, 2014

If you hate long division like I do, then this lesson will be very useful in showing you how to make the most out of your division tasks without losing sleep over it. It's easy, quick, and a whole lot of fun! If you haven’t already mastered your multiplication tables, make sure you have one handy to refer to as you go along.

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Download the student worksheet that goes with this lesson.

Many, many thanks go to Arthur Benjamin, a mathematics professor extraordinaire and professional magician who inspired much of this content we covered today.
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Quicker Multiplication

Monday December 23, 2013

If you don’t have the patience to do multiplication on paper for every single math problem that comes your way, then you’ll really enjoy this math lesson! You’ll be able to multiply one and two digit numbers in your head, which you’ll be able to use when checking your answers on a math test, or just whenever you need to multiply something quickly when paper’s not around.
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Download the student worksheet that goes with this lesson.

If you haven’t already mastered your multiplication tables, make sure you have one handy to refer to as you go along.
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Math from Left to Right

Monday December 9, 2013

In school, you are trained to solve math problems on paper, at a desk. The problem with that is, for most people, math problems don’t usually come with a desk or a pencil. They pop up in the checkout line when paying for groceries, figuring out your gas mileage at the pump, or when counting calories at a restaurant. Learning how to solve math problems in your head is an essential everyday life skill, especially if you don’t want to be ripped off in money transactions.

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Download the student worksheet that goes with this lesson.

Learning how to calculate in your head doesn’t have to be hard or scary, but it does require a little rewiring of the current math solving conditioning that you’ve already got in your brain. Specifically, we’re going to train your mind that when you solve math problems without paper, you must do it from left to right. It’s so much easier to think about math problems from left to right, so that’s how we’re going to do them.
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Multiplication Tables

Monday November 25, 2013

If you haven’t memorized your multiplication table yet, I am going to show you how to you need to memorize only three of the 400 numbers on a 20 times table in order to know your table.

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Download the student worksheet that goes with this lesson.

Math isn’t about solving problems on any one particular way, but rather it’s about puzzling the solution out multiple ways! The times table is essential to doing math in your head, but you don’t need to know every cell on the table by heart. With a couple of quick tips and tricks, you’ll be able to know your table up to 20 without a lot of memorization simply by being clever about the way you go about it.
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Magic of 11's

Monday October 28, 2013

This math lesson is so easy that one night, I wound up showing it to everyone in the pizza restaurant. Well, everyone who would listen, anyway. We were scribbling down the answers right on the pizza boxes with such excitement that I couldn’t help it – I started laughing right out loud about how excited everyone was about math - especially on a Saturday night.

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Download the student worksheet that goes with this lesson.

When you do this calculation in front of friends or family, it’s more impressive if you hand a calculator out first and let them know that you are ‘testing to see if the calculator is working right’. Ask for a two digit number and have them check the calculator’s answer against yours.
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Positive and Negative Integers

Friday December 7, 2012

Numbers that are not fractions or decimals, are called integers. Numbers like: 2 and 144 and 299,792,458 (that’s the speed of light in meters per second) are all integers!


Integers can be positive or negative. If the number is greater than zero, like 4, 16, 25… then it’s a positive integer. Negative integers are -15, -42, -1 million.


It’s important to know how to handle both positive and negative integers because they come up all the time in algebra. You probably already have experience in working with positive and negative decimals and fractions, so now let’s do a quick review so you can make sure you’ve mastered the basics.
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What is Math?

Tuesday July 31, 2012

What is math?  It can be compared to a very useful tool, or maybe a collection of tools. Sometimes textbooks concentrate a lot on teaching about the small details of each and every type of tool.  But it’s also really important to focus on how and when to use the different tools. This is my practical approach to teaching the subject. And it’s also important to note that math is much more than just numbers! If you’re really good with shapes and how they relate, you might enjoy geometry. And if you are good at solving puzzles, chances are that logic will be a great match for your skills.


NOTE: Be sure to pause the video when the timer reaches 6:30 to work on the Earn, Break Even, or Lose problem.


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Which did you like best – the Earn, Break Even, or Lose question, the circle drawing trick or the Bagels game? This might help you discover if you’re more interested in numerical problems, geometry, or logic. Try all of these with a friend. Which one do they prefer?


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How to Multiply by 12

Tuesday July 31, 2012

Do you think you'll need to know how to multiply by 12 or 11 more? Think of it this way: how often do you need to figure out how many dozen you need of something? It comes up a lot more than needing to know how many batches of 11, doesn't it? That's because of the way we've decided to group things mathematically as a society.

Here's why: We picked 12 based on how we used to count on our fingers using the "finger segment" system. If you look at your hands, you'll notice that your index finger has three segments to it. So does your middle finger, ring finger, and pinkie. Since you have four fingers, you actually have 12 sections for counting with (we're not including your thumb, which is the pointer... your thumb rests on the section you're currently on). When your thumb touches the tip of your index finger, that means "1". When your thumb touches the middle segment, that's "2", and the base segment is "3". The tip of your middle finger is "4", and so on. That's how we came to use the 12-in-a-batch system.

If you're wondering why we didn't use the 24-in-a-batch system (because you have two hands), that's because one hand was for 1-12 and the second hand indicated the number of batches of 12. So if your left hand has your thumb on the ring finger's base segment (9) and your right hand has the thumb touching the index finger's middle segment (2 complete batches of 12, or 2 x 12), the number you counted to is: 24 + 9 = 33.

Fortunately we now have calculators and a base-ten system, so this whole thing worked out well. But still the number 12 persists! So I thought you'd like this video, which expands on the idea of quickly multiplying two-digit numbers and three-digit numbers by eleven. This is very similar to the shortcut used when multiplying by eleven, but it also involves some doubling. Are you ready?

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Download Student Worksheet & Exercises

Isn’t this a really cool (and FAST) way to multiply by twelve? It's a lot faster than using the Babylonian finger-segment system. Try some problems on your own and check your work with a calculator.

How do you think this works?

Exercises

  1. 11 x 543
  2. 12 x 45
  3. 12 x 326
  4. 12 x 769
  5. 12 x 1345
  6. 12 x 3461
  7. 12 x 7532
  8. 12 x 8989
  9. 12 x 9999
  10. 12 x 98749

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Divisibility

Tuesday July 31, 2012

Can you look at a number and tell right away if it’s divisible by another number? Well, it’s pretty easy for 2 – if it’s an even number, it’s definitely divisible by two. Testing whether a number is divisible by five is easy as well. How can you tell?

In this video, I’ll show you some tricks to determine if a number is divisible by 3, 4, 6 and 7 before you start to divide. Some are simple and fast and some are a bit more complex. These can be very useful tricks for working with larger numbers (or just really fun to play with for a bit).

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Download Student Worksheet & Exercises

It’s pretty complex to be able to tell if a number is divisible by 7, but I think it's really neat that there’s a way to figure it out before you actually do the math. What do you think?

Exercises

  1. Identify the number(s) that are divisible by 2 in the following list.
    301, 3645, 3673
  2.  Identify the numbers that are divisible by 3 in the following list.
    3981, 430, 4598, 72624
  3. Which one of the following numbers is divisible by 7
    5894, 56723, 17259
  4. Is 2353740 divisible by 4?
  5. Which one of the following numbers is divisible by both 2 and 5?10002, 453970, 637385
  6.  A number is divisible of 2 and 3, will it be divisible by 5?
  7. If a number is divisible by 2 only, will it be divisible by 4?
  8. Which of the following numbers is divisible by 3?
    45769, 25784, 2391
  9. List any three 3-digit numbers that are divisible by 5.
  10. List two 4-digit numbers that are divisible by 4.

