[Source: Misconception Junction]
Thursday, September 30, 2010
Monday, September 27, 2010
Algebraic Story Problems Simplified
Applying The 5 Basic Concepts to algebra and algebraic story problems. Increasing problem solving skills by using concept based teaching, not algorithms which become meaningless and are easily forgotten.
Again although it is presented with clarity that makes it child's play, the student was a teenager in his junior year of highschool...you can easily see how 7 and 8 year olds on down to 5 and 6 year olds can do these kinds of problems if given enough time and examples to play with...
"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970
"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956
"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003
"People tend to forget that play is serious." ~David Hockney Contemporary British painter
"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE
"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru
Crewton Ramone's House of Math
Again although it is presented with clarity that makes it child's play, the student was a teenager in his junior year of highschool...you can easily see how 7 and 8 year olds on down to 5 and 6 year olds can do these kinds of problems if given enough time and examples to play with...
"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970
"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956
"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003
"People tend to forget that play is serious." ~David Hockney Contemporary British painter
"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE
"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru
Crewton Ramone's House of Math
Saturday, September 25, 2010
Crewton Ramone Does Algebra With 4 and 5 Year Olds.
This was a short fun little lesson with two young boys...and part way through I remembered to take out a camera.
The younger boy did not want to participate in the screencast but then he watched the finished version and had to prove to me it wouldn't take him a week and a half to count all those three's. First he counted by threes as far as he could which was 18. Then he went back and started counting by ones and lost count at 24...and ended up with 28 instead of 27...and then the third time he got it right. (The next day we were in the car skip counting and he skip counted by 2's, 3's, 4's and 5's all the way to 12.)
Now as you can see algebra is not out of reach of the mind of a young child if you present it at their level. Here is basically a lesson on counting and skip counting and the algebra is just along for the ride...
You can also see the kid is being a brat, when I ask what's 2x plus one x and he says butt x...owee x...but he recants at the end of the vid.
Here is a video of an actual session about a week later:
Be sure to share links to these vids with people you know who ave base ten blocks, especially from Math U See and Mortensen Math. Also Homeschoolers should be able to see how easy putting algebra into beginning lessons is...
Look over the website and this blog and you can see algebra is an integral part of the method and it's easy and fun.
Crewton Ramone's House Of Math.
The younger boy did not want to participate in the screencast but then he watched the finished version and had to prove to me it wouldn't take him a week and a half to count all those three's. First he counted by threes as far as he could which was 18. Then he went back and started counting by ones and lost count at 24...and ended up with 28 instead of 27...and then the third time he got it right. (The next day we were in the car skip counting and he skip counted by 2's, 3's, 4's and 5's all the way to 12.)
Now as you can see algebra is not out of reach of the mind of a young child if you present it at their level. Here is basically a lesson on counting and skip counting and the algebra is just along for the ride...
You can also see the kid is being a brat, when I ask what's 2x plus one x and he says butt x...owee x...but he recants at the end of the vid.
Here is a video of an actual session about a week later:
Be sure to share links to these vids with people you know who ave base ten blocks, especially from Math U See and Mortensen Math. Also Homeschoolers should be able to see how easy putting algebra into beginning lessons is...
Look over the website and this blog and you can see algebra is an integral part of the method and it's easy and fun.
Incorporate Algebra Immediately
Using Algebra To Teach Multiplication.
Crewton Ramone's House Of Math.
Monday, September 20, 2010
Y More Algebra
Yet another set of screencasts condensing an hour of tutoring into 5 minutes or so. Eventually I will go back and make some short videos or web pages that detail the specific concepts required to do the work, and how to teach those concepts to even very young children, however if you look around on this blog and at Crewton Ramone's House of Math most of what's here is already covered. I think by now the myth is dispelled that this is just for little kids...
Here is a set of three screencasts with another student on Algebra...about 13 and a half minutes worth, some may want to skip the nuts and bolts and just go to the third one where I talk about basic concepts:
Here is a set of three screencasts with another student on Algebra...about 13 and a half minutes worth, some may want to skip the nuts and bolts and just go to the third one where I talk about basic concepts:
Statistics
If more people understood statistics (and how they can be manipulated to make you think one ting when the data shows another) the government would have a much harder time fooling the people some of the time...
Happily they have done so much lying people are starting not to believe the government any of the time...which is just as bad. You should be able to tell the difference...using the mathematics as a guide.
Anyhow, here is a quick explanation of The Empirical Rule since I am on a kick where I show people I don't just do math for little kids...
A FB friend was embarrassed to ask me for further explanation because apparently she wasn't getting from here community college. My response:
No need to be embarrassed at all. That's what I'm here for...in fact please let some MCC students who are in college algebra like Math 23 know I exist. I hear many are failing Math 23: that's sick and wrong.
Anyhow:
The Empirical Rule says that if you go 1 standard deviation out from the mean that you will capture 68 % of your data. Go out one more standard deviation (thats 2 so far) and you will capture 95% of your data, go out one more standard deviation (thats 3 so far) and you will capture 99.7% of your data. That's it.
Ok, so what the heck does all of that mean?
Lets try a simple problem.
You ask a bunch of young children how many gifts they got for Xmas. Lets say that the average (mean) answer is 10 gifts. The standard deviation is 3. This means that you start at 10 and go one standard deviation in both directions (one out each way 1 "up" an 1 "down"). 1 standard deviation from the mean in both directions will give you 7 and 13. (10 + 3 and 10 - 3)
Why? Because the mean is 10 and the standard deviation is 3 and three above the mean is 13 and 3 below the mean is 7.
Thus, out of all the kids that we asked this question to, 68% of them answered that they received 7 to 13 gifts.
How do we know this? Because 1 standard deviation away (remember you have to go in BOTH directions) will capture 68% of the data.
1 standard deviation away captures 68% of the data.
Now, lets go 2 standard deviations away. If the mean is 10 and the standard deviation is 3, then 2 standard deviations away from the mean would be 4 and 16. (10 - 6 and 10 + 6 (and 6 = 3x2 the amount of the stan dev is 3 and the number of them is 2))
Since you went 2 standard deviations away from the mean you have captured 95% of your data.
That means that out of all those kids you asked, 95% of them said that they received between 4 and 16 gifts...statistically speaking.
