I did a few experiments. Apparently, nine planets is the answer they're looking for. I thought was just being funny.
I studied hard for my blood test, and got an A+. Clearly, it pays to study.
Thursday, October 19, 2006
Failed Supidity Test
So, i took this test of stupidity, and failed it pretty badly. Most people did much better. In fact, only 8% scored less stupid than i did. I just don't get it.
I did a few experiments. Apparently, nine planets is the answer they're looking for. I thought was just being funny.
I studied hard for my blood test, and got an A+. Clearly, it pays to study.
I did a few experiments. Apparently, nine planets is the answer they're looking for. I thought was just being funny.
I studied hard for my blood test, and got an A+. Clearly, it pays to study.
Tuesday, October 03, 2006
Superhero
Cool.
| You Are Batman |
 Billionaire playboy by day. Saving the world by night. And you're not even a true superhero. Just someone with a lot of expensive toys! |
Wednesday, September 27, 2006
No Prints for the Prince Needed
The Prince and the Pauper by Mark Twain is available on Libravox as audio. It is read by John Greenman, who has an excellent voice and delivery.
The book itself is a classic, must read, or at least listen. I was able to mostly listen to just one 20 (or so) minute chunk per day. A the end, though, i pretty much had to find out how it turned out. Should i say it has a happy ending? No. I won't. Feel free to consider the ending a mystery.
The basic plot is that Prince Edward of England switches with a poor boy who happens to look like him. A complication is that the King is ill. The interesting thing is that the Prince gets to see how the other half lives, and acts on it. Another interesting thing is the footnotes. It gives the work the feel of non-fiction, making one wonder just exactly what was, and what wasn't made up. Maybe it's non-fiction, and it really happened 1547 as narrated. You decide.
The book itself is a classic, must read, or at least listen. I was able to mostly listen to just one 20 (or so) minute chunk per day. A the end, though, i pretty much had to find out how it turned out. Should i say it has a happy ending? No. I won't. Feel free to consider the ending a mystery.
The basic plot is that Prince Edward of England switches with a poor boy who happens to look like him. A complication is that the King is ill. The interesting thing is that the Prince gets to see how the other half lives, and acts on it. Another interesting thing is the footnotes. It gives the work the feel of non-fiction, making one wonder just exactly what was, and what wasn't made up. Maybe it's non-fiction, and it really happened 1547 as narrated. You decide.
Monday, September 18, 2006
To Be A Republican
What if you grow up, go to school, decide to plug into society, only to discover that you are both scientifically literate, and a Republican? I mean, you might be a Republican sort of by default. Your parents are Republican, and have told you that the party is conservative. That sounds nice. But as time goes on, you start hearing Republicans, right from the top, talking about how ID should be taught in schools as science. You hear nonsense like "there's no quick answer to the fuel crisis". And it just continues. What do you do?
Friday, September 15, 2006
Eye color
| Your Eyes Should Be Brown |
 Your eyes reflect: Depth and wisdom What's hidden behind your eyes: A tender heart |
They are in fact, blue.
While we're at it:
| You Are 50% Left Brained, 50% Right Brained |
 The left side of your brain controls verbal ability, attention to detail, and reasoning. Left brained people are good at communication and persuading others. If you're left brained, you are likely good at math and logic. Your left brain prefers dogs, reading, and quiet. The right side of your brain is all about creativity and flexibility. Daring and intuitive, right brained people see the world in their unique way. If you're right brained, you likely have a talent for creative writing and art. Your right brain prefers day dreaming, philosophy, and sports. |
I'm of two minds on this one.
Thursday, September 07, 2006
The Invisible Man
I was going to write this review with the text set to white. You'd be able to read it only by highlighting it. For example: The Invisible Text. It's almost like a cypher. Only the enlightened can read it.
The Librivox recording of H. G. Wells's book, The Invisible Man was read by Alex Foster, of Nottingham. The narrator, Alex Foster, has a great voice for this book. It's a radio voice. There are few, if any, errors. And very importantly, it isn't an American accent. The story takes place, if i understand my geography correctly, near London, so having an accent from that area is a plus. And yet, the text is very clear, with no misunderstanding, even by an American such as myself.
Interestingly, the description for how invisibility works is strikingly believable. In high school chemistry class, they had you put a certain amount of water in a beaker, put in a Pyrex rod, add a certain amount of a clear liquid, mix it, and boom (well, it was a surprise, anyway), the Pyrex rod that's in the liquid vanishes. The index of refraction of the water was altered to match that of Pyrex. The Invisible man is invisible because he's not only transparent, but in index of refraction matches that of air. Yet, Wells doesn't go so far as to tell you the details on how the thing works, exactly. Just enough to get you going. Masterfully done.
Now, the story has been done again and again in literature. Typically, the rip offs change the man's character greatly. Sometimes they come up with solutions to his various problems. Problems? Sure, well, he's only really invisible when he's naked. That's a decided disadvantage when it's winter. And in summer, the bug bites must be terrible. The solution was actually presented in the book, though the author chooses not to have the character use it.
Wells clearly wanted to have the book stand on it's own. Not a serial like Tarzan. So, the Invisible Man is smart enough to be dangerous, but not smart enough to live forever. Many of the rip off's, including a TV series, have the Invisible Man with a support network, and enough smarts to do interesting things as a serial.
The original book stands the test of time. Speaking of time. The Librivox recording of The Invisible Man is only about five hours long. Keep in mind that reading the text yourself is typically about three times faster. So this is a fairly short piece of entertainment. It's broken up into fairly short readings. Sometimes three chapters in a single file, but always under about 35 minutes. The chapters must be very short. In any case, it means one can get through a whole scene, and have a convenient break point.
Now, i mostly listen to these things while doing something else. This summer, i've listened to several books while gardening. I bought a non-motorized lawn mower so that i can listen while doing that task. Most of my listening time, however, happens during my commute to work. In a break with tradition, i actually found myself speeding up a little during the most exciting parts. (This doesn't get me to speeding, exactly, as i drive slower than the limit as a fuel conservation measure - which saves me more than an estimated $100 per year). It's an hour each way, so it's roughly ten hours a week. Against ten hours a week, a five hour book is pretty easy. The Tarzan books were about eight hours each. And when I listened to those, it was about one per week. Imagine reading fifty books a year.
The Librivox recording of H. G. Wells's book, The Invisible Man was read by Alex Foster, of Nottingham. The narrator, Alex Foster, has a great voice for this book. It's a radio voice. There are few, if any, errors. And very importantly, it isn't an American accent. The story takes place, if i understand my geography correctly, near London, so having an accent from that area is a plus. And yet, the text is very clear, with no misunderstanding, even by an American such as myself.
Interestingly, the description for how invisibility works is strikingly believable. In high school chemistry class, they had you put a certain amount of water in a beaker, put in a Pyrex rod, add a certain amount of a clear liquid, mix it, and boom (well, it was a surprise, anyway), the Pyrex rod that's in the liquid vanishes. The index of refraction of the water was altered to match that of Pyrex. The Invisible man is invisible because he's not only transparent, but in index of refraction matches that of air. Yet, Wells doesn't go so far as to tell you the details on how the thing works, exactly. Just enough to get you going. Masterfully done.
