Like language, it's important that the students hear the patterns as well as see any patterns before they write down the symbols. Multiplication is a great example of this idea. Long before students see a multiplication table or worksheet young students should be singing songs, using blocks and hearing the patterns that are associated with the various multiplication tables. Then when they are exposed to the symbols, they understand what they mean. They understand that three times three is written 3 x 3 and that it really is the same as nine. The equals sign and all the symbols are understood. If your children are playing with blocks they can see that nine is a square number and what that means. Nine really is square even though the symbol for nine has curves and a circle. 9. Look at it, it doesn't look very square, little kids and even some older kids can get caught up in the symbols instead of understanding the concepts and what the symbols represent.
Parents and teachers can use worksheets to reinforce math learning but they should be used sparingly to introduce new ideas, if at all. With manipulative based teaching we always start in the concrete with base ten blocks, then move to sketching then at last to the symbols. Since most worksheets are symbol based it's only natural that they should be used last not first. Concept based teaching techniques emphasize understanding the concepts long before students see the symbols. In fact, a lot of little kids can start getting complex math concepts well before they can write complex symbols.
Using math worksheets to introduce math concepts is literally teaching backwards. First Grade Math Worksheets should be introduced after quite a bit of playing has been done. That way the worksheet is just practice that allows you to see how well they understand the math concepts you are teaching. They can be used for drills but using drills at an early age has unintended consequences, you don't want to turn them off at an early age and excessive drills will do just that eventually. The worksheets should be easy to begin with and then become more challenging as the student's confidence builds. They should be thought of as practice instead of as tests or drills or something to be fretted over. Some students develop math anxiety at an young age and worse test anxiety.
If the child firmly grasps the concepts any math worksheet should be simple or at worst “challenging.” If children don't have the writing skills required you can actually do the writing for them. Be sure THEY tell you what to write, you are not doing it for them just writing the symbols. This is more for parents or home schoolers because teachers in school will find this impossible unless the number of children is very small and we all know they rarely are.
Often times it's a good idea to play with the concepts for several days and then give the worksheet on Thursday. If the students don't complete it they can take it home and you can finish it off on Friday. If you are homeschooling or just giving your child a head start, be sure you play for a couple of days at least before you get out a worksheet. With first graders you can often use the same or very similar worksheets every few months and it will be new again. This is normal it takes quite a few impressions to get information into the long term memory. Many teachers lament that after Summer Vacation or even Christmas or Spring Break their students don't remember most of what they have been taught. It's still “in there” and this is a great time to bring it out with a practice sheet they are already familiar with.
Worksheets are great for reinforcement, and great teaching tools when used properly.
Using the Making Change Worksheets.
FREE WORKSHEETS HERE at Crewton Ramone's House of Math. More free worksheets coming soon.
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Saturday, January 15, 2011
Thursday, January 13, 2011
Getting Down With 3rd Power Algebra
We basically played getting to know you, and then went over the five basic concepts, played with the pieces to gain familiarity with the blocks, built some tens, did some multiplication and then moved on to algebra.
Before we started playing on the floor we did some drawing and of course a three period lesson to get comfortable with the pieces we were about to use on the floor. They got a chance to draw whatever they wanted and then we played a simple game where they had to tell me the factors and I had to draw a picture to see if our pictures matched. Similar to this post where the student got to draw anything he wanted. When I say "anything", I mean any picture of a third or fourth power expression.
Had a few games where we took the factors and built the rectangles...just drawing. But then for even more fun we played on the floor.
Note in the initial picture we have a drawing and some notation that does not fit the picture because the picture is taken after we did a drawing where one factor was x + 2, and then I added to the picture making the factor 2x + 2...and we hadn't changed the notation yet...they really get an intrinsic feel for the distributive theory when you present math this way. As time goes y and they see it a few times when given a formal presentation on the distributive theory they "get it."
Right now for the first introduction it's much more about counting, adding and multiplication. The algebra and factoring come along for the ride as it were, we tie it together with the "higher algebra."
"Main thing: we have fun", and even a ten year stayed "tuned in" for over two hours. Afterwards he told his mom, "it was fun."