Now lets go three standard deviations out. Remember this, the empirical rule is also called the 68-95-99.7 rule because it gives you that info every time.
Remember that: 68-95-99.7, a really fat pear shaped woman.
Go three standard deviations out from the mean and you get 1 and 19.
(10 - 9 and 10 + 9 which is just plus or minus 3 x 3).
3 standard deviations captures 99.7% of the data.
NOW, this means that out of all those kids you asked 99.7% of them said that they received from 1 to 19 gifts. The poor little kid who only got one present or maybe they were naughty and the fat rich spoiled little kid who got 19 presents are all in there. Now there may have been some kids who got ZERO and some who got 20 or more BUT The Empirical Rule says we get 99.7 which is almost all but not all but not all of them.
Can we go out another standard deviation, that is 4 standard deviations from the mean? In a world were we can have negative gifts we can...
Now what would happen if the standard deviation was only 2?
Get it? If not I am available at 6 or a little after and I charge 40 bucks an hour...if you would like FREE tutoring find me some parents who have kids and whom want math enrichment for them, every two classes they pay for you get a class FREE.
Also I'll give you a class for 30 bucks as an introductory offer...if you come here and if you promise to tell a few people who have young kids to come see me BEFORE they start having trouble with math...
A TI-83 calculator from Texas Instruments will do ALL of the work for you I am told but I don't know how to use one...
Copy a problem that's giving you a problem here for me to see...the video is dry and boring but the info is there...put "The Empirical Rule" into a Youtube search...
Happily they have done so much lying people are starting not to believe the government any of the time...which is just as bad. You should be able to tell the difference...using the mathematics as a guide.
Anyhow, here is a quick explanation of The Empirical Rule since I am on a kick where I show people I don't just do math for little kids...
A FB friend was embarrassed to ask me for further explanation because apparently she wasn't getting from here community college. My response:
No need to be embarrassed at all. That's what I'm here for...in fact please let some MCC students who are in college algebra like Math 23 know I exist. I hear many are failing Math 23: that's sick and wrong.
Anyhow:
The Empirical Rule says that if you go 1 standard deviation out from the mean that you will capture 68 % of your data. Go out one more standard deviation (thats 2 so far) and you will capture 95% of your data, go out one more standard deviation (thats 3 so far) and you will capture 99.7% of your data. That's it.
Ok, so what the heck does all of that mean?
Lets try a simple problem.
You ask a bunch of young children how many gifts they got for Xmas. Lets say that the average (mean) answer is 10 gifts. The standard deviation is 3. This means that you start at 10 and go one standard deviation in both directions (one out each way 1 "up" an 1 "down"). 1 standard deviation from the mean in both directions will give you 7 and 13. (10 + 3 and 10 - 3)
Why? Because the mean is 10 and the standard deviation is 3 and three above the mean is 13 and 3 below the mean is 7.
Thus, out of all the kids that we asked this question to, 68% of them answered that they received 7 to 13 gifts.
How do we know this? Because 1 standard deviation away (remember you have to go in BOTH directions) will capture 68% of the data.
1 standard deviation away captures 68% of the data.
Now, lets go 2 standard deviations away. If the mean is 10 and the standard deviation is 3, then 2 standard deviations away from the mean would be 4 and 16. (10 - 6 and 10 + 6 (and 6 = 3x2 the amount of the stan dev is 3 and the number of them is 2))
Since you went 2 standard deviations away from the mean you have captured 95% of your data.
That means that out of all those kids you asked, 95% of them said that they received between 4 and 16 gifts...statistically speaking.
Now lets go three standard deviations out. Remember this, the empirical rule is also called the 68-95-99.7 rule because it gives you that info every time.
Remember that: 68-95-99.7, a really fat pear shaped woman.
Go three standard deviations out from the mean and you get 1 and 19.
(10 - 9 and 10 + 9 which is just plus or minus 3 x 3).
3 standard deviations captures 99.7% of the data.
NOW, this means that out of all those kids you asked 99.7% of them said that they received from 1 to 19 gifts. The poor little kid who only got one present or maybe they were naughty and the fat rich spoiled little kid who got 19 presents are all in there. Now there may have been some kids who got ZERO and some who got 20 or more BUT The Empirical Rule says we get 99.7 which is almost all but not all but not all of them.
Can we go out another standard deviation, that is 4 standard deviations from the mean? In a world were we can have negative gifts we can...
Now what would happen if the standard deviation was only 2?
Get it? If not I am available at 6 or a little after and I charge 40 bucks an hour...if you would like FREE tutoring find me some parents who have kids and whom want math enrichment for them, every two classes they pay for you get a class FREE.
Also I'll give you a class for 30 bucks as an introductory offer...if you come here and if you promise to tell a few people who have young kids to come see me BEFORE they start having trouble with math...
A TI-83 calculator from Texas Instruments will do ALL of the work for you I am told but I don't know how to use one...
Copy a problem that's giving you a problem here for me to see...the video is dry and boring but the info is there...put "The Empirical Rule" into a Youtube search...
Sunday, September 19, 2010
After Math
Playing with electricity and math manipulatives. The culprits get in on the screencast and tell you a little about what went on in their own words.
What was once a bustling and busy math town with lots of buildings and trucks is reduced to rubble by Rooster and Cheetah-boy.
Evidence of a good time.
See other posts here on this blog about making it fun and pages over at Crewton Ramone's House of Math about how they learn addition, subtraction and multiplication from this. When you are at the house of math be sure to click on the pictures too...they take you places.
Absolutely recommended:
The 4 year old begged me to play with this from the moment he got up in the morning...the one we have is the Elenco Snap Circuits SC-500.
Evidence of a good time.
See other posts here on this blog about making it fun and pages over at Crewton Ramone's House of Math about how they learn addition, subtraction and multiplication from this. When you are at the house of math be sure to click on the pictures too...they take you places.
Absolutely recommended:
The 4 year old begged me to play with this from the moment he got up in the morning...the one we have is the Elenco Snap Circuits SC-500.
Combine-ing Tutorial
Keep simple addition simple...
Give your students an algorithm to solve problems that makes sense to them. Remember "no concept is beyond the grasp of a child, if it is presented at the child's level." When adding single digits that add up to more than ten break it down into small steps of addition rather than long counting...we will do the same with subtraction and multiplication too. But lets not get ahead of ourselves.