Now, the story has been done again and again in literature. Typically, the rip offs change the man's character greatly. Sometimes they come up with solutions to his various problems. Problems? Sure, well, he's only really invisible when he's naked. That's a decided disadvantage when it's winter. And in summer, the bug bites must be terrible. The solution was actually presented in the book, though the author chooses not to have the character use it.
Wells clearly wanted to have the book stand on it's own. Not a serial like Tarzan. So, the Invisible Man is smart enough to be dangerous, but not smart enough to live forever. Many of the rip off's, including a TV series, have the Invisible Man with a support network, and enough smarts to do interesting things as a serial.
The original book stands the test of time. Speaking of time. The Librivox recording of The Invisible Man is only about five hours long. Keep in mind that reading the text yourself is typically about three times faster. So this is a fairly short piece of entertainment. It's broken up into fairly short readings. Sometimes three chapters in a single file, but always under about 35 minutes. The chapters must be very short. In any case, it means one can get through a whole scene, and have a convenient break point.
Now, i mostly listen to these things while doing something else. This summer, i've listened to several books while gardening. I bought a non-motorized lawn mower so that i can listen while doing that task. Most of my listening time, however, happens during my commute to work. In a break with tradition, i actually found myself speeding up a little during the most exciting parts. (This doesn't get me to speeding, exactly, as i drive slower than the limit as a fuel conservation measure - which saves me more than an estimated $100 per year). It's an hour each way, so it's roughly ten hours a week. Against ten hours a week, a five hour book is pretty easy. The Tarzan books were about eight hours each. And when I listened to those, it was about one per week. Imagine reading fifty books a year.
Saturday, September 02, 2006
Gas prices lower
Notice gas prices (here in the States) have come down, just in time for Labor Day travel? This is in a complete break with tradition. I've not heard really anything in the news about it (not that i've looked). One might expect that whoever is responsible might trumpet their achievement.
It's almost as if it's an election year.
It's almost as if it's an election year.
Friday, August 25, 2006
Hyde and Seek
Just finished listening to the Librivox production of Robert Louis Stevenson's The Strange Case of Dr. Jekyll and Mr. Hyde. David Barnes, the narrator, has an excellent voice for this part for several reasons. For one, it isn't an American accent. It is believable that this voice is directly from a character out of the 1800's. Second, he has adopted a kind of bland style for this reading, which is totally in character with the story. It isn't sensational. Sure, it can mesmerize, and requires a bit more concentration and attention to get everything.
Apparently, i never read the story before. The dozens of Jekyll & Hyde references in comics, TV, etc., manage to mislead. Has no one read this book? For example, the Marvel Comics villain Mr Hyde is huge and strong like the Hulk, and Dr. Jekyll is small and spindly. This is in sharp contrast to Stevenson's vision. I also expected that Jekyll's motivation was going to be a sort of fountain of youth, rather than an exploration of consciousness. Seeking after youth might have been more believable, even if Dr. Jekyll's motives were supposed to be unselfish and pure.
Also, i'd thought of this classic as a bigger book. At just about three hours, it's really a short story. I find it easy enough to read about three times as fast as the spoken word. So it stands that i might have devoured the text in an hour. Had i known that, i'd likely have read it much sooner. It's also packaged in chunks just under an hour each. This made it easy enough for me to consume on my hour long commute, each way, every day.
Like Mary Wollstonecraft Shelley's Frankenstein, this science fiction work is also horror. I'm not really much into horror. Hyde is a monster. To look at him is to understand disfigurement, even though the eye does not find it. Ordinary onlookers are given a supernatural ability to sense evil.
So, i liked the book, the narrator, the audio quality, and the packaging. The Strange Case of Dr. Jekyll and Mr. Hyde is a classic that should not be missed. And, as both the text and the audio are available for free, there's hardly any excuse not to enjoy it.
Apparently, i never read the story before. The dozens of Jekyll & Hyde references in comics, TV, etc., manage to mislead. Has no one read this book? For example, the Marvel Comics villain Mr Hyde is huge and strong like the Hulk, and Dr. Jekyll is small and spindly. This is in sharp contrast to Stevenson's vision. I also expected that Jekyll's motivation was going to be a sort of fountain of youth, rather than an exploration of consciousness. Seeking after youth might have been more believable, even if Dr. Jekyll's motives were supposed to be unselfish and pure.
Also, i'd thought of this classic as a bigger book. At just about three hours, it's really a short story. I find it easy enough to read about three times as fast as the spoken word. So it stands that i might have devoured the text in an hour. Had i known that, i'd likely have read it much sooner. It's also packaged in chunks just under an hour each. This made it easy enough for me to consume on my hour long commute, each way, every day.
Like Mary Wollstonecraft Shelley's Frankenstein, this science fiction work is also horror. I'm not really much into horror. Hyde is a monster. To look at him is to understand disfigurement, even though the eye does not find it. Ordinary onlookers are given a supernatural ability to sense evil.
So, i liked the book, the narrator, the audio quality, and the packaging. The Strange Case of Dr. Jekyll and Mr. Hyde is a classic that should not be missed. And, as both the text and the audio are available for free, there's hardly any excuse not to enjoy it.
Friday, August 18, 2006
Har Har
Talk like a Pirate Day is coming. Now is the time to prepare with practice.
For example, har har. And, of course, Arrggg.
For example, har har. And, of course, Arrggg.
Friday, August 11, 2006
An odd thing
Son: I'm hungry.
Me: I suppose you want bubble gum. Or popcorn.
Son: I want a peanut butter and jelly sandwitch.
Me:I never wanted a normal child anyway.
Me: I suppose you want bubble gum. Or popcorn.
Son: I want a peanut butter and jelly sandwitch.
Me:
Wednesday, August 09, 2006
Another Meme Lemming
Don't participate with me on this. I did not send this to friends. If you do it, try to be clever.
The theory is that you will learn a lot of little known facts about your friends. It is fun and easy 48 questions to answer. If you're doing it, and are clever enough, then nothing will be learned by anyone. That's my goal.
01. FIRST NAME?
Stephen
02. WERE YOU NAMED AFTER ANYONE?
The 1st Christian martyr. See Acts Ch 6. He preached the obvious to his congregation, and they stoned him. It still happens. I've been there.
03. WHEN DID YOU LAST CRY?
A whole onion goes in my spaghetti. Best not to breath through your nose. So, don't talk.
04. DO YOU LIKE YOUR HANDWRITING?
No. It's painfully slow and barely legible. My typing is at least 8 times faster.
05. WHAT IS YOUR FAVORITE LUNCHMEAT?
I eat alot of Bologna. I like pastrami.
06. IF YOU WERE ANOTHER PERSON WOULD YOU BE FRIENDS WITH YOU?
Sure. I have lots of interesting things to say that i'd like to hear about.
07. DO YOU HAVE A JOURNAL?
Several. They document what I'm thinking about, not my life.
08. DO YOU STILL HAVE YOUR TONSILS?
Yes. If i'd had one more strep throat growing up, they'd have pulled them.
09. WOULD YOU BUNGEE JUMP?
I'd say no, but i did go up in a hot air balloon, by choice. It was fun.
10. WHAT IS YOUR FAVORITE CEREAL?
Cheerios, but variety is critical.
11. DO YOU UNTIE YOUR SHOES WHEN YOU TAKE THEM OFF?
Sometimes. Always for boots. Never for loafers.
12. DO YOU THINK YOU ARE STRONG?
For my 17 foot aluminum canoe, I'm strong. For my piano, i'm weak.