Find us on FaceBook
Go to Crewton Ramone's House of Math. (Home Page of My Website.)
Get Them Off Their Fingers And Into Math
Get Them Off Their Fingers And Into Math
By Crewton Ramone
Moving Towards Mastery
Mastering the 45 addends is an important step on the way to making computation easy. Addition is simple, if the concepts are understood. 5 + 7 is the same as 7 + 5 and when 7 and 5 get together it's always going to end in 2...so 17 + 5 and 15 + 7 are easy and students can also see that 37 + 5 is basically the same problem as the single digit problems with tens "just along for the ride." You would be amazed at the number of students who don't get that simple concept. They'll come up with 21 or 23 instead of 22 when adding 15 + 7. They can also use the simple "want to be a ten" algorithm to make it easy: 7 takes 3 from 5 making one ten and two, OR 5 takes 5 from 7 making one ten and two. Either way it's 12, and the best way to do it is the way the student likes best.
This method allows the student to get off their fingers by making "a ten and some more" when adding two numbers. As it turns out there are only 45 combinations...once students understand this simple "want to be a ten" algorithm addition becomes a lot easier and they can tackle bigger problems on their own. Then it just comes down to practice and repetition. Use a wide variety of problems to practice this skill and teach other concept the same time in order to keep the practice from becoming mind numbing drill work which will also turn students off to math.
Using their fingers is a step on the way to mastery of addition facts, unfortunately many students remain stuck at this step all the way into adulthood. For kinesthetic learners using fingers and hands IS IMPORTANT: that's HOW they learn, and you need to help them move past this: manipulatives are a great way to move them into "doing it their heads." For young students using fingers and hands is just natural...you can also spot the kinesthetic learners because they will rely more on their fingers and be slower to move on from them. This does not mean they are "slow" or any less able than visual or auditory learners, they grasp concepts just as fast or faster than those with other learning styles. We also find when it comes to sports and other activities requiring hand eye coordination (like arts and crafts) they often excel. Using your fingers is great! AND you need to get past that stage if you are going to be fast at addition and attain mastery. Being fast at addition leads to easy mastery of multiplication as an added bonus. They may even like math, why wouldn't they if it's fun and easy?
Many speed reading courses incorporate the use of the finger to guide the eye along the page, some use this to start, and then drop it for other courses this is the main stay of the course. Adding more sensory input increases learning, and in the case of reading the hand and the eye are integrally connected. The point is you want to encourage students to move through this step when it comes to the mathematics NOT discourage or skip the step all together. Some students will naturally NOT use their fingers when doing mental calculations...for those that do use their fingers later it will become a handy-cap. Counting quickly makes math easier, because all math is is counting; however, don't confuse computation with the mathematics. The mathematics is the use of computation and critical thinking skills to solve problems and express reality numerically.
Addition and subtraction as well as multiplication are just counting quickly. They are among the first steps to understanding math, and they should be mastered to ensure success. Using fingers can lead to a loss of accuracy too, often children (and adults) are off by one sometimes even two.
Practice with the addends verbally, build walls and towers, play games like what's under the cup, simple story problems and work sheets with pictures give the student the experience they need to make the transition from fingers to symbols to being able to do it "in their heads." Drawing rectangles and other math concepts as well as making drawings of the manipulatives they use, help the student make sense of the symbols and see what they are doing. It also adds variety, and helps students (and teachers) see that you use the same skill sets all through the mathematics, which is why you often see me use third and fourth power algebra to teach addition and multiplication facts.
Indeed if you carry the concept far enough they can also get off the symbols as it were and do it ALL in their heads if need be, no paper or pencil. This was illustrated perfectly by a five year old who is able to factor trinomials in his head because he can see the pictures when he hears expressions like x^2 + 3x +2, he can see it and tell you the sides. Or if you tell him the sides (x+3)(x+2) he can tell you the whole rectangle not because he is seeing symbols but because he is seeing PICTURES. Further he is "cementing" his addends and multiplication facts into his memory. How much easier is it to see 6 taking a 4 out of a 7 to make 13 when presented with a problem like x = 6 + 7 than to do algebra? It's also quite easy to see 6 + x = 13 or x + 7 = 13, especially if you give them a simple algorithm to solve these based concept of "want to be a ten." He also gets a ton of positive reinforcement because people think he is a little genius which motivates children to do more. Never underestimate the power of simple praise.