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What Day Were You Born On?

Tuesday July 31, 2012

This is not only a neat trick but a very practical skill - you can figure out the day of the week of anyone's birthday.

If you were born in the 20th Century, (1900-1999), we can use math to find out which day of the week you were born. If you’re a little too young for this, try it with a parent or grandparent’s birthday. Watch the video and I'll teach you exactly how it works.

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Download Student Worksheet & Exercises

Did it work?  You can check via the Time and Date website, or simply do an internet search for the year and the word calendar, such as, “1996 calendar.”

Note: the codes shown in the video are special just to the years in the 1900s. If you'd like to be able to expand this to other centuries, you'll need to use the codes listed below and learn how to shift them (like I did for you in the video).

What about years 2000-2099?

The general formula is: Month Code + Date + Year Code - (biggest multiple of seven).

For Nov. 18, 2006 = 2 + 18 + 0 = 20.

20 - (7 * 2) = 20 / 14 = 6 so Nov 18, 2006 is on a Saturday using the codes below! (Do you notice how the following codes are different than they were for 1900s?)

Day Codes:

  • Sunday = 0
  • Monday = 1
  • Tuesday = 2
  • Wednesday = 3
  • Thursday = 4
  • Friday = 5
  • Saturday = 6
  • Sunday = 0 or 7

Month Codes:

  • January = 6*
  • February = 2*
  • March = 2
  • April = 5
  • May = 0
  • June = 3
  • July = 5
  • August = 1
  • September = 4
  • October = 6
  • November = 2
  • December = 4

*For leap years (2000, 20004, 2008, 2012, 2016...) the code for Jan = 5 and Feb = 1.

 

Year codes:

  • 2000 = 0
  • 2001 = 1
  • 2002 = 2
  • 2003 = 3
  • 2004 = 5
  • 2005 = 6
  • 2006 = 0
  • 2007 = 1
  • 2008 = 3
  • 2009 = 4
  • 2010 = 5
  • 2011 = 6
  • 2012 = 1
  • 2013 = 2
  • 2014 = 3
  • 2015 = 4
  • 2016 = 6
  • 2017 = 0
  • 2018 = 1
  • 2019 = 2
  • 2020 = 4
  • 2021 = 5
  • 2022 = 6
  • 2023 = 0
  • 2024 = 2
  •  2025 = 3

We don't have to memorize 2000-2099 because we know how to divide numbers since the table repeats itself.

Here's how it works: if you need the code for 2061, divide 61 by 4 to get 15 (with a remainder of 1 that we ignore), so 2061 has a year code of 61 + 15 = 76. Don't forget to subtract out any multiple of 7, so we get 76 - 70 = 6. The year code for 2061 is 6!

This works the same way for the 1900s: Fir December 3, 1998 we have 98 divided by 4 which gives 24 (with a remainder of 2 that we ignore), so 1998 has a year code of 98 + 24 + 1 = 123. Now subtract out the biggest multiple of seven (which is 119) to get 123 - 119 = 4. 1998 has a year code of 4!

What about year codes for other centuries?

Did you notice how I added "1" to the year code in the previous example? That's because I had to shift it over since it's in the 1900s. For the 1800s we'd shift it by 3. Let me show you how:

Abraham Lincoln's birthday is Feb 12, 1809. 2009 has a year code of 4, that we need to add 3 to (this is the shift by 3), so we get 7 (which reduces down to zero). The year code for 1809 is 0.

So, his birthday is: 2 + 12 + 0 - 14 - (biggest multiple of seven) = 14 - 14 = 0.

Lincoln was born on a Sunday!

For 2100 dates, you'd need to add 5 to the year code (or subtract 2 from the year code). For example, 2109 has a year code of 4 + 5 = 9. Subtract out 7 gives a year code of 2. For 1700s, you'll treat them just like the 2100s.

Why does this work?

We're using a Gregorian calendar. While this type of calendar was created in 1580s, it wasn't until Wed, Sept 2, 1752 when it was adopted by England and American colonies. 1752 has a year code of zero. Which is why this method won't work for any dates before this, as they were on the Julian calendar. Note that the Gregorian calendar repeats itself every 400 years, so you can convert any future date into a date near 2000. For example, March 19, 2361 and March 19, 2761 will both be on a Sunday.

Exercises

Identify the days corresponding to the following dates given in the format,: mm/dd/yyyy

  1. 11/16/1997
  2. 1/1/1997
  3. 05/27/1995
  4. 08/15/1997
  5. 07/15/1977
  6. 03/01/1977
  7. 11/24/1974
  8. 06/27/1958
  9. In a certain family, Janet was born on May 20, 1992 while Lewis was born on March 31, 1996. Who was born on Sunday?
  10. On which day is April 30, 1960?

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Paperclip Trick

Tuesday July 31, 2012

For this puzzle, you’ll use three cups and eleven objects. The first challenge is to put an odd number of objects in each cup. Is this pretty simple? How many different combinations can you come up with for the eleven objects?


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Download Student Worksheet & Exercises


Now how about if we take an object away and use ten instead? Is this puzzle more challenging? Here’s a hint: can you figure out a way for an object to be in two different cups at the same time? Work on this for a little while prior to watching the solution.



Pretty cool, right? I hope you enjoyed this trick. Mathematics and paradoxes can really be a lot of fun!



Exercises


  1. What is an even number?
  2. What is an odd number?

If you have 8 paperclips and three cups, arrange the paperclips you that you have an odd number in each cup. Find three different solutions (arrangements) to solve this problem.


  1. First arrangement
  2. Second arrangement
  3. Third arrangement

Now you have 11 paperclips and three cups. Find two new solutions (ones we haven’t covered yet in this lesson) to having an odd number in each cup.


  1. First arrangement
  2. Second arrangement

Reduce your number to 10 paperclips. Find four new solutions (ones we haven’t covered yet in this lesson) to having an odd number in each cup. (Is it easier this time?)


  1. First arrangement
  2. Second arrangement
  3. Third arrangement
  4. Fourth arrangement

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New Year’s Puzzle

Tuesday July 31, 2012

This is a really fun riddle! It’s a math logic puzzle involving the calendar that will really blow your mind. Pay close attention to the clues I give in the video and see if you can work out how it works.  Pause the video at about the 1:30 mark if you would like to try and work out the answer before I show you how it works!


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What do you think about this riddle? It’s a fun puzzle and it shows you how to effectively use a timeline in order to solve a logic problem involving the calendar. Pretty cool, right? Sometimes drawing a diagram can help you to work out details of a puzzle by giving you a visual aid to reference.


Exercises


Your exercise for this lesson is to not only challenge someone else with this problem, but be able to explain it to them in a way that they understand the solution. Go for it!


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Logic Numbers

Tuesday July 31, 2012

This is a neat logic trick which allows you to flip over a stack of cards numbered 1-10. When you flip the back upright, they are in numerical order. There is a special way to make it work, so pay close attention to the video. I’ll show you exactly how it works.