13. WHAT IS YOUR FAVORITE ICE CREAM FLAVOR?
Cookie dough.
14. SHOE SIZE?
8 1/2.
15. FAVORITE COLOR?
Blue. No red! Ahhhhhgg...
16. WHAT IS THE LEAST FAVORITE THING ABOUT YOURSELF?
I don't listen to myself, so alot of wisdom is missed.
17. WHO DO YOU MISS THE MOST?
Kim Dyer, the blind astronomer.
18. DO YOU WANT EVERYONE TO SEND THIS BACK TO YOU?
No.
19. WHAT COLOR PANTS AND SHOES ARE YOU WEARING?
Blue. No red! Ahhhhhgg...
20. LAST THING YOU ATE?
Red hot potato chips.
21. WHAT ARE YOU LISTENING TO RIGHT NOW?
The computer fan. The other computer fan.
22. IF YOU WERE A CRAYON, WHAT COLOR WOULD YOU BE?
Blue. No red! Ahhhhhgg...
23. FAVORITE SMELL?
I don't get to smell nice things for more than a second. Only really foul things make an impression.
24. WHO WAS THE LAST PERSON YOU TALKED TO ON THE PHONE?
Dawn.
25. FIRST THING YOU NOTICE ABOUT PEOPLE YOU ARE ATTRACTED TO?
Something they said.
26. DO YOU LIKE THE PERSON WHO SENT THIS TO YOU?
Sure.
27. FAVORITE DRINK?
Water.
28. FAVORITE SPORT?
Running.
29. EYE COLOR?
Blue. No red! Ahhhhhgg...
30. HAT SIZE?
Blue. No red! Ahhhhhgg...
31. DO YOU WEAR CONTACTS?
Sometimes. I have them set up for super vision. Great for bird watching.
32. FAVORITE FOOD?
My spaghetti. The recipe changes most times i make it.
33. SCARY MOVIES OR HAPPY ENDING?
While i don't like scary movies, it's the story that matters. Give me a plot.
34. WHAT COLOR SHIRT ARE YOU WEARING?
Blue. No red! Ahhhhhgg...
35. SUMMER OR WINTER?
Fall. Fall colors are Blue. No red! Ahhhhhgg...
36. HUGS OR KISSES?
Is that all i get? Hugs, i guess.
37. FAVORITE DESSERT?
None. Really, i don't want dessert. I like deserts.
38. MOST LIKELY TO RESPOND?
No one.
39. LEAST LIKELY TO RESPOND?
Dawn.
40. WHAT BOOKS ARE YOU READING?
The Bible. Need to start another book. It's about 40 books a year. Maybe three at a time.
41. WHAT'S ON YOUR MOUSE PAD?
Son's artwork.
42. WHAT DID YOU WATCH LAST NIGHT ON TV?
Star Trek TNG. Five minutes on tape.
43. FAVORITE SOUNDS?
Chickadee's calls.
44. ROLLING STONES OR BEATLES?
Beatles.
45. THE FURTHEST YOU'VE BEEN FROM HOME?
M51, the Whirlpool Galaxy, about 37 million light years. I'm thinking about visiting a quasar at over 3 billion light years.
46. WHAT'S YOUR SPECIAL TALENT?
The future. But it's very not helpful or comforting.
47. AND WHERE WERE YOU BORN?
Ohio.
48. WHO SENT THIS TO YOU?
Craig.
The theory is that you will learn a lot of little known facts about your friends. It is fun and easy 48 questions to answer. If you're doing it, and are clever enough, then nothing will be learned by anyone. That's my goal.
01. FIRST NAME?
Stephen
02. WERE YOU NAMED AFTER ANYONE?
The 1st Christian martyr. See Acts Ch 6. He preached the obvious to his congregation, and they stoned him. It still happens. I've been there.
03. WHEN DID YOU LAST CRY?
A whole onion goes in my spaghetti. Best not to breath through your nose. So, don't talk.
04. DO YOU LIKE YOUR HANDWRITING?
No. It's painfully slow and barely legible. My typing is at least 8 times faster.
05. WHAT IS YOUR FAVORITE LUNCHMEAT?
I eat alot of Bologna. I like pastrami.
06. IF YOU WERE ANOTHER PERSON WOULD YOU BE FRIENDS WITH YOU?
Sure. I have lots of interesting things to say that i'd like to hear about.
07. DO YOU HAVE A JOURNAL?
Several. They document what I'm thinking about, not my life.
08. DO YOU STILL HAVE YOUR TONSILS?
Yes. If i'd had one more strep throat growing up, they'd have pulled them.
09. WOULD YOU BUNGEE JUMP?
I'd say no, but i did go up in a hot air balloon, by choice. It was fun.
10. WHAT IS YOUR FAVORITE CEREAL?
Cheerios, but variety is critical.
11. DO YOU UNTIE YOUR SHOES WHEN YOU TAKE THEM OFF?
Sometimes. Always for boots. Never for loafers.
12. DO YOU THINK YOU ARE STRONG?
For my 17 foot aluminum canoe, I'm strong. For my piano, i'm weak.
13. WHAT IS YOUR FAVORITE ICE CREAM FLAVOR?
Cookie dough.
14. SHOE SIZE?
8 1/2.
15. FAVORITE COLOR?
Blue. No red! Ahhhhhgg...
16. WHAT IS THE LEAST FAVORITE THING ABOUT YOURSELF?
I don't listen to myself, so alot of wisdom is missed.
17. WHO DO YOU MISS THE MOST?
Kim Dyer, the blind astronomer.
18. DO YOU WANT EVERYONE TO SEND THIS BACK TO YOU?
No.
19. WHAT COLOR PANTS AND SHOES ARE YOU WEARING?
Blue. No red! Ahhhhhgg...
20. LAST THING YOU ATE?
Red hot potato chips.
21. WHAT ARE YOU LISTENING TO RIGHT NOW?
The computer fan. The other computer fan.
22. IF YOU WERE A CRAYON, WHAT COLOR WOULD YOU BE?
Blue. No red! Ahhhhhgg...
23. FAVORITE SMELL?
I don't get to smell nice things for more than a second. Only really foul things make an impression.
24. WHO WAS THE LAST PERSON YOU TALKED TO ON THE PHONE?
Dawn.
25. FIRST THING YOU NOTICE ABOUT PEOPLE YOU ARE ATTRACTED TO?
Something they said.
26. DO YOU LIKE THE PERSON WHO SENT THIS TO YOU?
Sure.
27. FAVORITE DRINK?
Water.
28. FAVORITE SPORT?
Running.
29. EYE COLOR?
Blue. No red! Ahhhhhgg...
30. HAT SIZE?
Blue. No red! Ahhhhhgg...
31. DO YOU WEAR CONTACTS?
Sometimes. I have them set up for super vision. Great for bird watching.
32. FAVORITE FOOD?
My spaghetti. The recipe changes most times i make it.
33. SCARY MOVIES OR HAPPY ENDING?
While i don't like scary movies, it's the story that matters. Give me a plot.
34. WHAT COLOR SHIRT ARE YOU WEARING?
Blue. No red! Ahhhhhgg...
35. SUMMER OR WINTER?
Fall. Fall colors are Blue. No red! Ahhhhhgg...
36. HUGS OR KISSES?
Is that all i get? Hugs, i guess.
