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.
Friday, June 30, 2006
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.
Tuesday, June 20, 2006
Finger Arithmetic Part Five
Continuing finger arithmetic from Part Four. This one is called Part Five. It is the sixth part in the series.
In Part Three, we introduced the idea that sometimes you want to add something, but you have no fingers left to add. This part does that for the thumb. Here, we add five when the thumb is already set.
The first example is adding seven plus five. First, set seven. Do that by starting with a fist on both hands, adding two fingers to the right hand, then adding the right thumb. Now we want to add five. You want to add a right thumb, but your right thumb is already set. To do this, remember that 5 + 5 is the same as 5 + (10 - 5), which is rearranged as 5 - 5 + 10. Still have zero / seven on your hands? Good. Subtract five by tucking the right thumb down. Add ten by adding a finger to the left hand. Look at your hands. Read twelve.
The next example is adding six and five. First start with both fists. Set six on the right hand by adding a finger and thumb. Add five by subtracting the right thumb, and adding a finger on the left hand. Read the result: eleven.
The final example is adding nine and five. Start with both fists. Add all fingers and thumb on the right hand for nine. Subtract the right thumb and add a finger on the left hand. Read fourteen.
All examples: 5 + 5, 6 + 5, 7 + 5, 8 + 5, 9 + 5.
During the week, go over the previous lesson's examples. Stick to short practices every day. You don't have to do all the examples from all the lessons in one go. But you should sneak in all the examples for all the lessons over the course of the week. And every day should have this newest lesson.
The next lesson will get you started on single digit addition. It won't be the last word there, however. It seems that there is always something more to say.
In Part Three, we introduced the idea that sometimes you want to add something, but you have no fingers left to add. This part does that for the thumb. Here, we add five when the thumb is already set.
The first example is adding seven plus five. First, set seven. Do that by starting with a fist on both hands, adding two fingers to the right hand, then adding the right thumb. Now we want to add five. You want to add a right thumb, but your right thumb is already set. To do this, remember that 5 + 5 is the same as 5 + (10 - 5), which is rearranged as 5 - 5 + 10. Still have zero / seven on your hands? Good. Subtract five by tucking the right thumb down. Add ten by adding a finger to the left hand. Look at your hands. Read twelve.
The next example is adding six and five. First start with both fists. Set six on the right hand by adding a finger and thumb. Add five by subtracting the right thumb, and adding a finger on the left hand. Read the result: eleven.
The final example is adding nine and five. Start with both fists. Add all fingers and thumb on the right hand for nine. Subtract the right thumb and add a finger on the left hand. Read fourteen.
All examples: 5 + 5, 6 + 5, 7 + 5, 8 + 5, 9 + 5.
During the week, go over the previous lesson's examples. Stick to short practices every day. You don't have to do all the examples from all the lessons in one go. But you should sneak in all the examples for all the lessons over the course of the week. And every day should have this newest lesson.
The next lesson will get you started on single digit addition. It won't be the last word there, however. It seems that there is always something more to say.
Saturday, June 17, 2006
Finger Arithmetic Part Four
Continuing finger arithmetic from Part Three. This one is called Part Four. It is the fifth part in the series.
Bigger numbers are added to small numbers. It's an easy lesson that introduces thinking of bigger numbers as the sum of two smaller numbers. One of the smaller numbers is always five. In fact, when you set one of these numbers on a hand, the thumb is the five, and the fingers represent the other small number.
Let's say you have one, and want to add seven. For the moment, set seven on one hand. Make a fist. Add two fingers. Add the thumb. Seven is five plus two. So we can add these parts one at a time. Here are the steps. We're adding one plus seven. Set one by making a fist on the right hand, then add one finger. Add the 'two' of the seven by adding two fingers. Then add the five of the seven by adding the thumb. Read the answer. Uhm, let's see. There's a thumb. There are three fingers. That's eight.
Now we'll add three plus six. Set three by making a fist and adding three fingers. Six is five plus one. Add one by adding a finger. Add five by adding a thumb. Read the answer. Nine.
Try two plus seven. Set two. Add the two. Add the five. Read the result (nine). You did say it out loud, right?
Three plus five. Make a fist. Add three fingers. Add the thumb.
All of the examples: 0 + 5, 0 + 6, 0 + 7, 0 + 8, 0 + 9, 1 + 5, 1 + 6, 1 + 7, 1 + 8, 2 + 5, 2 + 6, 2 + 7, 3 + 5, 3 + 6, 4 + 5. Try them all.