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Does this make sense? What order do you think the cards need to go in so that the trick works? Use your logic skills to work it out.


Exercises


Your exercise for this lesson is to not only challenge someone else with this problem, but be able to explain it to them in a way that they understand the solution.


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Hex

Tuesday July 31, 2012

Hex is a super fun game! It starts with a grid of hexagons (six-sided shapes) and two players. You can color in any cell on your turn. The ultimate goal is to be the first one to complete a chain across to the other side of the board.


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Here’s a link to the game board for you to print and use.


Using the pie rule can help with the advantage that the first player gets. This means the second player can choose to switch positions with the first player after they’ve made their first move. Can you use your logic skills to find strategies that make getting across the board easier?
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Magic Squares

Tuesday July 31, 2012

Magic squares have been traced through history as known to Chinese mathematicians, Arab mathematicians, India and Egypt cultures. The first magic squares Magic squares have fascinated people for centuries, and historians have found them engraved in stone or metal and worn as necklaces. Early cultures believed that by wearing magic squares, it would ensure they had long life and kept them from getting sick.

Benjamin Franklin was well-known for creating and enjoying magic squares, and it was all the rage during his time. Here's the deal: we're going to arrange numbers in a way so that all the rows, columns, and even the diagonals add up to a single number (called a Magic Sum). In this video, I show you the first Magic Square published in Europe way back in 1514. Plus, I show you how to make your very own Magic Square. You can use it to test your friends.

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You can create a magic square that sums to any number by referencing the original "34" magic square. Ask a friend for a number larger than 34 (which is the smallest magic square you can create), and then follow these easy steps:

1. First take the number your friend gave you and subtract 34.
2. Divide your number from #1 by 4 and keep the remainder to use like this: the quotient is the first magic number and the quotient plus the remainder is the second magic number. For 67 the results are 8 and 9.
3. When you fill out a square in your new 4x4 magic square, peek at the 34-magic-square and see what's already in the box. If it's a 13, 14, 15, or 16, then add the second number to it and put it int he box. If not, add the first number to it.

Note that if your number is even (but not a multiple of 4) then you'll have the same number for your first and second numbers. That's okay!

Exercise

Find the value of the letters; A, B,C and D in the following upside-down magic square

18

A

61

D

81

98

91

B

88

C

68

96
  1. A
  2. B
  3. C
  4. D
  5. What is the sum of elements of any diagonal in the first magical square published in 1514?
  6. Find the element at the middle of a nine-element magic square.
  7. Draw a nine-element magic square.

Find the values of b and c in the following magic square.

16

2

c

10

11

8

6

7

d

b
  1. b
  2. c
  3. d

[/am4show]


Bagels

Tuesday July 31, 2012

If you’ve watched my “What Is Math?” video, you’ve seen a sample of the Bagels math logic game. This is one of my family’s favorites! It’s a guessing game, but you can use logic and strategy in order to guess the numbers very quickly. In this video, I’ll show you in more detail how it works. I’ll also show you how to use the game to guess numbers even larger than three digits. Once you’ve mastered the strategies in this game, you’ll never lose another game of Mastermind again.


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What do you think about using this method to guess 4 or 5 digit numbers? It’s not much more complicated than guessing smaller numbers, but it’s a lot to keep track of in your head.  So use a pencil and paper to give it a try.


Exercises


Your exercise for this lesson is to play this game (start with two-digit numbers) until you can see a pattern to quickly guess any number. Have fun!


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Dictionary

Tuesday July 31, 2012

If a friend had chose a three-letter word and asked you to guess it, how would you start? It seems like it might take a while to narrow it down, right? This is a neat word guessing game that uses some strategy to make the guessing both a little easier and more fun.  When you try to guess your partner’s three-letter word, they can simply give you one of two clues that will make it a bit easier to narrow down the answer. Watch the video for an explanation.


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So just by using words like “Not yet!” and “Too far!” you can make the game much more fun and interesting. Otherwise it might take a really long time to figure out the word!  If you and your friends start to get really good at this game, you can try it with four and five letter words to make it even more challenging.
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Tic Tac Toe

Tuesday July 31, 2012

The first folks to play this game lived in the Roman Empire, but it was called Terni Lapilli and instead of having any number of pieces (X or O), each player only had three, so they had to move them around to keep playing. Historians have found the hatch grid marks all over Rome. They have also found them in Egypt!


In 1864, the British called it “noughts and crosses”, and it was considered a “children’s game”, since they would play it on their slates. In recent times (1952), OXO was one of the first known video games, as the computer played games against a person.


Tic-Tac-Toe can be fun, but when you get a “cat’s game” (no winner), it can get a little boring pretty quickly, right? In this video, I’ll show you some cool ways to change the game to make it more interesting by changing one or two of the basic rules. It’s much more engaging and strategic that way! Currently there are over 100 variations of Tic-Tac-Toe, and I’m going to show you my favorite ones. In fact, last time I taught a live science workshop, all 120 kids played this at the same time with squeals of delight!


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Which variation of Tic-Tac-Toe did you like best? Do you think it changes the game a lot to let each player choose either X or O during their turn? The number Tic-Tac-Toe game is pretty neat – I’ve found it’s easier to keep track by starting with 9 and going down to 1, alternating turns and numbers as you go. Last One Wins is great, too, but 4-In-A-Row Tic-Tac-Toe may be my favorite. It’s really fun for the whole family to play!


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Rail Fence Cipher

Tuesday July 31, 2012

Cryptography is the writing and decoding of secret messages, called ciphers. Now  for governments these secret ciphers are a matter of national security. They hire special cryptanalysts who work on these ciphers using cryptanalysis. The secret is, solving substitution ciphers can be pretty entertaining! Ciphers are published daily in newspapers everywhere. If you practice encoding and decoding ciphers, you too can become a really great cryptanalyst.


In this video, I’ll show you how to use the Rail Fence Cipher. Before you start, say this three times fast: cryptanalysts use cryptanalysis to crack ciphers!


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How did you like the Rail Fence Cipher? Pretty neat, right? Would you rather encode or decode a cipher? I think both parts are fun. But if you’re encoding, just make sure the decoder knows the correct formula to use!


Exercises


Write the cipher of the following message:


  1. COME TOMORROW AT 2PM
  2. HE HAS ARRIVED AT THE AIRPORT
  3. HE IS CARRYING A BAG
  4. THEY ARE HERE NOW
  5. COME AT MY PLACE

Write the cipher of the following message (use a three row zigzag)


  1. COME TOMORROW IN MY OFFICE
  2. LEAVE THEM BEHIND
  3. WE WILL BE THERE SOON
  4. The cipher below was encoded using a two rows zigzag method with six letters in every row. Decode it.
    IMOIG OACMN NW
  5. The cipher below was encoded using a three rows zigzag method with four letters in every row. Decode it.
    ICINA ONOMM GW

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Twisted Path Cipher

Tuesday July 31, 2012

In this video, I demonstrate a Twisted Path Cipher. It uses a matrix and a path in order to encode your message. The shape of the path you create within the matrix of a Twisted Path Cipher determines how difficult it will be to break the code. Watch the video to learn exactly how it works.


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What did you think of the Twisted Path Cipher? Remember that it will be easier to break your code if you use straight lines, so consider using some extra tricks to make it more difficult. For example, spirals, and zigzags are super hard to crack, and paths don’t have to be continuous! If you’re encoding, just make sure that the decoder knows the correct path shape (or shapes) to use!