37. FAVORITE DESSERT?
None. Really, i don't want dessert. I like deserts.
38. MOST LIKELY TO RESPOND?
No one.
39. LEAST LIKELY TO RESPOND?
Dawn.
40. WHAT BOOKS ARE YOU READING?
The Bible. Need to start another book. It's about 40 books a year. Maybe three at a time.
41. WHAT'S ON YOUR MOUSE PAD?
Son's artwork.
42. WHAT DID YOU WATCH LAST NIGHT ON TV?
Star Trek TNG. Five minutes on tape.
43. FAVORITE SOUNDS?
Chickadee's calls.
44. ROLLING STONES OR BEATLES?
Beatles.
45. THE FURTHEST YOU'VE BEEN FROM HOME?
M51, the Whirlpool Galaxy, about 37 million light years. I'm thinking about visiting a quasar at over 3 billion light years.
46. WHAT'S YOUR SPECIAL TALENT?
The future. But it's very not helpful or comforting.
47. AND WHERE WERE YOU BORN?
Ohio.
48. WHO SENT THIS TO YOU?
Craig.
Tuesday, August 08, 2006
Finger Arithmetic Part Ten
Continuing finger arithmetic from Part Nine. This one is called Part Ten. It is the eleventh part in the series. It continues subtraction with two digit subtraction.
Some two digit subtraction is easy. Consider 34 - 12. Set 34. To subtract two, remove two fingers on the right hand. To subtract ten, remove one finger from the left hand. Read the answer: 22.
Sometimes, you need to borrow from the next digit up. For example, 34 - 16.
Set 34 on your hands. Now, six is the same as five plus one. That is, it is a thumb and a finger. You can subtract a finger from your right hand. You do not have a thumb to subtract. You can get where you want to go by considering that subtracting five is the same as adding five and subtracting 10: -5 = + 5 - 10. So, add a thumb to the right hand and subtract a finger from your left hand. Now you just need to subtract the ten of 16. Subtract another finger from your left hand. Read the answer. 18.
Next up is 31 - 8. This time, the ten's compliment is used. Set 31. Recognize that there is no way to subtract any part of 8 from it. Not 8, not 3. Consider than subtracting eight is the same as adding 2 and subtracting 10. -8 = +2 - 10. So, add two fingers to the right hand, and subtract one from the left hand. Read the answer: 23.
So, how do you do three digit arithmetic on two hands? You could try using your nose. If it's just a little over two digits (one hundred and something), then consider your nose to be zero or one hundred. Consider 157 - 59. Set 57 on your hands in the usual way. Consider that your nose is set. You don't have nine to subtract, so use the ten's compliment, one. Add one and subtract ten. Well, you can add one. To subtract ten, you must add four and subtract five. Now you need to subtract 50. You don't have 50, so you must add 50 and subtract 100. Add the left thumb. Remember that 100 is on your nose. Unset your nose. Read the result: 098.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This link provides two digit subtraction examples.
You might just want to go to the web site, so you can ask the generator yourself. Addition, subtraction or mixed problems, how many digits, more than just two numbers per problem? Answers on the same page or another page? Maybe you want one hundred pages to get you through vacation.
Remember to read the answers out loud. Practice every day that you eat. If you like, limit yourself to practice to those days of the week ending with 'y'. Enjoy yourself. With a little practice, two and three digit addition and subtraction can be highly reliable, fast and seemingly effortless.
Some two digit subtraction is easy. Consider 34 - 12. Set 34. To subtract two, remove two fingers on the right hand. To subtract ten, remove one finger from the left hand. Read the answer: 22.
Sometimes, you need to borrow from the next digit up. For example, 34 - 16.
Set 34 on your hands. Now, six is the same as five plus one. That is, it is a thumb and a finger. You can subtract a finger from your right hand. You do not have a thumb to subtract. You can get where you want to go by considering that subtracting five is the same as adding five and subtracting 10: -5 = + 5 - 10. So, add a thumb to the right hand and subtract a finger from your left hand. Now you just need to subtract the ten of 16. Subtract another finger from your left hand. Read the answer. 18.
Next up is 31 - 8. This time, the ten's compliment is used. Set 31. Recognize that there is no way to subtract any part of 8 from it. Not 8, not 3. Consider than subtracting eight is the same as adding 2 and subtracting 10. -8 = +2 - 10. So, add two fingers to the right hand, and subtract one from the left hand. Read the answer: 23.
So, how do you do three digit arithmetic on two hands? You could try using your nose. If it's just a little over two digits (one hundred and something), then consider your nose to be zero or one hundred. Consider 157 - 59. Set 57 on your hands in the usual way. Consider that your nose is set. You don't have nine to subtract, so use the ten's compliment, one. Add one and subtract ten. Well, you can add one. To subtract ten, you must add four and subtract five. Now you need to subtract 50. You don't have 50, so you must add 50 and subtract 100. Add the left thumb. Remember that 100 is on your nose. Unset your nose. Read the result: 098.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This link provides two digit subtraction examples.
You might just want to go to the web site, so you can ask the generator yourself. Addition, subtraction or mixed problems, how many digits, more than just two numbers per problem? Answers on the same page or another page? Maybe you want one hundred pages to get you through vacation.
Remember to read the answers out loud. Practice every day that you eat. If you like, limit yourself to practice to those days of the week ending with 'y'. Enjoy yourself. With a little practice, two and three digit addition and subtraction can be highly reliable, fast and seemingly effortless.
Monday, August 07, 2006
DVDs in the mail
Mostly, i only get spam and bad news (bills) by mail. I should write more letters. One letter i wrote (well, filled in the form, anyway) was to get a free DVD from my cereal box company. My son (9) picked out the movie from a short list. He picked Agent Cody Banks. We watched it. It's about an hour and a half. It has much of the James Bond gadgets and banter. The gadgets are toned down to familiar cell phones, video games, and cars. In a break with tradition, the cars aren't destroyed. Since Cody is supposed to be a 15 year old, the amount of sex is limited. Even in the banter. It's rated PG, but, for example, in the big fight scene, the 'villains', who were set up as bullies, and therefore deserved what they get, are thrown into a pool. It could nearly be rated G. For example, there is no swearing. Mom's hand covers the child's mouth when he says "Holy ...". What was he going to say? We'll never know.
So, it has action to rivet the attention of a nine year old. Yet no scary dreams. No foul language to be repeated ad nauseum.
Can't beat the price. We're practically addicted to Raisin Bran anyway.
I give it two thumbs up. If you've been following this blog, you'll note that one of the thumbs is worth five, and the other is worth fifty. That's better than Siskel and Ebert.
So, it has action to rivet the attention of a nine year old. Yet no scary dreams. No foul language to be repeated ad nauseum.
Can't beat the price. We're practically addicted to Raisin Bran anyway.
I give it two thumbs up. If you've been following this blog, you'll note that one of the thumbs is worth five, and the other is worth fifty. That's better than Siskel and Ebert.
Friday, August 04, 2006
Finger Multiplication Trick
When the student gets to multiplication, there is a problem. When learning addition, the student is tempted to count on their fingers to get the answer. For speed, the addition table should be memorized. Otherwise, they'll take quite a bit of time when it comes to 7 + 8.
For multiplication, figuring out 7 * 8 with repeated addition just doesn't work. And the third grader quickly memorizes the table.
