Developing User Interfaces

My buddy Craig put a note up on his blog with two links talking about the same issue. One was a developer griping about how he couldn't make any progress at the big company he was working for. The other talked about how the resulting user interface was too complicated. Both are good reads.

I agree with the developer. No matter how important you might think the design is, this is no way to run a business. Eight people worked for over a year to produce a simple menu. Developers actually want to get things done. Managers don't seem to understand this. A good manager gets a good developer to achieve good performance by getting out of their way. Most managers seem to think that they have to coax, cajole, or even threaten their staff. Very strange. My own performance has now varied by a factor of about thirty, by any measure. It hasn't been a matter of motivation, or being a team player or the tools provided, or even clarity of purpose. It has been entirely how much red tape is required. The less the better. Managers seem to think of their job as important. But their job is overhead, which should be minimized.

I mostly agree with Joel on this one. For an end user application, simplicity is king. My own Ipod Shuffle has a power switch. It's a three position switch. The three positions are off, sequential, and shuffle. The off position should have been eliminated. For one thing, it's unreliable. If i pause the device, it will eventually turn itself off. When i turn it back on with the play button, it picks up where it left off. But, if i turn it off with the switch, every now and then, when i turn it back on, it starts at the beginning of the first track, or worse, it starts at the beginning of a random track (because it's pretty easy to switch it to shuffle mode). Since there's no display on the Shuffle, and since i may have 50 tracks on it, and since the fast forward isn't all that fast, it can take twenty minutes to get back to where i was. So, i don't use off anymore. The other things that should have been fixed are the fast forward and rewind features. Rewind should be able to dig into the end of the previous track. For some of the two hour podcasts i listen to, failure to start where i left off after about, oh, an hour and 50 minutes, is frustratingly painful. In fact, faced with this, i mostly either skip the rest of the program or use a real computer for the last bit. Both reverse and fast forward need to be able to speed up (by skipping more content) in some reasonable way. What did Apple do instead with the new Shuffle? They removed the built-in USB connection. Now you need an extra dohickey to put more stuff on it. Apple also seems to want to add even more DRM to their stuff. I don't use DRM content. I won't be upgrading.

Haiku

Welcome to dump grief
My blog Predelusional
No one will read it.

Here, spam is allowed
On that one special entry
where it’s on-topic.

Heads!

Heads! You're going to have an above average day!

Over the past few weeks, i've run an experiment. In the morning, shortly after waking up, i flip a coin. It either says heads or tails. In fact, the coin i use has no possibility of landing on the edge. I've told myself that if it says heads then i'll have a good day. If it says tails, then i'll have a below average day. There are no average days with this scheme. The idea is to track the coin toss, to see how good a predictor it really is.

During the first week, i was surprised at how good a predictor is was. During the second week, i made extra sure that i used the same coin, for fear that the magic was only present in the first, one and only magic coin. And, i took extra care not to toss the coin more than once in a day, lest the coin become tired, or something else might happen to prevent it's magic from working. More on the magic coin in a moment. During the third week, i was looking for a coin with heads on both sides. These days were clearly better.

Well, they were better except for today. This afternoon, i feel the weight of the flu on me again, and i had the runs a couple times - quite painful, and it left me drained. The coin said heads. Well, the coin was tossed in the morning, and the morning was really quite good. After all, i'd had a good night's sleep. Let's see what the coin says now about the afternoon: Heads again. Well, maybe i'm under the weather, but i can still be upbeat, right? Yes, and that's why i'm looking for a coin with heads on both sides.

Superstition is easy to generate. And, when looking for patterns, you are very likely to find them, even if they do not exist. When you look up at the stars, there are at least three dippers. The Big Dipper (part of Ursa Major), the Little Dipper (Ursa Minor), and the Pleiades (M45) all have a dipper pattern. The stars are random, but here's a repeating pattern of not just two or three stars, but Seven Stars. How likely is that?

The coin i'm using is a program on my Palm Pilot. Now, i have two Palms. They're both quite old, and getting unreliable. I use one as a backup for the other. So they have identical programs and data. The better of the two is used as the primary. I recently switched primary and secondary. The other one hasn't gotten any better... The upshot is that i could probably get a program that always says Heads. I'm a web programmer, and could put up a trivial program that does this. In fact, any static web page will do. So when you want to know how your day will turn out, look up this web page. Your answer has been conveniently placed at the top, and in the title.

What to get me for Xmas

No, i'm not a topologist, but this is really cool, if expensive. It's a Drinking Mug Klein Bottle. Doubles as a barometer, for spooky weather prediction. One can even drink tea in it, though reading tea leaves won't predict the weather with as much reliability.

Monday, Monday

Yesterday was a day off at the biggest of the big three US Automotive companies. We got the day off to vote, which took all of a half hour. One supposes that if i had to vote in the morning or evening, then it would have taken much longer. If that's the price of democracy - having a day off from time to time, i suppose that's OK.

In any case, today feels like a Monday. Which means that this week has two Mondays. When i mentioned this to a random passer by at the soda vending machine, he said, "Well that's not right. We ought to have two Fridays." To which, i replied that this Monday we had this week on Monday was also a Friday. Figure that one out.

To have two Fridays in a week, you have to take off, not Tuesday, but Wednesday. This avoids having a day that is both the beginning of the week and the end of the week at the same time. Naturally, if you have a Wednesday off, you complain that you can't really do anything with it, like go up North and do some wilderness trip in a canoe or something, and it just breaks up the week for nothing. If you figure out some solution to this dilemma, let me know.

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.

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!

What Superhero Are You?

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.

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?

Eye color

Your Eyes Should Be Brown

Your eyes reflect: Depth and wisdom What's hidden behind your eyes: A tender heart

What Color Should Your Eyes Be?

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.

Are You Right or Left Brained?

I'm of two minds on this one.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.