Keep practicing Part Three during the week. It takes a bit for the Five's Complements to stick in your head. We'll need to expand on this idea soon. We're trying to keep it down to one new idea a week. However, you need to remember all the old lessons to get it all together.
Bigger numbers are added to small numbers. It's an easy lesson that introduces thinking of bigger numbers as the sum of two smaller numbers. One of the smaller numbers is always five. In fact, when you set one of these numbers on a hand, the thumb is the five, and the fingers represent the other small number.
Let's say you have one, and want to add seven. For the moment, set seven on one hand. Make a fist. Add two fingers. Add the thumb. Seven is five plus two. So we can add these parts one at a time. Here are the steps. We're adding one plus seven. Set one by making a fist on the right hand, then add one finger. Add the 'two' of the seven by adding two fingers. Then add the five of the seven by adding the thumb. Read the answer. Uhm, let's see. There's a thumb. There are three fingers. That's eight.
Now we'll add three plus six. Set three by making a fist and adding three fingers. Six is five plus one. Add one by adding a finger. Add five by adding a thumb. Read the answer. Nine.
Try two plus seven. Set two. Add the two. Add the five. Read the result (nine). You did say it out loud, right?
Three plus five. Make a fist. Add three fingers. Add the thumb.
All of the examples: 0 + 5, 0 + 6, 0 + 7, 0 + 8, 0 + 9, 1 + 5, 1 + 6, 1 + 7, 1 + 8, 2 + 5, 2 + 6, 2 + 7, 3 + 5, 3 + 6, 4 + 5. Try them all.
Keep practicing Part Three during the week. It takes a bit for the Five's Complements to stick in your head. We'll need to expand on this idea soon. We're trying to keep it down to one new idea a week. However, you need to remember all the old lessons to get it all together.
Friday, June 16, 2006
Make Mine a Double
Yesterday, i had a headache. It's a rare thing for me. I asked around at the office, and someone had some Motrin. It did the trick. In retrospect, it is possible i just needed a drink of water. Next time, i'm going to try the new double strength placebo.
Thursday, June 15, 2006
Phone Cord
I've run a research project to determine the answer to a question burning in the hearts of many: What is the minimum number of strings or ropes or cords that it takes to create a tangled spaghetti mess?
The answer appears to be one.
And you may have evidence of this within a small number of inches from where you sit. Look at the nearest phone cord. If it is anything like mine, it is a tangled mess. Every few days, i take the phone off the hook, dangle it by the cord, and let it unwind. Despite low use, and always putting it down without twisting it once, the cord is basically always a twisted mess.
But not at home. It's a cordless phone there.
I had to look up the spelling in a dictionary. Apparently, a phone chord is some sort of musical idea. It's an idea that rings a Bell.
The answer appears to be one.
And you may have evidence of this within a small number of inches from where you sit. Look at the nearest phone cord. If it is anything like mine, it is a tangled mess. Every few days, i take the phone off the hook, dangle it by the cord, and let it unwind. Despite low use, and always putting it down without twisting it once, the cord is basically always a twisted mess.
But not at home. It's a cordless phone there.
I had to look up the spelling in a dictionary. Apparently, a phone chord is some sort of musical idea. It's an idea that rings a Bell.
Wednesday, June 14, 2006
Caffeine
A few years ago, i developed arthritis in my shoulders. Call it bursitis. I could not raise my right arm higher than level. Cured, but now years later, i still reach for high shelf items with my left arm.
I was cured by stopping my intake of caffeine. I used to drink nearly a half gallon of Mt. Dew a day, though not on weekends. As my symptoms got worse, i noticed that it wasn't as bad on Sunday night as the rest of the week. As an experiment, i switched to Sprite and things improved. A month later, i had a cup of coffee, and it hurt for four days. No doubt about it. Caffeine. After ten months of abstinence, my symptoms rapidly vanished. Caffeine is a very stable chemical.
I asked around, and even doctors told me that there was no connection. Feh. Eventually i learned that caffeine can interfere with the body's intake of calcium. Now, the joints are affected first. Then the bones. So, i wondered if caffeine was big in osteoporosis.
It International Osteoporosis Foundation recently held a big congress (convention). Lots of risk factors for osteoporosis were enumerated. Their web site has a page on prevention. Caffeine is mentioned once, along with salt. You could easily miss it. At least it's mentioned.