There is a simple system for multiplication involving digits six and higher. And, it involves your fingers. Point your palms towards yourself with the finger tips of the hands pointing at each other. With the little fingers at the bottom, consider that your fingers represent the numbers six through ten. The little finger is six, the ring finger is seven, up to the thumb, which is ten.
We'll try 7 * 8 first. Seven is the ring finger of the left hand. Eight is the middle finger of the right hand. Order does not matter. Count the fingers to the bottom. That's 2 on the left hand and 3 on the right hand. 2 + 3 is 5. That's the ten's digit of 7 * 8. Examine the leftover fingers above. There are 3 on the left hand, and 2 on the right. Multiply these together. 2 * 3 = 6. That's the units digit. 7 * 8 = 56.
Consider 10 * 10. Ten fingers total below (and including) the thumbs. That's the ten's digit: 10. Zero fingers above. 0 * 0 = 0. That's the one's digit. 10 * 10 = 100.
I find myself somewhat reluctant to teach this tool. I mean, it works, yes. But does it accelerate the student, or retard progress? You decide.
For multiplication, figuring out 7 * 8 with repeated addition just doesn't work. And the third grader quickly memorizes the table.
There is a simple system for multiplication involving digits six and higher. And, it involves your fingers. Point your palms towards yourself with the finger tips of the hands pointing at each other. With the little fingers at the bottom, consider that your fingers represent the numbers six through ten. The little finger is six, the ring finger is seven, up to the thumb, which is ten.
We'll try 7 * 8 first. Seven is the ring finger of the left hand. Eight is the middle finger of the right hand. Order does not matter. Count the fingers to the bottom. That's 2 on the left hand and 3 on the right hand. 2 + 3 is 5. That's the ten's digit of 7 * 8. Examine the leftover fingers above. There are 3 on the left hand, and 2 on the right. Multiply these together. 2 * 3 = 6. That's the units digit. 7 * 8 = 56.
Consider 10 * 10. Ten fingers total below (and including) the thumbs. That's the ten's digit: 10. Zero fingers above. 0 * 0 = 0. That's the one's digit. 10 * 10 = 100.
I find myself somewhat reluctant to teach this tool. I mean, it works, yes. But does it accelerate the student, or retard progress? You decide.
Tuesday, July 25, 2006
Finger Arithmetic Part Nine - Subtraction
Continuing finger arithmetic from Part Eight. This one is called Part Nine. It is the tenth part in the series. It introduces subtraction.
Subtraction is the opposite of addition. It's sort of addition backwards. You might be able to figure it out, using what you've learned from addition. Indeed, i was unable to teach my eight year old subtraction. I announced that i would teach him, and he just went ahead and did it. Now, if he'd done it wrong, i'd have corrected him. And when he makes mistakes, i walk him through the steps. But he really seemed to go through all nine lessons in reverse, taking about ten seconds. I don't hold him back. The correct direction is forward to the goal.
In lesson zero, we had counting. Count from nine to zero. It was then pointed out that counting was adding one. Counting down is the same as subtracting one. Remember to say the answers out loud. Try counting from twenty to zero.
Now we'll subtract small numbers. Consider 4 - 3. Set four fingers and subtract three fingers. Read the result: One. This covers 1 - 1, 2 - 1, 3 - 1, 4 - 1, 2 - 2, 3 - 2, 4 - 2, 3 - 3, 4 - 3, 4 - 4. Practice these.
Some big numbers with small numbers are easy. Consider 9 - 3. Set nine. Take away three fingers. Read the answer: six. This covers 9 - 1, 9 - 2, 9 - 3, 9 - 4, 8 - 1, 8 - 2, 8 - 3, 7 - 1, 7 - 2, 6 - 1.
Next is a half carry, using Five's Compliments. Recall that the Five's Compliment of 1 is 4, and 4 is 1, and 2 is 3 and 3 is 2. Consider 7 - 3. Set seven. Note that there aren't three fingers to subtract. We're going perform this by observing that 7 - 3 is the same as 7 + 2 - 5. Remember that the Five's Compliment of three is two, so you add two and subtract five. Add two fingers. Subtract the thumb. Read the answer: four.
Subtracting five is easy. Consider 7 - 5. Set seven. Take away the thumb. Read the answer: two. This covers 9 - 5, 8 - 5, 7 - 5, 6 - 5, and 5 - 5.
Subtracting bigger numbers. Consider 9 - 7. Set nine. Seven is five plus two - thumb and two fingers. You have two fingers to take away, so do it. You have a thumb to take away, so do it. Read the answer: two. This covers 9 - 9, 9 - 8, 9 - 7, 9 - 6, 8 - 8, 8 - 7, 8 - 6, 7 - 7, 7 - 6, 6 -6. Need you be reminded to practice?
Next lesson: two digit subtraction. Bring your thinking caps.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This link provides two digit examples. As this lesson hasn't taught two digit subtraction, feel free to ignore any problems involving two digits anywhere.
You might just want to go to the web site, so you can ask the generator yourself. Addition, subtraction or mixed problems, how many digits, more than just two numbers per problem? Answers on the same page or another page? Maybe you want one hundred pages to get you through vacation.
Subtraction is the opposite of addition. It's sort of addition backwards. You might be able to figure it out, using what you've learned from addition. Indeed, i was unable to teach my eight year old subtraction. I announced that i would teach him, and he just went ahead and did it. Now, if he'd done it wrong, i'd have corrected him. And when he makes mistakes, i walk him through the steps. But he really seemed to go through all nine lessons in reverse, taking about ten seconds. I don't hold him back. The correct direction is forward to the goal.
In lesson zero, we had counting. Count from nine to zero. It was then pointed out that counting was adding one. Counting down is the same as subtracting one. Remember to say the answers out loud. Try counting from twenty to zero.
Now we'll subtract small numbers. Consider 4 - 3. Set four fingers and subtract three fingers. Read the result: One. This covers 1 - 1, 2 - 1, 3 - 1, 4 - 1, 2 - 2, 3 - 2, 4 - 2, 3 - 3, 4 - 3, 4 - 4. Practice these.
Some big numbers with small numbers are easy. Consider 9 - 3. Set nine. Take away three fingers. Read the answer: six. This covers 9 - 1, 9 - 2, 9 - 3, 9 - 4, 8 - 1, 8 - 2, 8 - 3, 7 - 1, 7 - 2, 6 - 1.
Next is a half carry, using Five's Compliments. Recall that the Five's Compliment of 1 is 4, and 4 is 1, and 2 is 3 and 3 is 2. Consider 7 - 3. Set seven. Note that there aren't three fingers to subtract. We're going perform this by observing that 7 - 3 is the same as 7 + 2 - 5. Remember that the Five's Compliment of three is two, so you add two and subtract five. Add two fingers. Subtract the thumb. Read the answer: four.
Subtracting five is easy. Consider 7 - 5. Set seven. Take away the thumb. Read the answer: two. This covers 9 - 5, 8 - 5, 7 - 5, 6 - 5, and 5 - 5.
Subtracting bigger numbers. Consider 9 - 7. Set nine. Seven is five plus two - thumb and two fingers. You have two fingers to take away, so do it. You have a thumb to take away, so do it. Read the answer: two. This covers 9 - 9, 9 - 8, 9 - 7, 9 - 6, 8 - 8, 8 - 7, 8 - 6, 7 - 7, 7 - 6, 6 -6. Need you be reminded to practice?