Once they learn some basic concepts and understand what the symbols mean math becomes easy and even fun. Being able to visualize what you are doing makes all the difference, it also makes it MUCH easier to commit to memory because the mind works in pictures not symbols, so memorizing the 45 addends and multiplication tables is easier because the mind can store pictures much more readily than symbols. Then when it is time to be recalled, a picture or the symbols or just words can easily be retrieved from that place we call the long term memory.
Have you ever known anybody that remembers phone numbers by picturing the keypad in their head? They may even point to the numbers and move their pointer finger on an imaginary keypad in the air as they are recalling the number. This is a visual kinesthetic way of storing long numbers. The brain works with pictures and this makes it easier to get the information out. How much simpler is it to add two numbers together than recite seven to ten digits? Especially if you have a method for visualizing them if you somehow forget?
A simple exercise: ask a student to picture a cow. Then ask if they saw C O W or a picture of a cow? Ask what color was it? This lets you know they weren't seeing symbols. The problem is with math most students have nothing to picture whether it's algebra or simple addition. The "trick" if there is one is to get the information into the long term memory so it easily recalled and it's pretty well proven that symbols, that is letters and numbers, are a difficult way to get information there.
Manipulatives are the perfect bridge to get information there. After all, it's never storage that's the problem it's retrieval.
Crewton Ramone is the alter ego of a fed up math tutor. More can be found by visiting these websites:
http://www.crewtonramoneshouseofmath.com/
http://crewtonramoneshouseofmath.blogspot.com/
Math really can be fun and easy.
Article Source: http://EzineArticles.com/?expert=Crewton_Ramone
“Teaching a child not to step on a caterpillar is as valuable to the child as it is to the caterpillar.” ~Bradley Millar
By Crewton Ramone
Moving Towards Mastery
Mastering the 45 addends is an important step on the way to making computation easy. Addition is simple, if the concepts are understood. 5 + 7 is the same as 7 + 5 and when 7 and 5 get together it's always going to end in 2...so 17 + 5 and 15 + 7 are easy and students can also see that 37 + 5 is basically the same problem as the single digit problems with tens "just along for the ride." You would be amazed at the number of students who don't get that simple concept. They'll come up with 21 or 23 instead of 22 when adding 15 + 7. They can also use the simple "want to be a ten" algorithm to make it easy: 7 takes 3 from 5 making one ten and two, OR 5 takes 5 from 7 making one ten and two. Either way it's 12, and the best way to do it is the way the student likes best.
This method allows the student to get off their fingers by making "a ten and some more" when adding two numbers. As it turns out there are only 45 combinations...once students understand this simple "want to be a ten" algorithm addition becomes a lot easier and they can tackle bigger problems on their own. Then it just comes down to practice and repetition. Use a wide variety of problems to practice this skill and teach other concept the same time in order to keep the practice from becoming mind numbing drill work which will also turn students off to math.
Using their fingers is a step on the way to mastery of addition facts, unfortunately many students remain stuck at this step all the way into adulthood. For kinesthetic learners using fingers and hands IS IMPORTANT: that's HOW they learn, and you need to help them move past this: manipulatives are a great way to move them into "doing it their heads." For young students using fingers and hands is just natural...you can also spot the kinesthetic learners because they will rely more on their fingers and be slower to move on from them. This does not mean they are "slow" or any less able than visual or auditory learners, they grasp concepts just as fast or faster than those with other learning styles. We also find when it comes to sports and other activities requiring hand eye coordination (like arts and crafts) they often excel. Using your fingers is great! AND you need to get past that stage if you are going to be fast at addition and attain mastery. Being fast at addition leads to easy mastery of multiplication as an added bonus. They may even like math, why wouldn't they if it's fun and easy?