For example,
8+7 = __
For a very small child and even some older students this is daunting because you run out of fingers and you can lose your place. You need two hands to represent 8 AND 7... unlike adding numbers 5 or less. Most students will not have this "memorized" although at Crewton Ramone's House of Math this will come naturally because we will build quite a few 15's, (AFTER we are quite comfortable building 9's and 10's) and soon the answer to 8+7 is as easy as 2+2.
Meantime we ask a bunch of simple questions:
What does 8 want to be? (All the single digits want to be a ten.)
8 wants to be 10.
What does 8 need to be 10?
2! (We have built 10 over and over again so this is easy.)
Is there a 2 in 7? (Of course, remember seven was having a party).
So the 8 takes the 2 out of 7 so it can be 10 and what's left?
5...so we have a 10 and a 5, what's that called?
15.
8+7 = 15.
As an aside, do you see where the "equals sign" comes from?
Fingers are good, this is better and faster. We want to get them off their fingers and into their heads, but they need to know what steps to take. You should also tell a story to add meaning.
If I have 8 kids in the classroom and 7 more kids come in how many kids do I have?
Don't stop there.
I also ask ta few more:
I'm building a 15 and I have 8 what do I need? (8+X=15).
I'm building a 15 and I have 7 what do I need? (7+X=15).
I have 8 chairs in my classroom but there are goning to be 15 kids coming how many more chairs do I need? (8+X=15).
I have 7 chairs in my classroom but there are goning to be 15 kids coming how many more chairs do I need? (7+X=15).
If I have 15 kids and 8 are boys how many are hermaphradites?
Just kidding.
Next step subtraction which is just small addition.
If I have 15 kids and 8 go to recess how many are left? ( 15-8=X )
If I have 15 kids and 7 go to recess how many are left? ( 15-7=X )
Need GIF
You can start to see that addition and subtraction really are inverse functions.
Note we take the number out of the ten! Not the five and the ten...in other words we don't "use up" the five and then take three more out of the ten for 15-8=X the 8 comes out of the 10. HUGELY IMPORTANT.
They should be able to see this after they have just done the addition but what if they come upon one of these problems all by themselves?:
15
-8
or
15
-7
But again just ask simple questions:
Can I take 8 out of 5?
No.
Where must I take it from?
The 10.
And what's left 2.
so 2 and 5 is 7.
Or faster...
Can I take 8 out of 5?
No.
What does 8 want to be?
10.
8 needs 2 to be 10 so lets just add 2 and 5 to get 7.
Skipped some steps there which confuses everybody and anybody who doesn't know all the steps. Kinda like how they teach algebra in regular skool.
Even faster. 15-7...
Do I have enough? (in the "ones place")
No.
Add 3 to 5 to get 8.
Done.
Look, it's this easy:
Need step where I show 3 all by itself...
I tell the students "this is why we love math because the answers are always the same. They don't change. Later when we add 28+7, 35 is EASY. Or 78+7, 85 is easy...pretty soon we can add any two numbers together...but this is step one. Then we can fool around with 80+70...but that's another story.
Give your students an algorithm to solve problems that makes sense to them. Remember "no concept is beyond the grasp of a child, if it is presented at the child's level." When adding single digits that add up to more than ten break it down into small steps of addition rather than long counting...we will do the same with subtraction and multiplication too. But lets not get ahead of ourselves.
For example,
8+7 = __
For a very small child and even some older students this is daunting because you run out of fingers and you can lose your place. You need two hands to represent 8 AND 7... unlike adding numbers 5 or less. Most students will not have this "memorized" although at Crewton Ramone's House of Math this will come naturally because we will build quite a few 15's, (AFTER we are quite comfortable building 9's and 10's) and soon the answer to 8+7 is as easy as 2+2.
Meantime we ask a bunch of simple questions:
What does 8 want to be? (All the single digits want to be a ten.)
8 wants to be 10.
What does 8 need to be 10?
2! (We have built 10 over and over again so this is easy.)
Is there a 2 in 7? (Of course, remember seven was having a party).
So the 8 takes the 2 out of 7 so it can be 10 and what's left?
5...so we have a 10 and a 5, what's that called?
15.
8+7 = 15.
As an aside, do you see where the "equals sign" comes from?
Fingers are good, this is better and faster. We want to get them off their fingers and into their heads, but they need to know what steps to take. You should also tell a story to add meaning.
If I have 8 kids in the classroom and 7 more kids come in how many kids do I have?
Don't stop there.
I also ask ta few more:
I'm building a 15 and I have 8 what do I need? (8+X=15).
I'm building a 15 and I have 7 what do I need? (7+X=15).
I have 8 chairs in my classroom but there are goning to be 15 kids coming how many more chairs do I need? (8+X=15).
I have 7 chairs in my classroom but there are goning to be 15 kids coming how many more chairs do I need? (7+X=15).
If I have 15 kids and 8 are boys how many are hermaphradites?
Just kidding.
Next step subtraction which is just small addition.
If I have 15 kids and 8 go to recess how many are left? ( 15-8=X )
If I have 15 kids and 7 go to recess how many are left? ( 15-7=X )
Need GIF
You can start to see that addition and subtraction really are inverse functions.
Note we take the number out of the ten! Not the five and the ten...in other words we don't "use up" the five and then take three more out of the ten for 15-8=X the 8 comes out of the 10. HUGELY IMPORTANT.
They should be able to see this after they have just done the addition but what if they come upon one of these problems all by themselves?:
15
-8
or
15
-7
But again just ask simple questions:
Can I take 8 out of 5?
No.
Where must I take it from?
The 10.
And what's left 2.
so 2 and 5 is 7.
Or faster...
Can I take 8 out of 5?
No.
What does 8 want to be?
10.
8 needs 2 to be 10 so lets just add 2 and 5 to get 7.
Skipped some steps there which confuses everybody and anybody who doesn't know all the steps. Kinda like how they teach algebra in regular skool.
Even faster. 15-7...
Do I have enough? (in the "ones place")
No.
Add 3 to 5 to get 8.
Done.
Look, it's this easy:
Need step where I show 3 all by itself...I tell the students "this is why we love math because the answers are always the same. They don't change. Later when we add 28+7, 35 is EASY. Or 78+7, 85 is easy...pretty soon we can add any two numbers together...but this is step one. Then we can fool around with 80+70...but that's another story.