Next lesson: two digit subtraction. Bring your thinking caps.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This link provides two digit examples. As this lesson hasn't taught two digit subtraction, feel free to ignore any problems involving two digits anywhere.
You might just want to go to the web site, so you can ask the generator yourself. Addition, subtraction or mixed problems, how many digits, more than just two numbers per problem? Answers on the same page or another page? Maybe you want one hundred pages to get you through vacation.
Thursday, July 13, 2006
All Wet
When Oxygen Tech played Hydrogen U.
The Game had just begun,
when Hydrogen scored two fast points
And Oxygen still had none.
Then Oxygen scored a single goal
And thus it did remain,
At Hydrogen 2 and Oxygen 1
Called because of rain.
The Game had just begun,
when Hydrogen scored two fast points
And Oxygen still had none.
Then Oxygen scored a single goal
And thus it did remain,
At Hydrogen 2 and Oxygen 1
Called because of rain.
Wednesday, July 12, 2006
Finger Arithmetic Part Eight
Continuing finger arithmetic from Part Seven. This one is called Part Eight. It is the ninth part in the series.
Back in Part Seven, we finished up addition of single digit numbers. We took care of carries with Ten's Compliments and Five's Compliments. In this lesson, we continue forward with two digit addition.
For example, how does one add 13 + 21? Set thirteen by making two fists, set three fingers on the right hand and one finger on the left hand. The twenty-one can be added in either order. Add twenty, then add one, or add one, then add twenty. These lessons always proceed from right to left. To add one to the three on the right hand, just add one more finger. To add twenty, just add two fingers to the left hand. Read the answer: 34.
The last example was easy. There were no carries. Consider adding 34 + 35. Set thirty four by making two fists, setting three fingers on the left hand and four fingers on the right hand. Add five (of 35) to the right hand by adding the thumb. Still no carry. Then consider adding thirty. You would add three fingers to the left hand, but there aren't three fingers to add. So, subtract the Five's Compliment of three, which is two fingers, and add five, which is the thumb. Read the answer: 69. This example added five, and also added using a Five's Compliment.
Consider 26 + 48. Set twenty six by starting with two fists. Set two fingers on the left and a finger and thumb on the right. We need to add eight. Eight is five plus three. You can add the three by adding three fingers. You can't add the five, so you must subtract five by subtracting the right thumb, and adding ten, which is adding one finger on the left hand. To add forty, you'd want to add four fingers to the left hand. However, there aren't enough fingers to add. So, you subtract the Five's Compliment of four, which is one, and add five, which is the thumb, to the left hand. Read the answer: 74. This example has a carry from the unit's digit (hand) to the ten's digit (hand), and also has a Five's Compliment add.
Consider 19 + 27. Set nineteen by making two fists, setting one finger on the left hand and all fingers and thumb on the right hand. To add seven, note that seven is five plus two. There aren't two fingers to add, so you use Ten's Compliment. Subtract the Ten's Compliment of seven, which is three, and add ten, which is one finger on the left hand. To add twenty, add two more fingers on the left hand. Read the answer: 46. Use Ten's Compliments for numbers over five, and Five's Compliments for numbers less than five.
Consider 46 + 14. You might still have 46 on your hands, or set 46. To add four, recognize that there aren't four fingers to add. Subtract the Five's Compliment of four, which is one, and add five. You already have the thumb up, so you subtract five (the thumb) and add ten. You don't have a finger to add to the left hand, so you subtract the Five's Compliment of one, which is four, and add five, which is the thumb. That was just to add the four of the fourteen. To add the ten of the fourteen, add one finger to the left hand. Read the answer: sixty. You would think that this is as complicated as carries get for finger addition. However, there is one more case.
Consider 37 + 63. Set thirty seven on your hands. You want to add three, but can't, as there are only two available fingers. So, you subtract two and add five. You can subtract two, but can't add five, as there is already a thumb set. You add five by subtracting five and adding ten, which is one finger on the left hand. Now you need to add sixty. Considering that sixty is 1 + 5, you note that you can't add one finger. So, you subtract the Ten's Compliment of six, which is four, and add ten - which is one hundred. Well, most people don't have another hand, so you'll have to remember it. Perhaps your nose. Read the answer. Remembering the one hundred, you find that the answer is: 100.
In the previous example, we used the Five's Compliment of three to add it to the existing seven. There were a number of confusing steps to get through adding just the one digit. While this method works, you could instead use the Ten's Compliment of three, which is seven. Here's how that works. Set thirty seven on your hands. To add three, subtract the Ten's Compliment of three, which is seven, and add ten. You can add the ten, so you just do it. I find it conceptually easier to use Five's Compliments for digits less than five, and Ten's Compliments for digits more than five. This always works, though it leads to extra steps now and then. As your proficiency improves, feel free to experiment with Ten's Compliments where they make sense.
You might spend a few weeks on this before moving on to subtraction.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This isn't the same link as in the Part Six. This link provides two digit examples.
The example generator is the same, with different parameters. This is the form that lets you select the parameters you might want. For example, if you have a Japanese Abacus, called a Soroban, you'll have more than two hands, as each hand is basically one rod of this device. Let's say that you have a child in elementary school. If they're reading for enjoyment, then handing them some books to read over the summer will allow them to advance, or at least not backslide too much. What about arithmetic? It is estimated that children backslide an average of about two and a half months over the summer. This problem generator can help. I try to work in five minutes with my son every day. There is also a problem generator for multiplication on my site. Feel free to use it for division problems as well.
Back in Part Seven, we finished up addition of single digit numbers. We took care of carries with Ten's Compliments and Five's Compliments. In this lesson, we continue forward with two digit addition.
For example, how does one add 13 + 21? Set thirteen by making two fists, set three fingers on the right hand and one finger on the left hand. The twenty-one can be added in either order. Add twenty, then add one, or add one, then add twenty. These lessons always proceed from right to left. To add one to the three on the right hand, just add one more finger. To add twenty, just add two fingers to the left hand. Read the answer: 34.
The last example was easy. There were no carries. Consider adding 34 + 35. Set thirty four by making two fists, setting three fingers on the left hand and four fingers on the right hand. Add five (of 35) to the right hand by adding the thumb. Still no carry. Then consider adding thirty. You would add three fingers to the left hand, but there aren't three fingers to add. So, subtract the Five's Compliment of three, which is two fingers, and add five, which is the thumb. Read the answer: 69. This example added five, and also added using a Five's Compliment.
Consider 26 + 48. Set twenty six by starting with two fists. Set two fingers on the left and a finger and thumb on the right. We need to add eight. Eight is five plus three. You can add the three by adding three fingers. You can't add the five, so you must subtract five by subtracting the right thumb, and adding ten, which is adding one finger on the left hand. To add forty, you'd want to add four fingers to the left hand. However, there aren't enough fingers to add. So, you subtract the Five's Compliment of four, which is one, and add five, which is the thumb, to the left hand. Read the answer: 74. This example has a carry from the unit's digit (hand) to the ten's digit (hand), and also has a Five's Compliment add.
Consider 19 + 27. Set nineteen by making two fists, setting one finger on the left hand and all fingers and thumb on the right hand. To add seven, note that seven is five plus two. There aren't two fingers to add, so you use Ten's Compliment. Subtract the Ten's Compliment of seven, which is three, and add ten, which is one finger on the left hand. To add twenty, add two more fingers on the left hand. Read the answer: 46. Use Ten's Compliments for numbers over five, and Five's Compliments for numbers less than five.