Exercises


Given the following message, what would be the best size of the table to use?


  1. COME TOMORROW
  2. WE ARE WAITING AT THE BUS STATION
  3. THE LETTER IS IN HIS BRIEFCASE
  4. HE WILL COME LATE TODAY

Identify the type of path indicated in the diagrams below


  1. twisted-path-cipher-1
  2. twisted-path-cipher-2

Write the cipher of the following message using the path in #5 above.


  1. I WILL LEAVE FOR UK TODAY
  2. AM ON MY WAY TO THE SCENE
  3. I WILL ATTEND THE OPENNING DAY
  4. I WILL BE THERE AT 2

[/am4show]


Shift Cipher

Tuesday July 31, 2012

Shift ciphers were used by Julius Caesar in Roman times. The key is a number which tells you how many letters you’ll shift the alphabet. These are fairly simple to encode and decode. However, you have to be extra careful when encoding because mistakes can throw off the decoding process. Watch the video to see why it’s important to double check your work!


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Do you see why it’s important to double check the encoding?  This is a simple code, but it’s easy to shift and end up with a jumble when your message is decoded. So always check your cipher with a practice decoding prior to sharing it.


Exercises


Use the key shift number 4 on the letters of alphabet to code or decode the following:


Encode the following statement:


  1. OUR SCHOOL WAS THE BEST
  2. I WAS THE BEST IN MATHEMATICS
  3. I AM THREE FEET TALL
  4. OUR SCHOOL HAS GOOD TEACHERS
  5. COME TO MY RESCUE

Decode the following:


  1. SAWNA HAWRE JCXQZ
  2. SDWQE OQDAM PAOQE KJXQZ
  3. LHAWO AYKIA QKZWU
  4. EWIKJ IUSWU
  5. ODAEO WCKKZ OEJCA NMXQZ

[/am4show]


Date Shift Cipher

Tuesday July 31, 2012

The Date Shift cipher is a much harder code to break than, for example, the more simple Shift cipher. This is because the shift number varies from letter to letter, and also because it’s polyalphabetic (this means that a single number can represent multiple letters). I’ll explain it all in the video.


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What do you think about the Date Shift cipher? The possibilities for numerical keys are endless. You can use the date you’re sending the message, birth dates, phone numbers, and more! Just remember to start decoding by writing the key numbers over the top of the encoded cipher. And always makes sure the decoder has the correct numerical key!


Exercises


  1. Which kind of key is used in date-shift ciphers?
  2. In which direction is the cipher shifted when decoding?
  3. How do you describe a cipher where a specific alphabetical letter represents more than one letter?

What would be the date shift key codes for the following?


  1. April 4th  1998 (Don’t forget that the key needs six digits! Use “04” for the date.)
  2. Jan. 28th 2012
  3. Nov. 30th 2011

Encode the following:


  1. COME TO MY HOME : March 16th 1999
  2. THEY HAVE JUST LEFT : June 1st 2001

What are the original messages? (These messages were sent on July 16th 1992)


  1. GUBZC GOGNZ
  2. MKFZV GAZTO GROZQ

[/am4show]


Pig Pen Cipher

Tuesday July 31, 2012

The Pig Pen cipher is of the most historically popular ciphers.  It was used by Freemasons a century ago and also by Confederate soldiers during the Civil War. Since it’s so popular, it’s not a very good choice for top secret messages. Lots of people know how to use this one! It starts with shapes: tic-tac-toe grids and X shapes. I really like it because coded messages look like they’re written an entirely different language! Watch the video to learn how it works.


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Isn’t this a fun one!  To make the cipher a little harder to crack, arrange the encoded message in groups of five characters. As always, remember that your intended recipient needs the Pig Pen key in order to decode your message.


Exercises


  1. What’s the difference between the second and the fourth pig pen?

Draw the following:


  1. The third pig pen
  2. The first pig pen

Using the following pig pen key, encode #4-7:



  1. GO TO SCHOOL
  2. COME BACK
  3. I WILL SLEEP LATER
  4. NORTHERN AMERICA

Using the pig pen key, decode the following messages:


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Polybius Checkerboard Cipher

Tuesday July 31, 2012

Polybius was an ancient Greek who first figured out a way to substitute different two-digit numbers for each letter. In the Polybius cipher we’ll use a 5×5 square grid with the columns and rows numbered. Take a look at the video and I’ll show you how it works.


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To make the Polybius more difficult to crack, you can write the alphabet backwards or in an up and down pattern rather than left to right. Just be sure the decoder knows if you’ve used a different path or pattern to encode.


Exercises


  1. Write the grid that is used to encode and decode messages in the Polybius Cipher. (Can you think up your own?)
  2. Identify the codes representing the following letters using the grid from the example in the lesson: A, O and C.

Encode the following statements using the Polybius Cipher grid from the main lesson:


  1. LET US LEAVE
  2. I AM LEAVING
  3. THEY WILL COME
  4. SHE IS HERE

Decode the following messages using the Polybius Cipher grid from the main lesson.


  1. 32-35-35-31-11-45-45-23-15-45-11-12-32-15
  2. 24-45-24-44-23-24-14-14-15-34
  3. 23-15-43-15-24-44-45-23-15-41-11-41-15-43
  4. 32-35-35-31-11-45-33-55-12-35-35-31

[/am4show]


Cracking Ciphers

Tuesday July 31, 2012

Cryptograms are solved by making good guesses and testing them to see if the results make sense. Through a process of trial and error, you can usually figure out the answer. Knowing some facts about the English language can help you to solve a simple substitution cipher. For example, did you know that an E is the most commonly-used letter in the English alphabet? It’s also the most commonly-used letter to end a word. Watch the video below to learn some more tips and tricks to get you on the right track to being an expert cryptogram solver!


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So, it helps to have a lot of words to work with so that you can begin to recognize patterns in the code.  Here are some examples from the video:


  • single letter words will most likely be either A or I
  • the most frequent two-letter words in English are OF, TO, and IN
  • the most frequently used three-letter words are THE and AND
  • finally, the most frequently occurring four-letter word in English is THAT

Additional tips include the fact that Q is almost always followed by U, and that N often (but not always) follows a vowel. Finally, if two code symbols occur in a row, they could be a consonant combination such as  LL, EE, SS, OO, TT, etc. The real trick to this is to try something, and then if it doesn’t work, go back and try something else. Get lots of practice by checking in newspapers and magazines for these popular puzzles. If you really like them, you can find puzzle books full of cryptograms. You’ll be an expert cipher solver in no time!


Exercises


  1. What does it mean by “cracking a cipher?”
  2. In there a difference between cracking and decoding a cipher?
  3. What is very important that a person should know before beginning the cracking process?
  4. What is the most common letter of alphabet that is usually at the end of a word?
  5. What is the most common letter that is usually at the beginning of a word?
  6. If you have a letter all by itself, what is it most likely to be?
  7. What are two of the most common two character words in sentences?
  8. What are two of the most common three character words in sentences?
  9. What is the most common four character word in sentences?

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$1 Word Search

Tuesday July 31, 2012

Have you ever heard of a dollar word search? It’s a special kind of puzzle where the letters in a word add up to a coin value. For example, an A is worth a penny, the letter B is worth two cents, C is worth three cents, and so on. Are you completely confused? That's okay!  Just watch the video and I’ll show you how it all works.