The thing is, when i've talked to people at risk for osteoporosis, like older women, they can't imagine giving up caffeine. They say that they drink decaf, but they have no idea how much caffeine is in it. And, it can vary by a factor of ten. And, products with caffeine don't have to say how much is in it. And, i'm pretty smart, but i have no idea how to perform a test to find out. I got through high school chemistry (with an A), but haven't had much since.
Caffeine is addictive. It's subtle. It won't let go of you, even after years of abstinence. The effects appear to be cumulative.
So i had this problem with my right foot. I thought my shoes were causing discomfort. I thought it was the way i was walking. But now i know that it is just taking longer to heal than other parts of my body. It's arthritis.
I was cured by stopping my intake of caffeine. I used to drink nearly a half gallon of Mt. Dew a day, though not on weekends. As my symptoms got worse, i noticed that it wasn't as bad on Sunday night as the rest of the week. As an experiment, i switched to Sprite and things improved. A month later, i had a cup of coffee, and it hurt for four days. No doubt about it. Caffeine. After ten months of abstinence, my symptoms rapidly vanished. Caffeine is a very stable chemical.
I asked around, and even doctors told me that there was no connection. Feh. Eventually i learned that caffeine can interfere with the body's intake of calcium. Now, the joints are affected first. Then the bones. So, i wondered if caffeine was big in osteoporosis.
It International Osteoporosis Foundation recently held a big congress (convention). Lots of risk factors for osteoporosis were enumerated. Their web site has a page on prevention. Caffeine is mentioned once, along with salt. You could easily miss it. At least it's mentioned.
The thing is, when i've talked to people at risk for osteoporosis, like older women, they can't imagine giving up caffeine. They say that they drink decaf, but they have no idea how much caffeine is in it. And, it can vary by a factor of ten. And, products with caffeine don't have to say how much is in it. And, i'm pretty smart, but i have no idea how to perform a test to find out. I got through high school chemistry (with an A), but haven't had much since.
Caffeine is addictive. It's subtle. It won't let go of you, even after years of abstinence. The effects appear to be cumulative.
So i had this problem with my right foot. I thought my shoes were causing discomfort. I thought it was the way i was walking. But now i know that it is just taking longer to heal than other parts of my body. It's arthritis.
Tuesday, June 13, 2006
Finger Arithmetic Part Three
Continuing finger arithmetic from Part Two. This one is called Part Three. It is the forth part in the series. Five's Complements are introduced. Clear as mud? Let's get started!
The Five's Complement of a number is the number you add to get five. So, the Five's Complement of one is four. That's because one plus four is five. Likewise, the Five's Complement of four is one. The other pair is two and three. The Five's Complement of two is three. Two plus three is five. And the Five's Complement of three is two.
Armed with this new knowledge, we tackle adding slightly bigger numbers. The very first example is 3 + 3. Start with a fist on the right hand. Put up three fingers. You want to add three fingers, but you don't have three fingers that can be added. The idea is to add five, and subtract the Five's Complement of three - which is two. So 3 + 3 = 3 + 5 - 2. However, do it in this order: 3 - 2 + 5. You have three fingers up on your right hand. Subtract two fingers, and add the thumb (five). That leaves you with your thumb (five) and one finger (one), for a total of six. Say six out loud.
The reason that the subtraction should be done first will become apparent in a later lesson. That lesson involves carries from one hand to the other. By performing the steps in this order, you can avoid ever having more than one pending operation. It is less confusing, and more reliable. Handling carries is the single biggest reason for error in traditional pencil and paper arithmetic.
Another example: 4 + 2. Start with a fist and set four fingers. The Five's Complement of two is three. So subtract three fingers. Then add the thumb for five. Read the answer out loud. Six.
Another example: 2 + 3. Start with a fist and set two fingers. The Five's Complement of three is two. Subtract two fingers and add the thumb (five). Read the answer: five. Note that you have no fingers up - just the thumb. You have five (the thumb) plus zero (no fingers). Zero is very important. Zero may mean nothing, but it isn't meaningless.
All of the examples: 1 + 4, 2 + 3, 2 + 4, 3 + 2, 3 + 3, 3 + 4, 4 + 1, 4 + 2, 4 + 3 and 4 + 4. Try them all. Don't forget to read the answer out loud.
When you are done with this lesson, practice some of the examples from previous lessons. Add small numbers. Do some counting. Remember to read the answers out loud. Practice five minutes a day. Five minutes each day for a week is worth more than twenty minutes each day for two days. And, five minutes can be squeezed into just about any schedule.