Saturday, September 18, 2010
Free Math Software: Addends.
Here is a two and a half minute screencast about the addends software. If you download it for use on your PC or Mac you may need the plug in but everything you need is there, it will tell you you need it, if you need it and give you a link and simple instructions...
If you have young students or preschoolers let them play with this.
You can go to the iTunes store and download it or you can go get Crewton Ramone's Absolutely Amazing Addends here.
Put it on your iPhone or play it on your iPod Touch, Mac or PC, soon it will work on iPad too but we need to make some upgrades in especially the graphics which make my kids laff but need to be more "professional" this is aimed at ages 3 to 7, of course older kids can use it but it really is made for the wee ones.
As I was making this post a boy who is just a week away from 4 came in and asked me if he could play...and I had to send him off to watch The Aristocats so I could finish.
It should hold their attention for a few minutes a day until they have mastered the addends for 9 and 10. My three and five year old enjoy it...need to get some video of them playing with an actual iPhone or iTouch and put it here. It's fun. Simple, silly, fun.
Here are actual children playing with it: (Their names have been changed to protect the innocent).
Take it away and let them play again another day...always keep them wanting more. Don't let them goof around with it until they are bored, especially now when it only has a few features...
More on addends here and here. Basic addition lessons here. Article on the importance of addends here.
If you have young students or preschoolers let them play with this.
You can go to the iTunes store and download it or you can go get Crewton Ramone's Absolutely Amazing Addends here.
Put it on your iPhone or play it on your iPod Touch, Mac or PC, soon it will work on iPad too but we need to make some upgrades in especially the graphics which make my kids laff but need to be more "professional" this is aimed at ages 3 to 7, of course older kids can use it but it really is made for the wee ones.
As I was making this post a boy who is just a week away from 4 came in and asked me if he could play...and I had to send him off to watch The Aristocats so I could finish.
It should hold their attention for a few minutes a day until they have mastered the addends for 9 and 10. My three and five year old enjoy it...need to get some video of them playing with an actual iPhone or iTouch and put it here. It's fun. Simple, silly, fun.
Here are actual children playing with it: (Their names have been changed to protect the innocent).
Take it away and let them play again another day...always keep them wanting more. Don't let them goof around with it until they are bored, especially now when it only has a few features...
More on addends here and here. Basic addition lessons here. Article on the importance of addends here.
Thursday, September 16, 2010
2 Hours in 10 Minutes...
Some times it feels like 10 minutes and two hours fly by.
Really.
Here are two 5 minute screencasts covering a two hour session with a student who is 11...his friend did not show up so it wasn't quite as much fun and we did not go as fast because as he said, "it's no fair trying to beat you, you already know all this stuff."
We did cover a lot of ground though. We had fun and two hours do go by FAST.
Here is the YouTube video on Cross Multiplication I talk about, and here is another follow up video on Cross Multiplication.
And here are links to my square numbers page and problem solving page.
If you see my add on Face Book (those who live on Maui) don't be afraid to click "like" or click through to my webpage...I am not paying per click but per thousand impressions...I did the math, PPC did not make any sense at all.
Really.
Here are two 5 minute screencasts covering a two hour session with a student who is 11...his friend did not show up so it wasn't quite as much fun and we did not go as fast because as he said, "it's no fair trying to beat you, you already know all this stuff."
We did cover a lot of ground though. We had fun and two hours do go by FAST.
Here is the YouTube video on Cross Multiplication I talk about, and here is another follow up video on Cross Multiplication.
And here are links to my square numbers page and problem solving page.
If you see my add on Face Book (those who live on Maui) don't be afraid to click "like" or click through to my webpage...I am not paying per click but per thousand impressions...I did the math, PPC did not make any sense at all.
Using Algebra To Teach Multiplication.
Here is a quick screencast about actually using algebra to teach multiplication (and basic operations like addition and subtraction) with base ten manipulatives and the Mortensen Math Method. Using a three period lesson and other basic concepts are covered at The House Of Math just click the basic concepts tab.
There are several things I didn't say in the screencast, that I will add here with regard to economy of counting and economy of symbol. With
x2 + x + 16
We talked about how much easier it was to use 4's than all the little units, and we later talked about how much easier it was to write 20 instead of draw 20 little dots and we also talked about how much faster it was to write
(x + 4)2 than (x + 4)(x + 4)...
You can actually see he wrote it that way on his paper, but above he left off the exponent when he re-wrote
(x + 2)(x+2) = (x + 2) I saw that right after he finished the page and handed it to me to look over. We talked about how important the "2" is in
(x + 2)2
And what it meant again.
For more on Problem Solving and Hero Zero go here, there's a Youtube video at leaste and little more explanation. The page still needs more work, but the video should help. I have been getting email where people ask me for more pages and screencasts and videos on certain topics but oddly enough nobody wants to donate so much as a cup of coffee...note the donate button conveniently located over there to your right....
Also be sure to find me on Face Book. I also am working diligently believe it or not to get some webcasts together for FREE, on the way to doing training via the WWW for an extremely reasonable fee. That way some of you in far flung places like Iran, Singapore, Kenya and Russia to name a few can get training...not to mention all you folks on Oahu and "the Mainland" as we like to say here in Hawaii.
Use one of the contact forms on my website.
x2 + x + 16
We talked about how much easier it was to use 4's than all the little units, and we later talked about how much easier it was to write 20 instead of draw 20 little dots and we also talked about how much faster it was to write
(x + 4)2 than (x + 4)(x + 4)...
You can actually see he wrote it that way on his paper, but above he left off the exponent when he re-wrote
(x + 2)(x+2) = (x + 2) I saw that right after he finished the page and handed it to me to look over. We talked about how important the "2" is in
(x + 2)2
And what it meant again.
For more on Problem Solving and Hero Zero go here, there's a Youtube video at leaste and little more explanation. The page still needs more work, but the video should help. I have been getting email where people ask me for more pages and screencasts and videos on certain topics but oddly enough nobody wants to donate so much as a cup of coffee...note the donate button conveniently located over there to your right....