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Were you able to use my hints to find some dollar words? Keep trying! It’s really fun and rewarding to find out which words work. Please add a comment below if you discover a new one. We would love to add it to our growing list of dollar words!

Exercises

  1. What is the word “bucket” worth?
  2. Determine the monetary value of the word “toilet.”
  3. What is a “starfish” worth?
  4. The shortest sentence in English is “Go.” How much is it equivalent to?

Which one of the following has the greatest monetary value?

  1. Supper, dinner, lunch
  2. Monday, Sunday, Tuesday

[/am4show]


Isn't that SUM-thing?

Tuesday July 31, 2012

This is a neat trick that you can use to really puzzle your friends and family. If someone gives you a three-digit number, you can actually figure out what the end result will be after you've received two additional numbers, but before you actually know what those numbers are. Does this sound confusing?  Watch the video and I’ll show you how it works.

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Were you able to figure this problem out? The real trick is that you’re simply adding 1,998 to the first number that you received. No matter which other two numbers are given to you, make sure the number you write down makes each pair of numbers' sum 999. If you do this correctly twice, then the row of numbers you add together will be the same as the initial number plus 1,998. Try it out and let me know if it works for you!

Exercises

Predict the end result for the following numbers:

  1. 235
  2. 988
  3. 002
  4. 999
  5. 427
  6. 777
  7. 559
  8. What would be the difference between a number 769 and its predicted result based on the above knowledge?
  9. A mathematician was given a number x and gave its end result as 2877. What is the value of x?
  10. Suzanne was asked by her friend to predict the end results of 932 within a few seconds. If she was given 432 as one of the two additional numbers to complete the proof of the predicted number, which number did she write immediately afterwards?

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Playfair Cipher

Tuesday July 31, 2012

This is a super hard cipher to break.  It’s encoded by taking pairs of letters and numbers from a matrix. There are three rules to follow.


  1. If both letters are in the same row, then use the letters immediately to the right of each other. (Think of the rows as wrapping from the right end back around to that same row’s left end).
  2. If both letters are in the same column, then use the letters immediately below them. If necessary, the bottom letter wraps back around to the top of the same row.
  3. If the two letters or numbers are in different rows and in different columns, then each letter is replaced by the letter in the same row that’s also in the same column of the other letter. Basically, you find each intersection of the pair. Use the letter or number below the pair and then the one above the pair.

Play Fair sounds really complicated, but that also makes it a tough code to crack! Watch the video and I’ll explain it all for you.


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Isn’t this cool? It makes a lot more sense when you see it in action, right? Remember: when decoding the Playfair cipher, you have to shift up instead of down and left instead of right. And it’s easy to make a mistake by encoding in the incorrect order. So always  double check your cipher before sending it on to the recipient. Mistakes make messages much harder for the decoder to interpret!


Exercises


  1. What is the name given to the following table?
A H M V L 3 Y D
X K B 5 P Z E O
N 7 W U F T 6 J
G R 2 Q C A I S

Use the table in 1 above to answer question 2 – 10.


What will be the cipher for the following?


  1. KB
  2. HR
  3. AR
  4. EU
  5. COME TO SCHOOL
  6. GO HOME THEN

Decode the following messages


  1. 73 3N SG YZ 6X
  2. SG MN YK A7 JO HD
  3. Why is it important the number of letters in the message to be encoded be even?

[/am4show]


Telephone Cipher

Tuesday July 31, 2012

Code machines – or cipher machines – can be used to encode and decode messages. One everyday example of a code machine that you can easily access is a telephone. Watch this video and I’ll show you how it works.


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What do you think about the Telephone Code? Remember to get those slash codes just right in order to make decoding easier for the message receiver. (No pun intended!)


Exercises


Encode the following using the telephone keypad:


  1. COME BACK
  2. LEAVE TODAY
  3. HE ARRIVED
  4. THEY WENT
  5. HE IS COMING
  6. REVEAL
  7. GO AHEAD

Decode the following ciphers


  1. 1 6 3 7 4   2  2
  2. 8 64  8 3   3 5 4 6 4   3 6  6
  3. 2 8 7  8 7   2 5 4 2

[/am4show]


Invisible Writing

Tuesday July 31, 2012

This is an alternate method of secret writing that’s completely different from encoding and decoding message ciphers. It involves using special inks that are invisible until something is done to make them appear on the paper. There are hundreds of formulas to make these special inks and some formulas even have multiple ways to develop the ink. Some recipes involve special chemicals, but many invisible inks can be made using materials that you have in your home. Watch the video and I’ll share a few recipes and teach you more about this method.


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Some of these are really simple, right?  I like the wet and dry method a lot. When using the milk writing method, how do you think you would get the milk to change color so that the message could be read?
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Scytale

Tuesday July 31, 2012

In this video I’ll show you how to use a actual cipher machine called a scytale. This was first used in ancient Greek and Roman times, most notably by the Spartans. To make a scytale, use a cylinder with a piece of paper wrapped around it. Then simply print your message in rows that run along the length of the cylinder. When the paper is unwrapped, the message is scrambled!  Watch the video and I’ll show you the trick to proper message decoding.


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Isn’t this cool?  It’s very important to make sure that the message’s intended recipient has a cylinder of the exact same size so that they can easily decode the message.


Exercises


  1. What is the name of the cryptographic machine that was first used by the ancient Greeks and in Roman times to send secret messages?
  2. What is the shape of the machine named above?
  3. Where is the message written when using this machine?
  4. Apart from the machine, what else is required to be able to encode the message?
  5. Who were the people who most notably used the type of cryptography named?
  6. What is the major problem that the recipient must figure out to easily decode the message?
  7. Is it true that first letter in the original message would be the first letter on the encoded message? Explain.

[/am4show]


Big Numbers

Tuesday July 31, 2012

Numbers really can be huge – some are too big to even imagine!  Have you ever seen a million pieces of candy? Or have you ever even tried to count to one million? In this video, we’ll try to figure out about how long it would take just to count to one million. I’ll also show you how to write some really big numbers!

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So there are 31,536,000 seconds in a year, but you couldn’t spend all of your time counting. Simply saying larger numbers will take much longer than a second! So with lots of breaks for sleeping, eating, and homework, it would take more than a year to count to a million…and most people get bored with counting way before that.

Exercises

  1. How many seconds are there in one hour?
  2. How many seconds are there in a day?
  3. How many days does a leap year have?
  4. Write a number greater than but closer to a billion.(Note the difference between the two should be less than 50)
  5. Write a number lesser than but closer to a billion.(Note the difference between the two should be less than 50)

Write the following numbers out numerically:

  1. A thousand billion
  2. A thousand million
  3. A hundred hundred
  4. Write a number that is 1 less than 100,000,000,000

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Exponents

Tuesday July 31, 2012

Have you ever heard someone refer to a “million billion” of something? Is that more or less than a “billion million?” In this video, I’ll show you how to write down these numbers and figure out which one is larger.

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Download Student Worksheet & Exercises

Did one of these numbers sound bigger to you? To me, they’re both a strange way to say the exact same number – which is actually a quadrillion!