The Five's Complement of a number is the number you add to get five. So, the Five's Complement of one is four. That's because one plus four is five. Likewise, the Five's Complement of four is one. The other pair is two and three. The Five's Complement of two is three. Two plus three is five. And the Five's Complement of three is two.
Armed with this new knowledge, we tackle adding slightly bigger numbers. The very first example is 3 + 3. Start with a fist on the right hand. Put up three fingers. You want to add three fingers, but you don't have three fingers that can be added. The idea is to add five, and subtract the Five's Complement of three - which is two. So 3 + 3 = 3 + 5 - 2. However, do it in this order: 3 - 2 + 5. You have three fingers up on your right hand. Subtract two fingers, and add the thumb (five). That leaves you with your thumb (five) and one finger (one), for a total of six. Say six out loud.
The reason that the subtraction should be done first will become apparent in a later lesson. That lesson involves carries from one hand to the other. By performing the steps in this order, you can avoid ever having more than one pending operation. It is less confusing, and more reliable. Handling carries is the single biggest reason for error in traditional pencil and paper arithmetic.
Another example: 4 + 2. Start with a fist and set four fingers. The Five's Complement of two is three. So subtract three fingers. Then add the thumb for five. Read the answer out loud. Six.
Another example: 2 + 3. Start with a fist and set two fingers. The Five's Complement of three is two. Subtract two fingers and add the thumb (five). Read the answer: five. Note that you have no fingers up - just the thumb. You have five (the thumb) plus zero (no fingers). Zero is very important. Zero may mean nothing, but it isn't meaningless.
All of the examples: 1 + 4, 2 + 3, 2 + 4, 3 + 2, 3 + 3, 3 + 4, 4 + 1, 4 + 2, 4 + 3 and 4 + 4. Try them all. Don't forget to read the answer out loud.
When you are done with this lesson, practice some of the examples from previous lessons. Add small numbers. Do some counting. Remember to read the answers out loud. Practice five minutes a day. Five minutes each day for a week is worth more than twenty minutes each day for two days. And, five minutes can be squeezed into just about any schedule.
Tuesday, June 06, 2006
Finger Arithmetic Part Two
Continuing finger arithmetic from Part One. This third part is called Part Two. We start addition. It may seem as if the lesson moves slowly. Take your time. The harder stuff builds on this easy stuff.
First, we'll add one and one. Start with a fist on your right hand. Put out a finger to represent one. Add another finger. Read the answer out loud: two.
You might think we've already covered this. And you'd be right. We have added one repeatedly in order to count. In some sense, this is nothing new.
Next example. Add one plus two. Start with a fist on your right hand. Put out a finger to set one. Add two fingers to it. Read the answer out loud: three.
Next example. Add two plus two. Start with a fist on your right had. Put two fingers out to set two. Add two fingers to it. Read the answer out loud: four.
The whole set of possible examples here are: 0 + 1, 0 + 2, 0 + 3, 0 + 4, 1 + 1, 1 + 2, 1 + 3, 2 + 2, 3 + 1. Practice these all week.
Extra credit. Add ten plus twenty. Start with a fist on your left hand. Put out a finger to set ten. Add two fingers to it. Read the answer out loud: thirty.
That's small number addition. Remember to practice the drills every day. Don't forget to bring your fingers with you, everywhere. Do you have five minutes? What are you waiting for?
First, we'll add one and one. Start with a fist on your right hand. Put out a finger to represent one. Add another finger. Read the answer out loud: two.
You might think we've already covered this. And you'd be right. We have added one repeatedly in order to count. In some sense, this is nothing new.
Next example. Add one plus two. Start with a fist on your right hand. Put out a finger to set one. Add two fingers to it. Read the answer out loud: three.
Next example. Add two plus two. Start with a fist on your right had. Put two fingers out to set two. Add two fingers to it. Read the answer out loud: four.
The whole set of possible examples here are: 0 + 1, 0 + 2, 0 + 3, 0 + 4, 1 + 1, 1 + 2, 1 + 3, 2 + 2, 3 + 1. Practice these all week.
Extra credit. Add ten plus twenty. Start with a fist on your left hand. Put out a finger to set ten. Add two fingers to it. Read the answer out loud: thirty.
That's small number addition. Remember to practice the drills every day. Don't forget to bring your fingers with you, everywhere. Do you have five minutes? What are you waiting for?
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