Many speed reading courses incorporate the use of the finger to guide the eye along the page, some use this to start, and then drop it for other courses this is the main stay of the course. Adding more sensory input increases learning, and in the case of reading the hand and the eye are integrally connected. The point is you want to encourage students to move through this step when it comes to the mathematics NOT discourage or skip the step all together. Some students will naturally NOT use their fingers when doing mental calculations...for those that do use their fingers later it will become a handy-cap. Counting quickly makes math easier, because all math is is counting; however, don't confuse computation with the mathematics. The mathematics is the use of computation and critical thinking skills to solve problems and express reality numerically.
Addition and subtraction as well as multiplication are just counting quickly. They are among the first steps to understanding math, and they should be mastered to ensure success. Using fingers can lead to a loss of accuracy too, often children (and adults) are off by one sometimes even two.
Practice with the addends verbally, build walls and towers, play games like what's under the cup, simple story problems and work sheets with pictures give the student the experience they need to make the transition from fingers to symbols to being able to do it "in their heads." Drawing rectangles and other math concepts as well as making drawings of the manipulatives they use, help the student make sense of the symbols and see what they are doing. It also adds variety, and helps students (and teachers) see that you use the same skill sets all through the mathematics, which is why you often see me use third and fourth power algebra to teach addition and multiplication facts.
Indeed if you carry the concept far enough they can also get off the symbols as it were and do it ALL in their heads if need be, no paper or pencil. This was illustrated perfectly by a five year old who is able to factor trinomials in his head because he can see the pictures when he hears expressions like x^2 + 3x +2, he can see it and tell you the sides. Or if you tell him the sides (x+3)(x+2) he can tell you the whole rectangle not because he is seeing symbols but because he is seeing PICTURES. Further he is "cementing" his addends and multiplication facts into his memory. How much easier is it to see 6 taking a 4 out of a 7 to make 13 when presented with a problem like x = 6 + 7 than to do algebra? It's also quite easy to see 6 + x = 13 or x + 7 = 13, especially if you give them a simple algorithm to solve these based concept of "want to be a ten." He also gets a ton of positive reinforcement because people think he is a little genius which motivates children to do more. Never underestimate the power of simple praise.
Once they learn some basic concepts and understand what the symbols mean math becomes easy and even fun. Being able to visualize what you are doing makes all the difference, it also makes it MUCH easier to commit to memory because the mind works in pictures not symbols, so memorizing the 45 addends and multiplication tables is easier because the mind can store pictures much more readily than symbols. Then when it is time to be recalled, a picture or the symbols or just words can easily be retrieved from that place we call the long term memory.
Have you ever known anybody that remembers phone numbers by picturing the keypad in their head? They may even point to the numbers and move their pointer finger on an imaginary keypad in the air as they are recalling the number. This is a visual kinesthetic way of storing long numbers. The brain works with pictures and this makes it easier to get the information out. How much simpler is it to add two numbers together than recite seven to ten digits? Especially if you have a method for visualizing them if you somehow forget?
A simple exercise: ask a student to picture a cow. Then ask if they saw C O W or a picture of a cow? Ask what color was it? This lets you know they weren't seeing symbols. The problem is with math most students have nothing to picture whether it's algebra or simple addition. The "trick" if there is one is to get the information into the long term memory so it easily recalled and it's pretty well proven that symbols, that is letters and numbers, are a difficult way to get information there.
Manipulatives are the perfect bridge to get information there. After all, it's never storage that's the problem it's retrieval.
Crewton Ramone is the alter ego of a fed up math tutor. More can be found by visiting these websites:
http://www.crewtonramoneshouseofmath.com/
http://crewtonramoneshouseofmath.blogspot.com/
Math really can be fun and easy.
Article Source: http://EzineArticles.com/?expert=Crewton_Ramone
“Teaching a child not to step on a caterpillar is as valuable to the child as it is to the caterpillar.” ~Bradley Millar
Wednesday, January 12, 2011
Notation Really Does Tell The Story
The point of this post isn't so much the mathematics that the students learned; there are plenty of "how to" posts on Equivalent Fractions, as well as other fractions concepts, Card Games and Algebra on this blog and on my website.