Exercises

Write out each number long-ways (with all the zeros written out):

  1. A thousand million
  2. A thousand billion
  3. Ten million
  4. A hundred billion

Write the exponential form (ten and a superscript) of the following numbers

  1. A thousand million
  2. A thousand billion
  3. Ten million
  4. A hundred billion

Determine the exponents of the following number if written in the form; ”ten and a superscript.”

  1. 10,000,000,000
  2. 100

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Factorials

Tuesday July 31, 2012

If I said “3!“, would you think the 3 is really excited, or that you have to shout the number?


In fact, it’s a mathematical operation called factorials, and boy are they fun! They may seem complicated at first, but they’re really a very basic concept. The exclamation point behind a number means that you multiply that number by each successively lower number, in order, until you get to one.


So 3! would be 3 x 2 x 1 = 6.


Take a look at the video for an explanation of how factorials work and how they can be used.


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Download Student Worksheet & Exercises


Can you see how factorials start to get really big, really quickly? The card deck is a really great example of this, because with 52 cards the factorial is 52!, which is a HUGE number. There are literally trillions and trillions and trillions of ways to arrange those cards.


Does 0! = 1 make sense to you?  If not, that’s okay. Just memorize this fact and tuck it away for later. It will come in handy some day in algebra and maybe even for calculus!


Exercises


  1. 6!
  2. 6!/4!
  3. How many ways can seven different cards arranged uniquely?
  4. 0! x 4!
  5. 3! x 4!
  6. 1! x 5!
  7. 2! x 0 x 6!
  8. 2! x 4!
  9. 3! x 2!
  10. 5! x 0! x 1! x 2!

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Checkerboard Paradox

Tuesday July 31, 2012

Once in awhile, mathematicians come up against something that really seems impossible on the surface. These seemingly “impossibilities” not only cause them to sit up and take notice, but often to create new rules about the way math works, or at the very least, understand math a little better.


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Be warned however, that some paradoxes are really false paradoxes, because they do not present actual contradictions, and are merely “slick logic” tricks. Other paradoxes are real, and these are the ones that shake the entire world of mathematics. There are several paradoxes that remain unsolved today. You can find a list of paradoxes here.


There are a lot of variations on the checkerboard paradox. Here’s one of my favorite paradox puzzles – can you explain it?


You’ll find need to download the PDF and cut out your four pieces.



Download Student Worksheet & Exercises


Need a HINT? I’ll give you a hint… look at the following picture:


If you cut the rectangle along the diagonal (the line that magically appears from one corner to the other) and then slide the lower triangle as shown, you can count the number of vertical lines and find that there are only nine! What happened to the tenth? You can make it magically appear if you slide the lower triangle back to its original position. So… my question to you is: Which is the line that has returned and where does it come from?


The secret is this: there is a progressive decrease in the length of the segments above the diagonal and a corresponding increase in the length of segments below. What happens is that eight of the ten lines are broken into two segments, then these sixteen segments are redistributed to form nine lines, each a trifle longer than before. Because the increase in the length of each line is slight, it is not immediately noticeable. In fact, the total of all these small increases exactly equals the length of one of the original lines. Therefore, there is actually not a line which vanishes.


Now… how would you explain the checkerboard paradox? Put your answer in the comment box below…


Exercises


Your exercise for this lesson is to not only challenge someone else with this problem, but be able to explain it to them in a way that they understand the solution.


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Probability

Tuesday July 31, 2012

In math, probability is how likely it is that something will occur (or not). Probability is expressed from a range from 0 to 1. A probability of zero means that a thing will definitely not happen – it’s impossible. But a probability of one means that it definitely will happen – it’s certain. Any number larger than 0, but smaller than 1 means that a thing might happen. The number 1/2, or one half, is right in the middle and it means there is a 50/50 chance. Do you think there’s a greater chance for a person to get struck by lightning, or to be hit by a meteorite?


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Download Student Worksheet & Exercises


Some key words that help with probability questions are OR and AND. When you see the word OR, it means you should be adding the possible outcomes to find out the probability whether one thing OR another will happen. The word AND means you will probably be multiplying to find the solution. Based on these rules and the information that I share in the video, what are your chances of being struck by lightning AND having a heart attack?


Exercises


  1. What is the probability of a coin showing tails when flipped?
  2. What is the probability of a coin showing heads twice in a row?
  3. What is the probability that heads or tails will show up in a toss?
  4. What is the probability that heads and tails will show up in two successive tosses?
  5. A die is rolled once: what is the probability that a four will show up?
  6. A die is rolled once: what is the probability that a three will show up?
  7. A die is rolled once: what is the probability that a four or a six will show up?
  8. A die is rolled twice: what is the probability that a four will show up in all the rolls?
  9. A die is rolled twice: what is the probability that a four and a two will show up?
  10. A die is rolled twice: what is the probability that the same number will show up in all the rolls?

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Three Doors

Tuesday July 31, 2012

Imagine that you are on a game show with a chance to win a car. There are three doors and the car is behind one of them. You just have to choose the correct door! You can use probability to get an possible advantage in choosing the correct door. Watch the video, and I will explain how it works.


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Download Student Worksheet & Exercises


So would you have changed your mind about your pick or stuck with the second door? Using probability, we can determine that door number 1 really is the door with the best odds for winning the car. Isn’t that interesting?


There were many math PhDs that disagreed with the right answer. There will always be someone who won’t believe it. But here’s the correct answer.


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Educational Games That Teach

Saturday January 22, 2011

If you've ever wanted to sneak a peek into my cabinet of educational games and books for kids, now is your chance. Use this list for gift ideas, boredom busters, and just plain family fun. Some of these games you can pick up at the store, and the rest are the home-made, print-it-out, cut-and-play variety that your kids will really learn from.

I first made this list because I felt that so many games are watered-down versions of either bingo or "roll the dice and see where you land", with the occasional card pick. I was curious to see if there were any truly great educational games still available, or if they were all just brain candy.

My games listed here are designed to develop strategy, critical thinking, and chaotic surprise in addition to having the kids learn practical knowledge along the way (not trivial fluff). And when a kid memorizes the card deck, it works in their favor because now they know the entire periodic table.

Here you'll find games including arithmetic, fractals, equations, chemistry, physics, and more. If you have any you'd like to add to the pile, just submit it in the comments section so everyone can benefit. Are you ready?

Note: This list is growing so please check back for updates!

Favorite Books

Favorite Resource for Science Supplies

A lot of science supplies can be purchased online these days, especially the hard to find stuff. However, if you're in the market for oddball items from a company that reuses industrial overruns, here it is:

  • RAFT Resource Area For Teaching RAFT (Resource Area For Teaching). When I was first starting out, I would take a pickup truck to RAFT in San Jose and load up on everything I needed to teach science for the month. Since I was teaching at 60 different schools (about 50 classes per week), I went through a LOT of materials... and I knew I had to get them inexpensively. RAFT has grown a lot over the years, and if you've never had the opportunity before, now is your chance to check it out for yourself.
  • Educational Innovations is the place I got a lot of my physics stuff when I was teaching at the university.
  • Sci-Supply is an inexpensive physics store with lots of great stuff for smart kids.
  • Science First is where I get a lot of my higher-end, more commercial grade physics demos.