Also be sure to find me on Face Book. I also am working diligently believe it or not to get some webcasts together for FREE, on the way to doing training via the WWW for an extremely reasonable fee. That way some of you in far flung places like Iran, Singapore, Kenya and Russia to name a few can get training...not to mention all you folks on Oahu and "the Mainland" as we like to say here in Hawaii.
Use one of the contact forms on my website.
Tuesday, September 14, 2010
Precalculus is childs play...
I spend so much time with the little kids people think we don't do "higher math" at Crewton Ramone's House of Math....
Boils down to simple concepts...applied.
Here is a problem at random that we worked on:
I am inhibited by the fact that I only have 5 minutes to screencast, or 10 minutes on yourtube...here is a problem solving page that shows the exact same CONCEPTS we used to do this pre-calc problem.
Okay, now I must do a page to go along with square numbers about Pythagorean Theorem, because this student did not do so well when it came to "Distance Formula" and finding the mid-point of the line. Distance Formula in 5 minutes or less...
Now once you have watched that, finding the midpoint of the line problems are also EASY:
Here is another problem from the session my job is making it easy and understandable:
One thing I left out of the screencast was the drawing of the graph, which is kind of crucial for understanding...otherwise it's just some symbols. Those symbols describe a graph...and I made him draw it out so the answer makes MORE sense.
One more very easy problem solving question and that's it for this blog post. I want to do webinars to teach homeschoolers and teachers how to get from the so called "simple math" to the more "complex math" or "harder higher math".
With reading, watching vids and screencasts this post should take you about half an hour to 45 min...but it should show you where it is we are going with the foundations set up for preschoolers and kindergartners with concept based manipulative teaching. I will come back and add more later so you may want to come back and see if I've added updates.
Many of the students that were taught with this method as youngsters go on to ace the "higher math"...and understand it. This post should help you see why.
Get it? "Y"!!! OMG I'm the funniest MF you know.
Boils down to simple concepts...applied.
Here is a problem at random that we worked on:
I am inhibited by the fact that I only have 5 minutes to screencast, or 10 minutes on yourtube...here is a problem solving page that shows the exact same CONCEPTS we used to do this pre-calc problem.
Okay, now I must do a page to go along with square numbers about Pythagorean Theorem, because this student did not do so well when it came to "Distance Formula" and finding the mid-point of the line. Distance Formula in 5 minutes or less...
Now once you have watched that, finding the midpoint of the line problems are also EASY:
Here is another problem from the session my job is making it easy and understandable:
One thing I left out of the screencast was the drawing of the graph, which is kind of crucial for understanding...otherwise it's just some symbols. Those symbols describe a graph...and I made him draw it out so the answer makes MORE sense.
One more very easy problem solving question and that's it for this blog post. I want to do webinars to teach homeschoolers and teachers how to get from the so called "simple math" to the more "complex math" or "harder higher math".
With reading, watching vids and screencasts this post should take you about half an hour to 45 min...but it should show you where it is we are going with the foundations set up for preschoolers and kindergartners with concept based manipulative teaching. I will come back and add more later so you may want to come back and see if I've added updates.
Many of the students that were taught with this method as youngsters go on to ace the "higher math"...and understand it. This post should help you see why.
Get it? "Y"!!! OMG I'm the funniest MF you know.
Monday, September 13, 2010
Math With The Wee Ones
Stop me before I screencast again!
Math concepts like multiplication made easy for pre-scoolers...
Crewton Ramone's House Of Math.
I am currently searching for math enrichment students...if you know of any. I would also like to put together some webinars so I can teach others to teach this way...
Math concepts like multiplication made easy for pre-scoolers...
Crewton Ramone's House Of Math.
I am currently searching for math enrichment students...if you know of any. I would also like to put together some webinars so I can teach others to teach this way...
First Lame Attempt...this post may disappear.
Got a long way to go but I'm starting to see how to do it.
Note I didn't use blocks at all just symbols (so it's kind of a joke) of course nobody gets inside jokes with yourself...this would be HOW NOT TO TRY AND TEACH IT. They can't see what they are doing...
But with a little imagination and a lot more editing you could see the blocks dancing around. The ultimate goal is Math Music vids that kids will actually watch and learn from...kids sing along and dance around every time I play that music...then a kids show that teaches math...like Bill Nye the Science Guy meets Pee-Wee Herman meets Monty Python in a Good Eats-esque, Between the Lions modern Mathematical Electric Company joy ride... from watching this you won't get that but some people might get an idea of where I want to go...with a ton more editing and pictures and video...
http://screencast.com/t/OTdkNjc0MmE
"Music is the pleasure the human mind experiences from counting without being aware that it is counting." ~Gottfried Leibniz
More at crewton ramones house of math!
Find me on Face Book.
Note I didn't use blocks at all just symbols (so it's kind of a joke) of course nobody gets inside jokes with yourself...this would be HOW NOT TO TRY AND TEACH IT. They can't see what they are doing...
But with a little imagination and a lot more editing you could see the blocks dancing around. The ultimate goal is Math Music vids that kids will actually watch and learn from...kids sing along and dance around every time I play that music...then a kids show that teaches math...like Bill Nye the Science Guy meets Pee-Wee Herman meets Monty Python in a Good Eats-esque, Between the Lions modern Mathematical Electric Company joy ride... from watching this you won't get that but some people might get an idea of where I want to go...with a ton more editing and pictures and video...
http://screencast.com/t/OTdkNjc0MmE
"Music is the pleasure the human mind experiences from counting without being aware that it is counting." ~Gottfried Leibniz
More at crewton ramones house of math!
Find me on Face Book.
Sunday, September 12, 2010
Incorporate Algebra Immediately
Just fooling around with Jing, I made a screen cast that talks about using algebra "from the get go" with kids.
Eventually there will be a webpage on Crewton Ramone's House of Math with some of these pictures and this screencast. Also when I have more time you will see all the pictures with written descriptions and perhaps some additional information not covered in the screencast. When you get to my house of math, click the algebra, square #'s, and problem solving tabs for more...but there is also a lesson on combining like terms which may not be as easy to find...
But this is a great fast way to take a bunch of pictures and make them make sense...
Feel free to leave a comment or ask a question...or find me on Face Book where we can have more of a dialogue.
Also for more right here on this blog here is a post about actually using algebra to teach basic operations not just incorporating it...