The point of this point is to draw your attention to the student's notation as a big clue to how well you are doing at getting whatever concept you are teaching across. Here it starts out "all hamajang" as we say in Hawaii and quickly turns into clear, neat notation. You can actually see the confidence build in the notation.
You can also see it here in the drawing and notation if you know what you are looking for, as he becomes more comfortable with the concepts and just drawing and counting the sides his pictures and notation get "neater" or "nicer", as I often admonish my students "Write neatly. Neatness counts." And we laugh at how punny that is.
Here is a quick screencast covering the lesson and the concept that the notation is an important clue for you as the teacher. I use these because the example is dramatic and you can't miss it you may find it more subtle with your own children or students.
Find us on FaceBook
Go to Crewton Ramone's House of Math. (Home Page of My Website.)
The point of this point is to draw your attention to the student's notation as a big clue to how well you are doing at getting whatever concept you are teaching across. Here it starts out "all hamajang" as we say in Hawaii and quickly turns into clear, neat notation. You can actually see the confidence build in the notation.
You can also see it here in the drawing and notation if you know what you are looking for, as he becomes more comfortable with the concepts and just drawing and counting the sides his pictures and notation get "neater" or "nicer", as I often admonish my students "Write neatly. Neatness counts." And we laugh at how punny that is.
Here is a quick screencast covering the lesson and the concept that the notation is an important clue for you as the teacher. I use these because the example is dramatic and you can't miss it you may find it more subtle with your own children or students.
Find us on FaceBook
Go to Crewton Ramone's House of Math. (Home Page of My Website.)
Saturday, January 8, 2011
Self Directed Math Enrichment
Well, sort of. When most people think of self directed they think of free schools where the kids do what they want and end up learning very little because for the most part they just goof off.
This is Directed Discovery (one of the concepts I talk about on the Basic Concepts page ), where they get to do what they want within certain guidelines. In this case it was just draw rectangles and count the sides.
There will be a few more links added to this page as time goes by. For now Here are the usual links and the two I talk about in the screencast.
You can find Timez Attack on my multiplication page and this is the blog post where you see him playing it. Pretty cool when his parents have to make him stop playing a game that teaches multiplication...and now it can be used as a reward for good behavior or doing chores or whatever. Learning is fun. He was markedly better at multiplication but still has quite a ways to go as they say. He is also almost completely off his fingers when doing addition, the skills sets he is acquiring will last his entire life. It's also helping in the classroom because math is easier when you can count fast.
There is also the element of increased self confidence and self esteem...because he knows that doing algebra is something "none of my friends can do." Apparently he was showing some of his friends what he does after school on Fridays...
And here is a link to the rules of the card game multiplication facts war I talk about in the video. The woman who wrote this page wrote me an email to complain that I had infringed her copyright by cutting and pasting the rules from her page. There will be a blog post about that later. So I went back and changed my page and reworded the rules and renamed some of the games. I am interested to see if she is claiming she made up these games, I've been playing them for many years...
Find us on FaceBook
Go to the House of Math. (Home Page.)
Let this not apply to you:
“I had, out of my sixty teachers, a scant half dozen who couldn't have been supplanted by phonographs.” ~Don Herold
"Any teacher that can be replaced by a computer should be replaced by a computer"
~Isaac Asimov
This is Directed Discovery (one of the concepts I talk about on the Basic Concepts page ), where they get to do what they want within certain guidelines. In this case it was just draw rectangles and count the sides.
You can find Timez Attack on my multiplication page and this is the blog post where you see him playing it. Pretty cool when his parents have to make him stop playing a game that teaches multiplication...and now it can be used as a reward for good behavior or doing chores or whatever. Learning is fun. He was markedly better at multiplication but still has quite a ways to go as they say. He is also almost completely off his fingers when doing addition, the skills sets he is acquiring will last his entire life. It's also helping in the classroom because math is easier when you can count fast.
There is also the element of increased self confidence and self esteem...because he knows that doing algebra is something "none of my friends can do." Apparently he was showing some of his friends what he does after school on Fridays...