Favorite Science Games

Math Games

  • Equate the Math version of Scrabble, which is great for kids that are getting the hang of arithmetic
  • Best Dice Game for honing math skills - I keep a set in my purse wherever I go (no kidding!)
  • Monopoly using a third and fourth die to calculate tax for purchases or compound interest (for rate and time); federal income tax brackets (which depend on your capital) replaces the 'income tax' square... we try to make it as realistic as we can, and even do the 'bidding option' stated in the rules when buying property.
  • Mathematician Dice
  • Cryptarithms (one of my favorite math games - it's the image of "SEND MORE MONEY" at the above right - you have to figure out what number each letter represents!)
  • More Math Recommendations

Awesome Games Overall

  • Chess find a 34-piece set (with four queens) and a vinyl mat

Intelligent Music for Kids

(that doesn't make adults want to rip their hair out)

Here's the video of the Element Song:

 

 

Here's the video of the Nano Song:

 

Note: You can find more songs at the Harvard Physics Song site, but be sure to preview them before sharing them with your kids as they are more appropriate for college-level students!

What Pi Sounds Like by Michael Blake (see video below):


Math Recommendations

Wednesday January 20, 2010

readbookMost resources that public school advisers suggest for gifted or bright kids are a ‘mile wide and an inch deep’ – they don’t really go into depth on any one area. After traveling to dozens of home school conventions for several years across the country and seeing what math options are out there, I searched for more options than what’s traditionally on the exhibit floor.


After talking with math professors from Harvey Mudd, Stanford, Princeton, UCLA, and others, I thought you might like to know about their recommendations for resources that might be useful to you on how to deliver math skills in a way that really lasts.


For kids just starting out with Math: Dr. Wright’s Kitchen Table Math


For kids not quite ready for Algebra: Singapore Math Series


For kids Algebra through Calculus: Art of Problem Solving


These two work well together, and lead right into each other. If you’re looking for a DVD series, then you’ll want to get Arthur Benjamin’s 24-lecture ‘Joy of Mathematics’ DVDs.


More Math Resources

These resources are for kids that are really into math and enjoy diving deep:


  • Go Figure A totally cool book about numbers that my kids love to read in carpool.
  • Why Pi? is the second book that builds more on the ideas from Go Figure
  • Story of Math is a 2-volume DVD set you can find at your library that focuses on how and why math was developed and the current ideas about who discovered what and when.
  • Fractals – Hunting the Hidden Dimension This is a Nova documentary you can find at the library which has enough plain-English for everyone. By the way, fractals are fragmented geometric shapes split into parts, each of which is approximately a reduced-size copy of the whole thing. Fractals are between dimension 2 and 3, depending on their depth.
  • Games for Math – this book is a treasure-trove of math games you can make out of papers, scissors, and a little time. We’ve done a lot of these with our kids when they were in K-2nd grade. Find it at your library so you can browse through it yourself.
  • Ten Marks A math curriculum that’s aligned with state standards.

How to Add and Multiply Quickly in your Head

Sunday December 20, 2009

Want a peek under the 'hood' of my brain when I do a mental math calculation? This video is a slow-motion, step-by-step snapshot of what goes on when I add numbers in my head. The first thing you need to learn is how to add from LEFT to RIGHT, which is opposite from most math classes out there. I'll show you how to do this - it's easy, and essential to working bigger numbers in your head.

Here's what you do:
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Download Student Worksheet & Exercises

Exercises

  1. 23 + 74
  2. 48 + 169
  3. 627 + 192
  4. 799 + 5692
  5. 562 + 658
  6. 20 x 236
  7. 400 x 41
  8. 300 x 344
  9. 50 x 239
  10. 203 x 456

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Easy Dice Game for Honing Math Skills

Thursday December 3, 2009

Did you know I carry a set of dice in my pocket just for this game? It's as old as the hills and just as fun to play now as it was when I was a little math whiz back in 2nd grade.  (No kidding - when we had 'math races', I was always team captain.  Not quite the same thing as captain on the soccer field, though...)

This is one of those quick-yet-satisfying dice games you can play to hone your thinking skills and keep your kids busy until the waiter arrives with your food.  All you need are five or six standard 6-sided dice and two 12-sided dice.  (Note - if you can't find the 12-sided dice, just skip it for now.  You can easily substitute your brain for the 12-sided dice.  I'll show you how.)
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You need to do two things to play this game. You can use a calculator with this game, but usually the kids without the calculator win the round, as it usually takes longer to punch in the numbers than figure out the different possibilities in your head (and that's what you're working on, anyway!) If  your kid is a highly visual learner, then hand them a scratch pad and a pencil so they can scribble down stuff as they go.

Download Student Worksheet & Exercises

First, roll the two 12-sided dice. Multiply the two numbers in your head.  If you rolled a 6 and 6, you'd now have 36. That's your target number.  If you don't have the 12-sided dice, just think up two numbers, each between 1 and 12 and use those.

Next, roll the 6-sided dice. Now, using your arithmetic skills, figure out a way to add, subtract, multiply or divide those three numbers to get the number you rolled with the first set.  So if you rolled six 6-sided dice and got 4, 5, 2, 1, 1, 5, you could do this:

(Red numbers are the ones rolled on 6-sided dice.)

(4 x 5) - 2 = 18

18 x (1 + 1) = 36

You don't have to use all the numbers, but you can't double up and use a 4 twice if you only rolled one 4.  And that's it!  It's loads of fun and engaging, because it's got more than one answer.  And sometimes there's no answer (although rarely!). As you get faster and better at this game, try taking away one or two of the dice.  It's more challenging.

HOT TIP: You can add in the use of exponents when your kids get the hang of the game. An exponent tells you how many times to multiply a number by itself. For example, a 2 with a 3 exponent looks like: 23 = 2 x 2 x 2 = 8. To use exponents, simply use one of the numbers as an exponent. For example, if you rolled five 6-sided dice and got 5, 2, 3, 2, 4, you can do this to get 36 (given 36 came from the 12-sided dice):

(Red numbers are the ones rolled on 6-sided dice.)

(5 x 2) = 102 = 100

100 - (43) = 36

When your kids get good, you can up the ante and use a set similar to what I have in my purse: one 20-sided double dice and a handful of 6-sided. Math craze, anyone?

Exercises

No dice? Try these combinations that I rolled and recorded for you. I rolled six 6-sided dice and two 12-sided dice. Can you figure out a combination that would make each target number? Remember that the target number is the product (multiplication) of the two numbers from the 12-sided dice.

6-sided dice               12-sided dice

  1. 2,3,5,6,1,3         ---     10,2
  2. 4,3,6,4,5,3         ---     12,9
  3. 1,6,4,4,2,1         ---     5,8
  4. 4,1,1,1,2,3         ---     3,9
  5. 1,6,6,5,5,1         ---     9,7
  6. 2,1,4,5,2,2         ---     6,3
  7. 3,1,6,5,4,1         ---     11,4
  8. 4,3,6,4,5,3         ---     12,7
  9. 2,2,3,3,4,6         ---     4,6
  10. 3,5,6,1,3,3         ---     6,9

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Multiplying 2-Digit Numbers by 11

Sunday September 20, 2009

Here's our first MATH lesson. It is so easy that one night, I wound up showing it to everyone in the pizza restaurant. Well, everyone who would listen, anyway. We were scribbling down the answers right on the pizza boxes with such excitement that I couldn't help it - I started laughing right out loud about how excited everyone was about math... especially on a Saturday night.