Consider 46 + 14. You might still have 46 on your hands, or set 46. To add four, recognize that there aren't four fingers to add. Subtract the Five's Compliment of four, which is one, and add five. You already have the thumb up, so you subtract five (the thumb) and add ten. You don't have a finger to add to the left hand, so you subtract the Five's Compliment of one, which is four, and add five, which is the thumb. That was just to add the four of the fourteen. To add the ten of the fourteen, add one finger to the left hand. Read the answer: sixty. You would think that this is as complicated as carries get for finger addition. However, there is one more case.
Consider 37 + 63. Set thirty seven on your hands. You want to add three, but can't, as there are only two available fingers. So, you subtract two and add five. You can subtract two, but can't add five, as there is already a thumb set. You add five by subtracting five and adding ten, which is one finger on the left hand. Now you need to add sixty. Considering that sixty is 1 + 5, you note that you can't add one finger. So, you subtract the Ten's Compliment of six, which is four, and add ten - which is one hundred. Well, most people don't have another hand, so you'll have to remember it. Perhaps your nose. Read the answer. Remembering the one hundred, you find that the answer is: 100.
In the previous example, we used the Five's Compliment of three to add it to the existing seven. There were a number of confusing steps to get through adding just the one digit. While this method works, you could instead use the Ten's Compliment of three, which is seven. Here's how that works. Set thirty seven on your hands. To add three, subtract the Ten's Compliment of three, which is seven, and add ten. You can add the ten, so you just do it. I find it conceptually easier to use Five's Compliments for digits less than five, and Ten's Compliments for digits more than five. This always works, though it leads to extra steps now and then. As your proficiency improves, feel free to experiment with Ten's Compliments where they make sense.
You might spend a few weeks on this before moving on to subtraction.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This isn't the same link as in the Part Six. This link provides two digit examples.
The example generator is the same, with different parameters. This is the form that lets you select the parameters you might want. For example, if you have a Japanese Abacus, called a Soroban, you'll have more than two hands, as each hand is basically one rod of this device. Let's say that you have a child in elementary school. If they're reading for enjoyment, then handing them some books to read over the summer will allow them to advance, or at least not backslide too much. What about arithmetic? It is estimated that children backslide an average of about two and a half months over the summer. This problem generator can help. I try to work in five minutes with my son every day. There is also a problem generator for multiplication on my site. Feel free to use it for division problems as well.
Friday, June 30, 2006
Finger Arithmetic Part Seven
Continuing finger arithmetic from Part Six. This one is called Part Seven. It is the eighth part in the series.
Ten's Compliments. Back in Part Six, we added 7 + 8. We set 7, and added 8 by adding 3 then 5. Adding 3 involved a carry, generating an addition of 5 while remembering that we still have to add 5. Very complicated. This Ten's Compliments idea reduces the steps, and having to remember upcoming steps. It is similar to Five's Complements, introduced in Part Three.
The Ten's Compliment of a number is the number you add to get ten. For now, we'll only use the Ten's Compliment of numbers greater than five. So, the Ten's Compliment of six is four. The Ten's Compliment of seven is three. The Ten's Compliment of eight is two. And the Ten's Compliment of nine is one.
So how does this help? Let's return to the dreaded seven plus eight example. Start with two fists, then set two right hand fingers and the thumb. You'd like to add eight, which is five plus three, but you don't have three to add. Eight is ten minus two (the Ten's Compliment of eight is two). Subtract the Ten's Complement, which is done by subtracting both right fingers. Then add ten by adding a finger to the left hand. Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers). Again, we added 7 + 8, which is 7 - 2 + 10.
How about six plus seven from the last lesson? You do this the same way it was done in the previous lesson. When you have six set, you don't have three fingers to subtract, and you do have two fingers to add. The way it works is that you always have exactly one of these options.
The relevant examples are 6 + 9, 7 + 9, 8 + 9, 9 + 9, 7 + 8, 8 + 8, 9 + 8, 8 + 7, 9 + 7, 9 + 6.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This is the same link as in the previous lesson.
Technically, we really introduced the Ten's Compliment of five, which is five in Part Five. It wasn't called that, and it just seems simpler to treat it as a special case.
Stay tuned for the introduction of two digit addition.
Ten's Compliments. Back in Part Six, we added 7 + 8. We set 7, and added 8 by adding 3 then 5. Adding 3 involved a carry, generating an addition of 5 while remembering that we still have to add 5. Very complicated. This Ten's Compliments idea reduces the steps, and having to remember upcoming steps. It is similar to Five's Complements, introduced in Part Three.
The Ten's Compliment of a number is the number you add to get ten. For now, we'll only use the Ten's Compliment of numbers greater than five. So, the Ten's Compliment of six is four. The Ten's Compliment of seven is three. The Ten's Compliment of eight is two. And the Ten's Compliment of nine is one.
So how does this help? Let's return to the dreaded seven plus eight example. Start with two fists, then set two right hand fingers and the thumb. You'd like to add eight, which is five plus three, but you don't have three to add. Eight is ten minus two (the Ten's Compliment of eight is two). Subtract the Ten's Complement, which is done by subtracting both right fingers. Then add ten by adding a finger to the left hand. Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers). Again, we added 7 + 8, which is 7 - 2 + 10.
How about six plus seven from the last lesson? You do this the same way it was done in the previous lesson. When you have six set, you don't have three fingers to subtract, and you do have two fingers to add. The way it works is that you always have exactly one of these options.
The relevant examples are 6 + 9, 7 + 9, 8 + 9, 9 + 9, 7 + 8, 8 + 8, 9 + 8, 8 + 7, 9 + 7, 9 + 6.
Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This is the same link as in the previous lesson.
Technically, we really introduced the Ten's Compliment of five, which is five in Part Five. It wasn't called that, and it just seems simpler to treat it as a special case.
Stay tuned for the introduction of two digit addition.
Tuesday, June 27, 2006
Finger Arithmetic Part Six
Continuing finger arithmetic from Part Five. This one is called Part Six. It is the seventh part in the series.
Single Digit Addition. No new concepts. That's not really true. We're going to combine previous concepts to handle more complicated carries. You'll need to be able to do this eventually, but these examples will be simplified in the next lesson.
We'll start with an easy example: six plus seven. Start with two fists. Set six by adding a finger and the thumb to the right hand. Seven is two plus five. Add the two of the seven by adding two fingers. You want to add the thumb, but the thumb is already set. So subtract five (the thumb) and add ten (a finger on the left hand). Read the answer: thirteen.
Let's add eight plus nine. Two fists, then set three fingers and the thumb on the right hand. Nine is five plus four. You want to add the four, but you don't have four fingers to add. So, you subtract the Five's Complement of four, which is one. You want to add the five (from the Five's Complement), but you already have that set. So, you must subtract five (the thumb) and add ten (a finger on the left hand). Then, you must go back and add the five from the nine. So add the right thumb. Read the result: seventeen.
Now, let's do the really hard one. That's right, the dreaded seven plus eight. Start with two fists, then set the two right hand fingers and the thumb. Eight is three plus one. You want to add three, but can't, so you subtract the Five's Complement of three, which is two - which is done by subtracting both right fingers. You want to add five, but already have a thumb set. So, you subtract five (the thumb) and add ten (a finger on the left hand). Now you need to go back and add the five from eight (the right thumb). Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers).