And here is a link to the rules of the card game multiplication facts war I talk about in the video. The woman who wrote this page wrote me an email to complain that I had infringed her copyright by cutting and pasting the rules from her page. There will be a blog post about that later. So I went back and changed my page and reworded the rules and renamed some of the games. I am interested to see if she is claiming she made up these games, I've been playing them for many years...
Find us on FaceBook
Go to the House of Math. (Home Page.)
Let this not apply to you:
“I had, out of my sixty teachers, a scant half dozen who couldn't have been supplanted by phonographs.” ~Don Herold
"Any teacher that can be replaced by a computer should be replaced by a computer"
~Isaac Asimov
Friday, January 7, 2011
Playing Math, Story Problems Fractions and More.
More work with my Autistic student. She was happy to report her school work with fractions was "too easy."
I treat her pretty much like any other kid and use the same basic lessons to provide powerful understanding of math concepts. After the concepts sink in math itself is pretty easy.
It was late when I made this screencast and my verbalization of the story problem in the middle is quite screwed up, lol!! One day will learn how to edit. I left it instead of re-cutting it because even with the verbal errors I think the concept comes through at last, and you can see even if you make a mistake you can still do a lesson. So many parents and teachers never get started for fear of "doing it wrong", some of you may have even gotten it better due to my errors because you thought to yourself "what he's trying to say is..." Anyhow here it is correctly:
If each student got one bottle of water we could give 120 students one bottle each.
If each student got 2 bottles each we could give 60 students 2 bottles each.
If each student got 3 bottles only 40 students would get water, if we gave each student 4 then we could only give 30 students water...when I was doing it with her I was saying correctly and she understood what I meant. In the picture we see 120 broken into 4 groups of 30 each...we could also form a rectangle and count the sides.
Here is a good reason to use rectangles instead of circles or pies when presenting fraction concepts. being able to draw it demonstrates comprehension and moves the student from the concrete to pictures to symbols naturally. For more on what that picture represents and how we develop the concept of equivalent fractions go here.
Find us on FaceBook
Go to Crewton Ramone's House of Math. (Home Page of My Website.)
If you donate a buck you get a password...the password is worth more than a buck...unlocks "advanced algebra" page and soon a screencast channel that will have all manner of instructive scereen casts on topics you can't get anywhere else...the videos on the password pages contain less errata.
“The authority of those who teach is often an obstacle to those who want to learn.” ~
Marcus Tullius Cicero
I treat her pretty much like any other kid and use the same basic lessons to provide powerful understanding of math concepts. After the concepts sink in math itself is pretty easy.
It was late when I made this screencast and my verbalization of the story problem in the middle is quite screwed up, lol!! One day will learn how to edit. I left it instead of re-cutting it because even with the verbal errors I think the concept comes through at last, and you can see even if you make a mistake you can still do a lesson. So many parents and teachers never get started for fear of "doing it wrong", some of you may have even gotten it better due to my errors because you thought to yourself "what he's trying to say is..." Anyhow here it is correctly:
If each student got one bottle of water we could give 120 students one bottle each.
If each student got 2 bottles each we could give 60 students 2 bottles each.
If each student got 3 bottles only 40 students would get water, if we gave each student 4 then we could only give 30 students water...when I was doing it with her I was saying correctly and she understood what I meant. In the picture we see 120 broken into 4 groups of 30 each...we could also form a rectangle and count the sides.
Find us on FaceBook
Go to Crewton Ramone's House of Math. (Home Page of My Website.)
If you donate a buck you get a password...the password is worth more than a buck...unlocks "advanced algebra" page and soon a screencast channel that will have all manner of instructive scereen casts on topics you can't get anywhere else...the videos on the password pages contain less errata.
“The authority of those who teach is often an obstacle to those who want to learn.” ~
Marcus Tullius Cicero
Wednesday, January 5, 2011
Tie It Together With 3rd Power Algebra
A session with a 7 year old boy and an 8 year old girl where we play math and have fun.
Surprisingly, there were a few tears on the part of the boy when he got an answer wrong while we did 3rd power algebra but as per usual with kids this age he was laughing and having fun a few minutes later as he easily saw what to do to get the right answer...I cheered him up with 3rd power algebra! Try that in high schools across America. Big difference when you can see what you are doing.
