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Oh, math horror story, 2 actually since I had this happen twice: I was in the grocery store and beans were on sale, so I got a flat and put 12 cans in, neatly lined up, 3x4. Both times the clerk counted each can. (different clerks) Adult people, who probably went thru at least 10th grade in school, did not know that 3x4=12. I could almost see it if it were 8x9 or something.
Did any of you ever learn the finger trick of doing the 9 times table on your hands? You put your two hands together and if the problem is 9x5, you count to your fifth finger (from the left hand pinky) and all the fingers to the left of the fifth one are tens, and all the fingers to the right of it are ones. So, to the left of the fifth finger are four fingers (40), and to the right of it are five fingers, thus 45. And of course, the digits should always add up to nine, so 4+5=9. Anything divisible by nine should add up to nine if you add up the digits, so 1845 is also divisible by nine. I thought that was so nifty when I learned about it a few years ago. Too late for me, I'd already learned 9X the painful way, but I'm glad I did. I think you should sweat to learn the dry facts, then get creative and learn to do the fun stuff with them. I always told my kids that it would get more fun as school went on. I have no problem with manipulatives, esp if it helps them visualize what they're doing, but they should learn the facts too--they shouldn't learn to be that dependent on a calculator. I also made sure that my kids learned to count back change--hardly anyone knows how anymore, so if the store has a power outage they have to close b/c the majority of clerks can't count back change. That's pretty pathetic really.
While doing some research yesterday, I came across some references to this math curriculum, "Investigations in Numbers, Data, and Space". Here are some sample problems--the last one really got me. This is math? So then I went on our state's website and pulled up some sample math curriculum and it was pretty similar to what I see here. Apparently they don't teach "dry facts" in the schools--they prefer to let kids reinvent the wheel. I want to be a teacher, but if I have to teach this &%$#, I'll pull my hair out. Oh, and they don't encourage them to memorize math facts or teach them to do addition facts by carrying to the next place value. I must be out of touch--we homeschooled. Anyone had experience with this curriculum? Parents or teachers?
This seems like *soft math* meaning that it IS VERY LIKELY intended for some of the 3rd graders that are more educationally challenged or behind because english is their 2nd language or they just moved to the country and have had sporadic schooling.
My youngest just finished 3rd grade and he was doing all of the standard 32 x 14 = ? type math that I saw when I was his age.
Side Note: They still do teach *some* dry facts in school but I was never a huge fan of that. The world is a lot bigger place and you cannot know everything. Additionally, you can access information instantaneously without having to walk\ride to the library so the value of knowing tons of facts is worth less than problem solving and other skills.
Did any of you ever learn the finger trick of doing the 9 times table on your hands? You put your two hands together and if the problem is 9x5, you count to your fifth finger (from the left hand pinky) and all the fingers to the left of the fifth one are tens, and all the fingers to the right of it are ones. So, to the left of the fifth finger are four fingers (40), and to the right of it are five fingers, thus 45. And of course, the digits should always add up to nine, so 4+5=9.
I also taught my students the "11 trick," and they thought it was pretty impressive:
11 x 23 = ???
Take the number being multiplied by 11, separate the digits and put an underscore between them: 2__3. Add the two numbers together and put the sum in between them: 2 + 3 = 5 .... 2_5_3 -- and that's your answer.
This works for most 2-digit numbers and can even be done with larger numbers (but it takes a bit more work).
You can't use reasoning and logic if you haven't mastered basic computation skills. Abstract ability is built on the concrete. For example, try telling a student to solve this problem: "Mr. Jones can correct 150 quizzes in 50 minutes. His student aide can correct 150 quizzes in 75 minutes. Working together, how many minutes will it take them to correct 150 quizzes?" It's difficult for a student to "problem solve" if they don't know how to determine what 150 divided by 50 is (or they never memorized 15 divided by 5), they can't write an algebraic equation from the information given, and they don't know how to solve for x.
You are correct, but I am assuming that the children already have a grip on basic arithmetic.
I also taught my students the "11 trick," and they thought it was pretty impressive:
11 x 23 = ???
Take the number being multiplied by 11, separate the digits and put an underscore between them: 2__3. Add the two numbers together and put the sum in between them: 2 + 3 = 5 .... 2_5_3 -- and that's your answer.
This works for most 2-digit numbers and can even be done with larger numbers (but it takes a bit more work).
This only works until 45, then after that you have to add the first numbers together:
11 x 46 = ???