When you do this calculation in front of friends or family, it's more impressive if you hand a calculator out first and let them know that you are 'testing to see if the calculator is working right'.  Ask for a two digit number and have them check the calculator's answer against yours.

If you really want to go crazy, you can have math races against the calculator and its operator, just as the Arthur Benjamin video shows.  (Only you don't need to do the squaring of five-digit numbers in your head!)  Have fun!
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Download Student Worksheet & Exercises

So here's the deal:

11 x 23 = ?

Take the 23 and spread it apart, so it looks like "2 3" with a space in the middle. Now add 2 + 3 to get: 2 + 3 = 5 and insert the 5 into the space. So...

11 x 23 = 253

That's it. How cool is that??

What about this one? 11 x 45 = ?

Spread apart the 4 and 5, then insert the sum of the 4 and 5 in between to get:

11 x 45 = 495

Whoa...!!! This stuff is soo cool! But wait a second... you hit a speed bump when you try this one:

11 x 86 = ?

It seemed a bit ridiculous to get: 11 x 86 = 8146. The answer should be a 3-digit number, not 4! So, check again and then find that you need to 'carry' the one to the first digit, so it becomes:

11 x 86 ==> 8(14)6 ==> = 946

And of course, if you can do 86, you have to give 99 a try:

11 x 99 ==> 9(18)9 ==> 1,089

Now you give yourself a few different numbers to try. Check your answer with a calculator!

Tell me how YOU think this works in the comment field below!

Exercises

  1. 11 x 11
  2. 11 x 27
  3. 11 x 43
  4. 11 x 49
  5. 11 x 50
  6. 11 x 67
  7. 11 x 79
  8. 11 x 89
  9. 11 x 92
  10. 11 x 96

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Multiplying 3-Digit Numbers by 11

Saturday September 19, 2009

If you can multiply 11 by any 2-digit number, then you can easily do any three digit number. There's just an extra step, and make sure you always start adding near the ones so you can see where to carry the extra if needed.
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Click the player to learn how to multiply any three-digit number by eleven:

Download Student Worksheet & Exercises

Tell me how YOU think this works in the comment field below!

Exercises

  1. 11 x 163
  2. 11 x 235
  3. 11 x 345
  4. 11 x 479
  5. 11 x 659
  6. 11 x 748
  7. 11 x 997
  8. 11 x 982
  9. 11 x 873
  10. 11 x 769

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Mental Mathemagic

Thursday August 20, 2009

We're going to throw in a few math lessons here and there, so if math really isn't your thing, free free to just watch the videos and see what you think. All of these lessons require only a brain, and once in awhile paper and pencil, so this area is 'materials-free' and jam-packed with great mathematical content. If you're the parent, stick a calculator in your pocket and test out your kids as they go along.

Some of what we cover here is based on the book "Secrets of Mental Math" by Arthur Benjamin, an incredible professor at Harvey Mudd College. He's also known as the "Lightning Human Calculator". Here's a video about him you may enjoy:
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We're going to break down the steps to really getting to know numbers and put it into a form that both you and your kids can use everyday, including shopping at grocery stores, baking in the kitchen, working on the car, and figuring out your taxes. It's a useflu tool for flexing your mind as well as appreciating the simplicity of the numerical world.

You can learn this stuff provided you already know how to add and subtract, as well as your multiplication tables. Sound like fun? Then let's get started! Click here for your first lesson.[/am4show]


Squaring Two-Digit Numbers

Monday August 3, 2009

This neat little trick shortcuts the multiplication process by breaking it into easy chunks that your brain can handle. The first thing you need to do is multiply the digits together, then double that result and add a zero, and then square each digit separately, and finally add up the results.

Slightly confused? Great - we made a video that outlines each step. There's a definite pattern and flow to it. With practice, you will be able to do this one in your head within a very short time. Have fun!
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Click the player to learn how to square any two-digit number:

 

Download Student Worksheet & Exercises

Tell me how YOU think this works in the comment field below!

Exercises

  1. 〖21〗^2
  2. 〖43〗^2
  3. 〖37〗^2
  4. 〖69〗^2
  5. 〖99〗^2
  6. 〖82〗^2
  7. 〖58〗^2
  8. 〖64〗^2
  9. 〖53〗^2
  10. 〖86〗^2

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Rare Scrabble Words

Tuesday April 21, 2009

If you really want to baffle Aunt Edna next time she visits, then these tips are for you. As a kid, I was never very good at Scrabble, mostly because I played with adults and my word range simply wasn’t as large… so it was highly unfair.


Here’s a way to tip the scales if you feel like you’re in the same boat as I was. The words below can score you big points, both on the board (if you use the triple boxes) and also in the eyes of your family!


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  • fixy (fussy)
  • mazy (confusing)
  • guaiac (bean)
  • azym (type of bread)
  • oyez (“SILENCE!”)
  • zyme (enzyme)
  • aalii (type of tree)
  • pyx (tiny box)
  • zax (tool used for roofing)
  • vizy (to inspect)
  • quay (small wharf)

Win a Bet in Scrabble Are there any words in the English language that use a, e, i, o, u, and y (as a vowel) all in their correct order?  Actually there are two:


  • facetiously (not meant to be taken seriously, humorous)
  • abstemiously (to eat and drink sparingly)

If you like both Scrabble and doing math, then you’ll want to take a look at Equate, which is the mathematical version of Scrabble. I’ve played this type of math game a lot over the years with my kids, and it’s always fun to watch their development grow.


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How to Square Bigger Numbers Faster in your Head

Thursday July 31, 2008

Squaring three-digit numbers is one of the most impressive mental math calculations, and it doesn't take a whole lot of effort after you've mastered two-digits. It's like the difference between juggling three balls and five balls. Most folks (with a bit of practice) can juggle three balls. Five objects, however, is a whole other story (and WOW factor).

Once you get the hang of squaring two-digit numbers, three-digit numbers aren't so hard, but you have to keep track as you go along. Don't get discouraged if you feel a little lost. It's just like anything you try for the first time... when you're new at something, in the beginning you aren't very good at it. But with practice, these steps will become second nature and you'll be able to impress your friends, relatives, and math teachers.

The video below has two parts:

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Download Student Worksheet & Exercises

Exercises

  1. 〖93〗^2
  2. 〖193〗^2
  3. 〖979〗^2
  4.  〖249〗^2
  5. 〖415〗^2
  6. 〖84〗^2
  7. 〖573〗^2
  8. 〖333〗^2
  9. 〖757〗^2
  10. 〖696〗^2

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How does a Two-Fingered Alien Count?

Monday July 21, 2008

One day, my kid asked me how a calculator comes up with its answers. That's a great question, I thought. How does a calculator do math?

After thinking about it, I realized this was a great way to teach him about binary numbers. I am going to show you how to not only count in binary, but also help you understand the basis of all electronic devices by knowing this key element.

 

 

 

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Download Student Worksheet & Exercises

By asking questions, you can discover a lot of what you already know about a subject. In this case, students usually know how to count to 100 or even 1,000, but they don’t consciously know why the numbers change in the sequence that they do. In this activity, we’re going to explore how quantities are represented by numerals (digits 0 through 9), and then learn how you can change the number of numerals and count in different bases. In the instructional video, we’re learning base 2 and 10, but you can use this to represent any base to count in.

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