Here is a quick sketch of a "big" problem.
(2x3 + 9x2 + 16x + 12) ÷ (2x2 + 5x + 6)
Tears over math is a silly thing especially when you can see the answers. Mostly we played games drew pictures...and learned a lot of math concepts along the way.
Find us on FaceBook
Go to the House of Math. (Home Page.)
“You can get help from teachers, but you are going to have to learn a lot by yourself, sitting alone in a room.” ~Theodore Seuss Geisel 'Doctor Seuss'
Surprisingly, there were a few tears on the part of the boy when he got an answer wrong while we did 3rd power algebra but as per usual with kids this age he was laughing and having fun a few minutes later as he easily saw what to do to get the right answer...I cheered him up with 3rd power algebra! Try that in high schools across America. Big difference when you can see what you are doing.
(2x3 + 9x2 + 16x + 12) ÷ (2x2 + 5x + 6)
Tears over math is a silly thing especially when you can see the answers. Mostly we played games drew pictures...and learned a lot of math concepts along the way.
Find us on FaceBook
Go to the House of Math. (Home Page.)
“You can get help from teachers, but you are going to have to learn a lot by yourself, sitting alone in a room.” ~Theodore Seuss Geisel 'Doctor Seuss'
Moving Towards Mastery
Here is another enrichment session with a 6th grader That flew by.
"It felt like 5 minutes..."
That's when you know you are doing it right. Learning is fun and time flies when you are having fun.
First we looked over the left over lesson from the 4 and 5 year old and talked about equivalent fractions.
Then we wrote out a few equivalent fractions all the way to 12...1/2, 1/3, 1/4, 3/4, 5/7's...later will do other combinations.
Then we built all 45 addends. He tried to stand them up and goofed around a bit while he made them. I encourage this. Then we did "drills" verbally what's 7 + 5, what's 37 + 5, what's 25 + 7, what's 97 + 5? etc...did lots of them for various addends the idea is to get him off his fingers. Using your fingers is great! But you need to get past that stage if you are going to be fast and attain mastery.
Using fingers is a step on the way to mastery, unfortunately many students remain stuck at this step all the way into adulthood. For kinesthetic learners using fingers and hands IS IMPORTANT, that's HOW they learn, and you need to help them move past this, manipulatives are a great way to move them into "doing it their heads." For young students using fingers and hands is just natural...you can also spot the kinesthetic learners because they will rely more on their fingers and be slower to move on. This does not mean they are slow or any less able then visual or auditory learners, they grasp concepts just as fast or faster than those with other learning styles. We also find when it comes to sports and other activities requiring hand eye coordination (like arts and crafts) they often excel.
Many speed reading courses incorporate the use of the finger to guide the eye along the page, some use this to start, and then drop it for other courses this is the main stay of the course. Adding more sensory input increases learning, and in the case of reading the hand and the eye are integrally connected. The point is you want to encourage students to move through this step when it comes to the mathematics NOT discourage or skip the step all together. Some students will naturally NOT use their fingers when doing mental calculations...
After addends we played cards. Not poker, but war. We played multiplication facts war where we each put down two cards and multiplied them together; as an added bonus we couldn't start another round until he told me the difference between our scores. It was fun although I beat him.
Then because he had behaved will wrote neatly and did all the work I asked him without a single complaint I let him play Timez Attack for about 10 minutes...he really had fun with it and when it was time for class to be over he wasn't ready to leave...
"Always leave them wanting more..." as some famous circus guy once said...
Find us on FaceBook
Go to the House of Math. (Home Page.)
“If I am walking with two other men, each of them will serve as my teacher. I will pick out the good points of the one and imitate them, and the bad points of the other and correct them in myself.” ~Kung Fu-tzu Confucius
"It felt like 5 minutes..."
That's when you know you are doing it right. Learning is fun and time flies when you are having fun.
First we looked over the left over lesson from the 4 and 5 year old and talked about equivalent fractions.
Then we wrote out a few equivalent fractions all the way to 12...1/2, 1/3, 1/4, 3/4, 5/7's...later will do other combinations.