4__6; 4 + 6 = 10
now add the 1 from the 10 with the 4 from the 46 and put the 0 in the middle to get 506.
11 x 46 = 506.
The first two are good examples of using math in real life. Most of the time, when you're adding two numbers, you don't have time to whip out a calculator or write it down on paper, so I especially like the second one.
The third one is absurd as a math example, LOL. What is the point of that (as far as math class goes)?? To get the kids' attention and then teach them about the calendar? I'd hope that that would have been covered before third grade!
We homeschool, and I don't go for drilling kids on addition or multiplication tables. We use a more open-ended math curriculum (Miquon) that teaches them how to think, not just a bunch of formulas to memorize in the early years. I don't remember reciting multiplication tables in the 80s, but I do know them, so who knows?
Have you ever considered doing the problem in your head? Why does adding a couple of numbers require a calculator or a piece of paper? Using a calculator teaches them to think? I would imagine it does just the opposite.
My mother was a math whiz (to be honest mom was a cottin' pickin' genius). When I was young I was always amazed that she could take a string of numbers and add then together in her head. I asked how she did it and she told me she kept a blackboard in her head and wrote the numbers on it.
I was so impressed that I put a blackboard in my head also and have been using it ever since. It takes a pretty complex set of numbers to send me to a calculator.
Herein lies one issue with teaching math....there are kids/adults who can intuitively know the answer to that type of problem without having to go through the basics to get there. It's just how it is, and for those kids/adults drills are not necessary. It's a natural ability to have an automatic understanding of the outcome, without going step by step.
I was that way with higher math. I could come up with the answer, but when the teacher wanted me to show it step by step, I oftentimes could not.
My 5 yr old is similarly attuned to math. He will start Kindergarten in the fall and has the understanding of how multiplication and division works, and he can do basic problems easily enough when given in just numbers. However, give him a real life situation and he's got the answer without thinking of it in formulaic progression.
For instance, we were discussing ordering pizza one day and we had many more people to eat than usual. He heard how many people and he then told us how many pizzas he thought we should get. He was right on the money, yet couldn't really tell us why he was right or how he figured it out. He just knew. And he certainly hasn't mastered math basics.
Yes, he has. What he hasn't mastered is the ability to explain how he reaches the answer.
Did any of you ever learn the finger trick of doing the 9 times table on your hands? You put your two hands together and if the problem is 9x5, you count to your fifth finger (from the left hand pinky) and all the fingers to the left of the fifth one are tens, and all the fingers to the right of it are ones. So, to the left of the fifth finger are four fingers (40), and to the right of it are five fingers, thus 45. And of course, the digits should always add up to nine, so 4+5=9.
Excellent post stepka!
Similar, yes. Any number multiplied by 9 is the same number multiplied by nine minus itself.
9*7 = (10*7)-7 = 63
And of course the quick check: Does 6 + 3 = 9?
Times nines throw a lot of people so these "short cuts" do help.
BTW: When doing the hand version place your hands with the thumbs together and count the pinkie when you start. In the example above you end up on the left hand thumb so you have the fingers (4) on the left hand open and all the fingers and the thumb on the right hand open (5).
I mention this because I was not aware of the method and placed my hands with the pinkies together, which caused a bit of confusion.
This is a really good method for doing nines so I wanted to be sure everyone understood it.
Have you ever considered doing the problem in your head? Why does adding a couple of numbers require a calculator or a piece of paper? Using a calculator teaches them to think? I would imagine it does just the opposite.
HP had a graphing calculator out a few years ago that not only gave the answer, it also showed the steps to solving the problem. As you may have guessed, this calculator was banned from most classrooms and it has been off the market for a while now. HP claims that the calculator was supposed to help with the learning (by showing the steps) but of course kids just copied the steps down onto paper when they were required to show their work.
Besides some basic trig and log functions I find that using a calculator is more of a pain in the behind then just solving the problem on paper. Heck, you can find you answer with a slide rule almost just as fast (or faster if you don't know how to use a scientific or graphing calculator).
This only works until 45, then after that you have to add the first numbers together:
Not necessarily. Try 11 x 62 -- that equals 682.
Quote:
Originally Posted by K-Luv
11 x 46 = ???
4__6; 4 + 6 = 10
now add the 1 from the 10 with the 4 from the 46 and put the 0 in the middle to get 506.
11 x 46 = 506.
I guess "the rule" would be that the two numbers added together have to be less than 10, or else you have to start including the first number?
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