Eventually there will be a webpage on Crewton Ramone's House of Math with some of these pictures and this screencast. Also when I have more time you will see all the pictures with written descriptions and perhaps some additional information not covered in the screencast. When you get to my house of math, click the algebra, square #'s, and problem solving tabs for more...but there is also a lesson on combining like terms which may not be as easy to find...
But this is a great fast way to take a bunch of pictures and make them make sense...
Feel free to leave a comment or ask a question...or find me on Face Book where we can have more of a dialogue.
Also for more right here on this blog here is a post about actually using algebra to teach basic operations not just incorporating it...
Friday, September 10, 2010
Number Identification
Here is a short simple post on number identification, with a short tangent down the SPED, Dyslexia path...
Find me on Face Book.
Crewton Ramone's House of Math for more.
Find me on Face Book.
Crewton Ramone's House of Math for more.
Wednesday, September 8, 2010
MAKE MATH FUN.
Making math fun is not as hard as it sounds. If you are working with little kids it had better be fun or they don't really want to do it.
And even then some of the more "challenging" students may not want to do math, no matter what you do. Might as well have a good time if you can though. Math Fun is a term many people have a hard time with. How do you make math fun?
Here is a 5 min screencast of what you see here with audio:
http://screencast.com/t/MGJiODI5O I skipped the squares because that should get it's own little audio clip. I just figured out how to embed the "video" into the blog but I've only had the software for about 15 min so I'm just fooling around now...might have to get the pro version for a whopping 15 a year...
My first try at a screen cast: http://screencast.com/t/Y2VlMDkzODA Here is a board set up for learning addition and multiplication as well as some algebra. The towers or building need to be skip counted, tens need to be delivered to the tens depot...all manner of games can be played here. Math land or Math Town is a fun place to learn. 
Some people drawn in makes it fun. These are not towers but robots with green units for heads. 
Here a ten ton truck loaded with a nine and a unit makes it way to the ten depot. 
Math robot with lots of addends for 8, 9 and 10. 
They are just playing blocks learning about 400, 4x2 and addends for 7. 
A city of multiplication facts. 
A pyramid of square numbers. A ton of math can be taught here. Geometric progression. Square roots, various values of x2 etc. Another thing I didn't mention in the screencast is children can discover for them selves that 22 is 4 times bigger than 12 and that 42 is 4 times bigger than 22 even though 2 is only 1 x 2, and 4 is only 2 x 2. In other words the base is only twice as big but when you raise to a second power it's more than twice as big. Let them make up their own rules and discover if the pattern is consistent...is 82 four times bigger than 42? 
What do the pictures have to do with math. Nothing. We were just having FUN with addends from 11 to 18. Note the child used one hand to write his name forwards and his other hand to write his name backwards, just for fun. There's a genius trapped inside every child. 
This was a "cake" we made with the nines are the cake the sevens are the frosting, 7 x 9 = 9 x 7. A concept many students have to see to believe when they are first starting out. 
Cakes need candles. We can skip count by three and the six is just two threes stuck together...we could only skip count to 24...and the kid was 7 years old...we also do algebra and division 63/x = 7 and 63/x = 9 in addition to x/9 = 7 and x/7 = 9...it's easy when you can see it...MAKE MATH FUN. Don't make it hard. "Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE More at My House of Math.
Like my Facebook Page.
Group Learning Is Best.
Talk about "directed discovery"!
Many of the concepts he talks about for teaching are already understood and in use in "my method". Or should I say the method I use. Here is a great example of group learning while having fun and playing games.
This group of homeschoolers turns integers into child's play.
You want blocks or tutoring? Contact me here.
Find me on Face Book.
And now Instagram too.
Math Webinars
I just went through several math webinars from various companies on several different platforms. They all looked basically the same. Person talking over slides. Boo.
I promise not to do webinars like this. I'll have streaming video showing the blocks/manipulatives, not static slides with words and mathematical symbols on them...
The platform I have chosen is dimdim, no software to download just use your web browser...with this platform I can stream you video, share my desktop, use a whiteboard, share online video, share webpages etc...and I could do slides too but...
I can also use this to tutor...two way video, shared whiteboard: it really is getting to the point where it's almost like being there. Just a few years ago this wasn't possible.
I plan on doing webinars for FREE to start and then eventually charging 100 bucks for 20 - 30 hours of training.
The online tutoring will be 40.00 an hour...I think you will be quite amazed at how far the technology has progressed...you really can "interact."
Scroll down to the bottom of this page to be notified:
http://www.crewtonramoneshouseofmath.com/math-tutoring-on-Maui.html
Also check out the rest of my website:
http://www.crewtonramoneshouseofmath.com/
Imagine being able to participate in videos like this, ask questions while you see what's happening and not be limited to 10 minutes:
http://www.crewtonramoneshouseofmath.com/problem-solving.html
Many people have a set of blocks or manipulatives and then go "now what?" Here is a chance to find out how to best use your blocks...and if you don't have a set you can use mine as it were. And ask questions. And get direction(s). And more.
I promise not to do webinars like this. I'll have streaming video showing the blocks/manipulatives, not static slides with words and mathematical symbols on them...
The platform I have chosen is dimdim, no software to download just use your web browser...with this platform I can stream you video, share my desktop, use a whiteboard, share online video, share webpages etc...and I could do slides too but...
I can also use this to tutor...two way video, shared whiteboard: it really is getting to the point where it's almost like being there. Just a few years ago this wasn't possible.
I plan on doing webinars for FREE to start and then eventually charging 100 bucks for 20 - 30 hours of training.
The online tutoring will be 40.00 an hour...I think you will be quite amazed at how far the technology has progressed...you really can "interact."
Scroll down to the bottom of this page to be notified:
http://www.crewtonramoneshouseofmath.com/math-tutoring-on-Maui.html
Also check out the rest of my website:
http://www.crewtonramoneshouseofmath.com/
Imagine being able to participate in videos like this, ask questions while you see what's happening and not be limited to 10 minutes:
http://www.crewtonramoneshouseofmath.com/problem-solving.html
Many people have a set of blocks or manipulatives and then go "now what?" Here is a chance to find out how to best use your blocks...and if you don't have a set you can use mine as it were. And ask questions. And get direction(s). And more.