Then we built all 45 addends. He tried to stand them up and goofed around a bit while he made them. I encourage this. Then we did "drills" verbally what's 7 + 5, what's 37 + 5, what's 25 + 7, what's 97 + 5? etc...did lots of them for various addends the idea is to get him off his fingers. Using your fingers is great! But you need to get past that stage if you are going to be fast and attain mastery.
Using fingers is a step on the way to mastery, unfortunately many students remain stuck at this step all the way into adulthood. For kinesthetic learners using fingers and hands IS IMPORTANT, that's HOW they learn, and you need to help them move past this, manipulatives are a great way to move them into "doing it their heads." For young students using fingers and hands is just natural...you can also spot the kinesthetic learners because they will rely more on their fingers and be slower to move on. This does not mean they are slow or any less able then visual or auditory learners, they grasp concepts just as fast or faster than those with other learning styles. We also find when it comes to sports and other activities requiring hand eye coordination (like arts and crafts) they often excel.
Many speed reading courses incorporate the use of the finger to guide the eye along the page, some use this to start, and then drop it for other courses this is the main stay of the course. Adding more sensory input increases learning, and in the case of reading the hand and the eye are integrally connected. The point is you want to encourage students to move through this step when it comes to the mathematics NOT discourage or skip the step all together. Some students will naturally NOT use their fingers when doing mental calculations...
After addends we played cards. Not poker, but war. We played multiplication facts war where we each put down two cards and multiplied them together; as an added bonus we couldn't start another round until he told me the difference between our scores. It was fun although I beat him.
Then because he had behaved will wrote neatly and did all the work I asked him without a single complaint I let him play Timez Attack for about 10 minutes...he really had fun with it and when it was time for class to be over he wasn't ready to leave...
"Always leave them wanting more..." as some famous circus guy once said...
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“If I am walking with two other men, each of them will serve as my teacher. I will pick out the good points of the one and imitate them, and the bad points of the other and correct them in myself.” ~Kung Fu-tzu Confucius
Monday, January 3, 2011
Equivalent Fractions With The Wee Ones
Equivalent Fractions teaches multiplication. It all goes together so while they learn fractions concepts they learn multiplication or in this case they get to practice it...but when we get to the higher numbers they'll be learning the higher multiplication tables.
It's easy to see that 1/3rd and 6/18ths are the same. They can see it.
People often ask the ridiculous question: "Do they need to have the blocks with them to do math?"
The other night without blocks or even symbols just verbally I asked him what the factors of x2 + 3x + 2 where and he looked up for a moment and said X plus one and X plus 2...then before naps today I asked him, "if the sides are x plus 2 and x plus 3 what's the whole thing?"
He thought out loud and said, "one x square, three and two...five x's and four...no I mean six...six would fit in there cuz it's three and two."
No blocks or symbols. It's the same when you teach any language to babies: they hear it FIRST before they ever see an ABC...just because they can't write symbols doesn't mean they can't learn math.
Further the average student can't multiply 15 x 17 in their heads...because they need to have the symbols and a pencil and something to write on. My students can see the answer is 255 or at worst can add 100, 120 and 35...
Here in this video they have seen this a couple of times before without symbols and for the first time they see the symbols for fractions today, and the symbols make sense and are easy to comprehend because they have heard them before.
You can see their progress with multiplication if you have been following this blog...they still can't tell you 4 x 5 off the top of their heads but give them a little time and they can figure it out...and the more we learn fractions the better they'll get.
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“Men must be taught as if you taught them not, And things unknown proposed as things forgot.” ~Alexander Pope
Sunday, January 2, 2011
What square root means...
Using playdoh to get a feel for square numbers.
Square root means make a square and count one side...but how do you make a square with a two or a three? Playdoh to the rescue.
Use the blocks to help students use their imagination...they can see what the numbers and symbols mean.
Here is another short vid on square numbers...and here is a whole lot more on square numbers at CRHOM.
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Go to the House of Math. (Home Page.)
“The point is to develop the childlike inclination for play and the childlike desire for recognition and to guide the child over to important fields for society. Such a school demands from the teacher that he be a kind of artist in his province.”
~Albert Einstein
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