At this point, you can add any two single digit numbers. There are a few examples to try below. But none of the books have enough examples. Since you can't have too many examples, you are referred to an example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. Bookmark the link.
Single Digit Addition. No new concepts. That's not really true. We're going to combine previous concepts to handle more complicated carries. You'll need to be able to do this eventually, but these examples will be simplified in the next lesson.
We'll start with an easy example: six plus seven. Start with two fists. Set six by adding a finger and the thumb to the right hand. Seven is two plus five. Add the two of the seven by adding two fingers. You want to add the thumb, but the thumb is already set. So subtract five (the thumb) and add ten (a finger on the left hand). Read the answer: thirteen.
Let's add eight plus nine. Two fists, then set three fingers and the thumb on the right hand. Nine is five plus four. You want to add the four, but you don't have four fingers to add. So, you subtract the Five's Complement of four, which is one. You want to add the five (from the Five's Complement), but you already have that set. So, you must subtract five (the thumb) and add ten (a finger on the left hand). Then, you must go back and add the five from the nine. So add the right thumb. Read the result: seventeen.
Now, let's do the really hard one. That's right, the dreaded seven plus eight. Start with two fists, then set the two right hand fingers and the thumb. Eight is three plus one. You want to add three, but can't, so you subtract the Five's Complement of three, which is two - which is done by subtracting both right fingers. You want to add five, but already have a thumb set. So, you subtract five (the thumb) and add ten (a finger on the left hand). Now you need to go back and add the five from eight (the right thumb). Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers).
At this point, you can add any two single digit numbers. There are a few examples to try below. But none of the books have enough examples. Since you can't have too many examples, you are referred to an example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. Bookmark the link.
| 6 + 4 10 | 3 + 3 6 | 4 + 6 10 | 8 + 5 13 | 4 + 8 12 | |||||||||||||||
| 9 + 8 17 | 6 + 2 8 | 7 + 8 15 | 4 + 3 7 | 5 + 8 13 | |||||||||||||||
| 1 + 5 6 | 7 + 9 16 | 3 + 6 9 | 6 + 1 7 | 5 + 6 11 | |||||||||||||||
Wednesday, June 21, 2006
Charter School
I went to public schools through high school. I was offered the chance to go to a private high school, but turned it down. I could only see disadvantages. I wasn't interested enough to investigate the alternative.
I did OK at public school, though i can't say i was very enthusiastic. One day at home, my Dad asked me for my report card. I remembered using it as a bookmark, and went to fetch it. My Dad looked at it, then said that he'd have rather seen it than read about it in the newspaper - the honor roll. Why was that news? I was always on the honor roll. I said i'd try to show him the report card, but knew that i had so little interest in it that it would likely slip my mind.
The pace at school was slow, but i didn't mind - i was patient. Teachers saw i was bored, and gave me extra stuff to do. It did not bother me that i didn't get any credit for it. It wasn't enough. I bought a computer (in 1975, about as powerful as your watch) and taught myself machine language programming. I picked up a Japanese abacus (Soroban) and taught myself mental arithmetic. After three months, I computed a 10 digit sin(x) in my head using Taylor series. I was the only junior in the new high school calculus course.
But i would have done OK anywhere. I probably wasn't an average child after all. But where could i have excelled?
My son is in a charter school, and just finished 3rd grade. You get to go to a charter school if a parent fills out the forms and the school isn't already full.
He doesn't just get it like i did. And he won't stick with it forever like i would. So his mom and i help him out every day, and all weekend, and all summer. When the teacher calls one of us, we take it very seriously. I've gotten him through addition and subtraction. It took four years, but i've gotten him to read for enjoyment (meaning all the time). I've helped him with fractions and concepts of perimeter and area. We quiz him relentlessly on spelling, social studies and Spanish. His Mom has been, uhm, instrumental in getting him to be without peer on violin and piano.
The charter school has parents who care about their kids. After dropping their kids to the school in the morning, they'll often have discussions about school for an hour or so. I can't imagine that there is a single parent there who doesn't return a teacher's phone call right away.
I was very excited about this school after a 'parents day'. I got an appointment to sit in on a class for an hour, while my son was still in preschool. The teacher read a story to the kids, who all sat quietly in rapt attention. Even my son. Then, the kids each got out a rug, and some materials, and sat for at least twenty minutes working with them. Even my son. One child came over to the table i was sitting at. Soon a teacher came over and also sat down. The child began reading a book, out loud, fluently. It had to be 2nd grade level or better. But this was preschool.
OK, so when i was in 1st grade, i could read that well, probably better. But i was not encouraged to do so. No one else was doing it. We could pick any book out of the school's library to read, but they kept shepherding me to the See Jack Run section. So i read my older brother's books at home. Things happened in those books. You know, like real stories. At my son's charter school, it's OK to excel. This is Very exciting.
I did OK at public school, though i can't say i was very enthusiastic. One day at home, my Dad asked me for my report card. I remembered using it as a bookmark, and went to fetch it. My Dad looked at it, then said that he'd have rather seen it than read about it in the newspaper - the honor roll. Why was that news? I was always on the honor roll. I said i'd try to show him the report card, but knew that i had so little interest in it that it would likely slip my mind.
The pace at school was slow, but i didn't mind - i was patient. Teachers saw i was bored, and gave me extra stuff to do. It did not bother me that i didn't get any credit for it. It wasn't enough. I bought a computer (in 1975, about as powerful as your watch) and taught myself machine language programming. I picked up a Japanese abacus (Soroban) and taught myself mental arithmetic. After three months, I computed a 10 digit sin(x) in my head using Taylor series. I was the only junior in the new high school calculus course.
But i would have done OK anywhere. I probably wasn't an average child after all. But where could i have excelled?
My son is in a charter school, and just finished 3rd grade. You get to go to a charter school if a parent fills out the forms and the school isn't already full.
He doesn't just get it like i did. And he won't stick with it forever like i would. So his mom and i help him out every day, and all weekend, and all summer. When the teacher calls one of us, we take it very seriously. I've gotten him through addition and subtraction. It took four years, but i've gotten him to read for enjoyment (meaning all the time). I've helped him with fractions and concepts of perimeter and area. We quiz him relentlessly on spelling, social studies and Spanish. His Mom has been, uhm, instrumental in getting him to be without peer on violin and piano.
The charter school has parents who care about their kids. After dropping their kids to the school in the morning, they'll often have discussions about school for an hour or so. I can't imagine that there is a single parent there who doesn't return a teacher's phone call right away.
I was very excited about this school after a 'parents day'. I got an appointment to sit in on a class for an hour, while my son was still in preschool. The teacher read a story to the kids, who all sat quietly in rapt attention. Even my son. Then, the kids each got out a rug, and some materials, and sat for at least twenty minutes working with them. Even my son. One child came over to the table i was sitting at. Soon a teacher came over and also sat down. The child began reading a book, out loud, fluently. It had to be 2nd grade level or better. But this was preschool.
OK, so when i was in 1st grade, i could read that well, probably better. But i was not encouraged to do so. No one else was doing it. We could pick any book out of the school's library to read, but they kept shepherding me to the See Jack Run section. So i read my older brother's books at home. Things happened in those books. You know, like real stories. At my son's charter school, it's OK to excel. This is Very exciting.
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