Saturday, September 4, 2010
Little Kids Do A Little Math
This whole "lesson" lasted about 45 minutes, which is long "lesson" for kids this age, but as long as their attention was engaged and it was easy and fun we kept going. So, really it was just play time although the older student knew he was "learning stuff". Obviously, a little more went on here than I was able to capture in pictures. With children this age the camera is a HUGE distraction so I only managed to snap 6...and then took a couple of the book so you could see that too. We spent much more time with the blocks than the books BTW.
Here we are b uilding 10's and 9's...the older boy is 5 the younger 3 almost 4. The older boy can answer without looking, "what does two need to be a ten?"
2 + x = 10,
In fact he knows his tens addends so well he doesn't have to think about it. Mastery.
We are doing this for the benefit of the younger student. Incorporate algebra immediately. The concept of "x" is easy if they've been playing with it since they were little.
Doing nines is also easy but takes a little thinking. They are almost mastered. Why people don't teach little kids algebra from the get go is beyond me. Here one child is counting units the younger child is counting x. (In the mathematics "x" IS the plural.)
The younger student is "building stairs" with x's, basically he is playing with them and using his imagination. X is simple concept. We continue on with the basic concept that the numbers have TWO parts, the "how many" part and the "what kind" part. When the tens are on the smooth side we call them x. (At this age he still calls them "exes.") He is counting out x.
x + x = 2x.
This is no big deal.
2x + x = 3x...I have spent time in high school and college classes explaining where the "two" came from in x + x, and how we got 3 when adding 2x + x because the one is invisible and x + x being 2x doesn't make any sense. Text books say "the one is understood" ...except it isn't. These children will never have this problem. Further we talk about x2 + x2 making 2x2, didn't get a picture of it but it's them playing with the big red squares. I have seen numerous college aged students add x2 + x2 and get x4!!!!! I'm the only one right? The system in place for mathematics instruction in the USA is broken. Anyhow, before I go off on a diatribe, these little kids can see that two red squares have nothing to do with 4...if the red squares are called x2 (x-squared) then two of them are simply 2x2. Painfully obvious. In the Montessori method they say "visually obvious". Little kids doing algebra? YES, THEY CAN.
Building 8's.
When we build eights he has to get out blocks to make sure... Just because he is familiar with the addends for 10 and 9 does NOT mean he is automatically able to do 8's...many teachers fail to recognize this. They need to learn addends just like they have to practice ABC's...there are only 25 addends from 1 to 10 and 45 single digit addends in all ending with 9+9.
Note I told him to build 8's I didn't tell him to start in any certain order, like 1+7, 2+6, etc he's just building...note we aren't using any symbols or drawing. Just because the child can write doesn't mean they can't learn "complex" math concepts. Later we can go back and use symbols...and know what they MEAN.
Just fooling around, they got out a ruler because I said, "measure it to make sure"...I meant measure with the blocks and they knew it, but since we are just having fun we played with the ruler too. Measurement is an important area of study in math.
Then of course we measured with a pen. Have fun with it. Math time doesn't have to be serious at all...
The 3 year old can't make numbers but he can point to the right answer. This page is fun because it has a lot to count...6 "problems". Again, the numbers have the "how many" part and the "what kind" part. Here we are learning units or ones, tens and hundreds. Just matching the picture and the symbols...900 is square and we can count it by three's...
The 3 year old is given pause when counting tens: "Oh man this is gonna take forever" he starts counting the tens one unit at a time then I show him we can just count 10, 20 30...this is not the first time he has seen this book and it will be new every time for about another 18 times...repetition is the mother of skill. At this age repeating it over and over again is natural and fun. Which is why this is a great time to teach multiplication songs...it will be fun and easy and avoid tedium later when the brain has moved onto a stage of development where repetition is not as large a part of the child's learning modality.
This page which came after the other page shown, (note the page numbers) is not as much fun because there isn't as much to count...or so says the 3 year old. I'd say he's the fun expert.
Here is more on counting and combining like terms.
Much more at Crewton Ramone's House Of Math.
"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970
"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956
"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003
"People tend to forget that play is serious." ~David Hockney Contemporary British painter
"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE
"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru
More math quotes and more education quotes at my site.
Here we are b uilding 10's and 9's...the older boy is 5 the younger 3 almost 4. The older boy can answer without looking, "what does two need to be a ten?"
2 + x = 10,
In fact he knows his tens addends so well he doesn't have to think about it. Mastery.
We are doing this for the benefit of the younger student. Incorporate algebra immediately. The concept of "x" is easy if they've been playing with it since they were little.
Doing nines is also easy but takes a little thinking. They are almost mastered. Why people don't teach little kids algebra from the get go is beyond me. Here one child is counting units the younger child is counting x. (In the mathematics "x" IS the plural.)
The younger student is "building stairs" with x's, basically he is playing with them and using his imagination. X is simple concept. We continue on with the basic concept that the numbers have TWO parts, the "how many" part and the "what kind" part. When the tens are on the smooth side we call them x. (At this age he still calls them "exes.") He is counting out x.
x + x = 2x.
This is no big deal.
2x + x = 3x...I have spent time in high school and college classes explaining where the "two" came from in x + x, and how we got 3 when adding 2x + x because the one is invisible and x + x being 2x doesn't make any sense. Text books say "the one is understood" ...except it isn't. These children will never have this problem. Further we talk about x2 + x2 making 2x2, didn't get a picture of it but it's them playing with the big red squares. I have seen numerous college aged students add x2 + x2 and get x4!!!!! I'm the only one right? The system in place for mathematics instruction in the USA is broken. Anyhow, before I go off on a diatribe, these little kids can see that two red squares have nothing to do with 4...if the red squares are called x2 (x-squared) then two of them are simply 2x2. Painfully obvious. In the Montessori method they say "visually obvious". Little kids doing algebra? YES, THEY CAN.
Building 8's.
When we build eights he has to get out blocks to make sure... Just because he is familiar with the addends for 10 and 9 does NOT mean he is automatically able to do 8's...many teachers fail to recognize this. They need to learn addends just like they have to practice ABC's...there are only 25 addends from 1 to 10 and 45 single digit addends in all ending with 9+9.
Note I told him to build 8's I didn't tell him to start in any certain order, like 1+7, 2+6, etc he's just building...note we aren't using any symbols or drawing. Just because the child can write doesn't mean they can't learn "complex" math concepts. Later we can go back and use symbols...and know what they MEAN.
Just fooling around, they got out a ruler because I said, "measure it to make sure"...I meant measure with the blocks and they knew it, but since we are just having fun we played with the ruler too. Measurement is an important area of study in math.
Then of course we measured with a pen. Have fun with it. Math time doesn't have to be serious at all...
The 3 year old can't make numbers but he can point to the right answer. This page is fun because it has a lot to count...6 "problems". Again, the numbers have the "how many" part and the "what kind" part. Here we are learning units or ones, tens and hundreds. Just matching the picture and the symbols...900 is square and we can count it by three's...
The 3 year old is given pause when counting tens: "Oh man this is gonna take forever" he starts counting the tens one unit at a time then I show him we can just count 10, 20 30...this is not the first time he has seen this book and it will be new every time for about another 18 times...repetition is the mother of skill. At this age repeating it over and over again is natural and fun. Which is why this is a great time to teach multiplication songs...it will be fun and easy and avoid tedium later when the brain has moved onto a stage of development where repetition is not as large a part of the child's learning modality.
This page which came after the other page shown, (note the page numbers) is not as much fun because there isn't as much to count...or so says the 3 year old. I'd say he's the fun expert.
Here is more on counting and combining like terms.
Much more at Crewton Ramone's House Of Math.
"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970
"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956
"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003
"People tend to forget that play is serious." ~David Hockney Contemporary British painter
"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE
"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru
More math quotes and more education quotes at my site.
Thursday, September 2, 2010
Math: basic fractions not Algebra
"I don't know what the hell I'm doing." ~Frustrated student.
The text book one of my students uses. Currently he is doing fractions...and has a test that we were studying for. This is quite common even up to the college level, reviewing fractions because the students forget the rules. I would prefer to teach fractions using algebra but in this case we don't have the time it takes to develop the concepts...I had one hour. So I used the 5 basic concepts
to bring home the point that the rules did not change we can't add the numbers unless they are SAME. And Pointed out the numbers have two parts the "how many" part and the "what kind" part. With fractions the numerator tells how many and the denominator (de nome of it) tells what kind. Have to be the same KIND before we can add.
So basically we did an hour on "fractions". Here we are adding two mixed numbers. We talked a lot about multiplying by 1 and that "one" could be 2/2, 3/3 etc. And how numbers have to be same before we can add, subtract or divide them. Felt sorry for him because we had to spend an hour basically on fractions by himself. It would have been more fun if he had another student there and we could mix it up and actually do some algebra but we didn't have time. He did say he didn't mind because "you have a way of explaining it that's easy and kinda fun, my teacher makes it confusing and hard."
That's because his teacher is teaching the same way we have been teaching for decades, never mind that it doesn't work, using rules and memorization instead of concepts and algorithms based on those concepts. He teaches the way he was taught to teach...so all the way to college, students forget what they learned in 4th grade about fractions. If we taught English this way nobody would speak the freaking language...and math is a language why not teach it that way?
Rather than convert the mixed numbers into improper fractions, I showed him how to add and subtract using the associative property of addition. I didn't tell him that; we just "added up the parts." First the whole numbers then the fractions...if the fractions ended up being improper we just added one to the whole number...7 1/2 + 6 3/4 for example. 7 + 6 = 13 then 1/2 + 3/4 = 5/4 so 13 + 5/4 = 14 1/4.
"Wow! That's easier."
7 3/8 + 9 1/4 = 7 + 9 + 3/8 + 2/8 = the easy way.
59/8 + 72/8 = the hard way.
We had to go over common denominators, equivalent fractions, and improper fractions. It was not tremendous fun but he did enjoy it because he knew he was going to ace the test, now that he understood "what the hell he was doing."
Note how the blocks are set up to show that 3/4=6/8=9/12=12/16.
I keep threatening to build a fractions page at Crewton Ramone's House of Math...but so far I haven't.
And BTW if you are on Maui, or anywhere on the planet for that matter I can do tutoring with you.
The text book one of my students uses. Currently he is doing fractions...and has a test that we were studying for. This is quite common even up to the college level, reviewing fractions because the students forget the rules. I would prefer to teach fractions using algebra but in this case we don't have the time it takes to develop the concepts...I had one hour. So I used the 5 basic concepts
to bring home the point that the rules did not change we can't add the numbers unless they are SAME. And Pointed out the numbers have two parts the "how many" part and the "what kind" part. With fractions the numerator tells how many and the denominator (de nome of it) tells what kind. Have to be the same KIND before we can add.
So basically we did an hour on "fractions". Here we are adding two mixed numbers. We talked a lot about multiplying by 1 and that "one" could be 2/2, 3/3 etc. And how numbers have to be same before we can add, subtract or divide them. Felt sorry for him because we had to spend an hour basically on fractions by himself. It would have been more fun if he had another student there and we could mix it up and actually do some algebra but we didn't have time. He did say he didn't mind because "you have a way of explaining it that's easy and kinda fun, my teacher makes it confusing and hard."
That's because his teacher is teaching the same way we have been teaching for decades, never mind that it doesn't work, using rules and memorization instead of concepts and algorithms based on those concepts. He teaches the way he was taught to teach...so all the way to college, students forget what they learned in 4th grade about fractions. If we taught English this way nobody would speak the freaking language...and math is a language why not teach it that way?
Rather than convert the mixed numbers into improper fractions, I showed him how to add and subtract using the associative property of addition. I didn't tell him that; we just "added up the parts." First the whole numbers then the fractions...if the fractions ended up being improper we just added one to the whole number...7 1/2 + 6 3/4 for example. 7 + 6 = 13 then 1/2 + 3/4 = 5/4 so 13 + 5/4 = 14 1/4.
"Wow! That's easier."
7 3/8 + 9 1/4 = 7 + 9 + 3/8 + 2/8 = the easy way.
59/8 + 72/8 = the hard way.
We had to go over common denominators, equivalent fractions, and improper fractions. It was not tremendous fun but he did enjoy it because he knew he was going to ace the test, now that he understood "what the hell he was doing."
Note how the blocks are set up to show that 3/4=6/8=9/12=12/16.
I keep threatening to build a fractions page at Crewton Ramone's House of Math...but so far I haven't.
And BTW if you are on Maui, or anywhere on the planet for that matter I can do tutoring with you.