Measuring obesity with BAI

I'm not real super interested in obesity or calculations of people's weights, fat levels etc. but I ran across something half interesting that might be of interest to you.

It is a new way to measure obesity or if a person is underweight, normal weight, or overweight -- and it doesn't even use your weight in the calculation!

Murray has blogged about it at New measure of obesity – body adiposity index (BAI)


He also made a calculator for it that compares your "results" as far as BMI and this new index, BAI.

This new index uses your height and a measurement around the hips, and it's still somewhat experimental in the fact that it hasn't been thorougly tested in all races.


The formula is

  hip (cm)
-------------   −  18
[height(m)]1.5

The resulting number should be a close estimate to your body fat percentage.


Just for the record, or if you are curious, I am of normal weight, and supposedly have about 29% body fat according to that calculation. Which, 29% body fat sounds high but it seems to be perfectly normal for females. It makes me think of this age-old saying "Human body is 70% water." That just can't be, not for females anyway. I would be 70% water, 29% fat, and 1% all the other stuff...???
 
Ok, upon checking I find that indeed, the human body is NOT 70% water. Females average 55% water and males 60% water, but obese people may only be 45% water.

Measuring obesity with BAI

I'm not real super interested in obesity or calculations of people's weights, fat levels etc. but I ran across something half interesting that might be of interest to you.

It is a new way to measure obesity or if a person is underweight, normal weight, or overweight -- and it doesn't even use your weight in the calculation!

Murray has blogged about it at New measure of obesity – body adiposity index (BAI)


He also made a calculator for it that compares your "results" as far as BMI and this new index, BAI.

This new index uses your height and a measurement around the hips, and it's still somewhat experimental in the fact that it hasn't been thorougly tested in all races.


The formula is

  hip (cm)
-------------   −  18
[height(m)]1.5

The resulting number should be a close estimate to your body fat percentage.


Just for the record, or if you are curious, I am of normal weight, and supposedly have about 29% body fat according to that calculation. Which, 29% body fat sounds high but it seems to be perfectly normal for females. It makes me think of this age-old saying "Human body is 70% water." That just can't be, not for females anyway. I would be 70% water, 29% fat, and 1% all the other stuff...???
 
Ok, upon checking I find that indeed, the human body is NOT 70% water. Females average 55% water and males 60% water, but obese people may only be 45% water.

Points on math education

I've been lazy lately when it comes to blogging and I'm sorry for that. I've been sort of taking time off from computer work and painting some windows since it just needs done at our house. I view it sort of as "therapy", since it's so different from the computer work and I just take my time and I don't have to think that hard. I like painting.

Anyways, I foud something really nice at Mathmom's. She's written, I feel, an excellent piece about problems in math education in elementary grades. Her point of view is of classroom instruction, but it's still really relevant even for homeschoolers. Some excerpts:

On calculators:

But to be honest, as much as I hate calculator use in school, in this age of calculators and computers, efficiency at hand computation is not, IMO, the most critical math skill for kids to learn. I am NOT saying that it should be ignored, or that kids should be allowed to skip it, and just use calculators in class (see rant linked above). But it is not, IMO, the be all and end all of math education, nor is it a prerequisite, IMO, for studying anything else.

What I consider even more important is a strong sense of number. I want kids who know immediately when the answer they got (either by hand computation or with a calculator) is way off. I want kids who have an instinctive understanding of the distributive law before it is ever formally taught or named (12 sevens is obviously the same as 10 sevens and 2 more sevens). I want kids who know when the amount of change handed to them makes no sense. I would rather have a kid who can multiply 64 x 25 mentally (by halving 64 twice and doubling 25 twice, to see that it's equal to 16 x 100 = 1600) than a kid who can sit down and carry out the long multiplication with pencil and paper, by rote.

I feel that we need to consider several things when it comes to calculators. It's best when the kids can do mental calculations and do paper-and-pencil methods, including understanding why they work. Calculators should be used judiciously, but used. Like she mentions, number sense is of paramount importance so that kids can estimate their answers and tell if the calculator "got it wrong" (e.g. they punched wrong buttons).

On spiraling curricula:

Steve is right that a spiral curriculum can lead to a lax attitude of "it's ok if they don't master this now, because they'll see it again later" that goes on ad infinitum, and the kid never masters anything. This is clearly no good. But the solution isn't necessarily to take away the spiraling for those who need it, IMO. The solution is to have limits - for example, it's ok if they don't completely "get" long multiplication when it's previewed in 3rd grade, or even when it's introduced more formally in 4th, but they have to get it when it's reviewed in 5th, or they shouldn't move on.

This sounds like a really sane approach.

She also talks about including non-routine problems for ALL students to solve. I definitely recommend this practice and have written about it before! MathMom gives several good reasons for this:

1. First, it provides a fabulous way of helping students to appreciate the uses of the procedures and skills they have learned or are learning.

2. Second, this is the kind of thing that "real mathematicians" do! ... A "mathematician" does not sit down and solve 25 ratio and percent word problems, knowing exactly which skills are required to perform the computations. Instead, she investigates "puzzles", looks for interesting patterns makes new discoveries, generalizes results.

3. Third, it develops self esteem and confidence.

4. Fourth, it builds transferrable problem solving skills.

Read it all at Ramblings of a math mom: Math wars.

Points on math education

I've been lazy lately when it comes to blogging and I'm sorry for that. I've been sort of taking time off from computer work and painting some windows since it just needs done at our house. I view it sort of as "therapy", since it's so different from the computer work and I just take my time and I don't have to think that hard. I like painting.

Anyways, I foud something really nice at Mathmom's. She's written, I feel, an excellent piece about problems in math education in elementary grades. Her point of view is of classroom instruction, but it's still really relevant even for homeschoolers. Some excerpts:

On calculators:

But to be honest, as much as I hate calculator use in school, in this age of calculators and computers, efficiency at hand computation is not, IMO, the most critical math skill for kids to learn. I am NOT saying that it should be ignored, or that kids should be allowed to skip it, and just use calculators in class (see rant linked above). But it is not, IMO, the be all and end all of math education, nor is it a prerequisite, IMO, for studying anything else.

What I consider even more important is a strong sense of number. I want kids who know immediately when the answer they got (either by hand computation or with a calculator) is way off. I want kids who have an instinctive understanding of the distributive law before it is ever formally taught or named (12 sevens is obviously the same as 10 sevens and 2 more sevens). I want kids who know when the amount of change handed to them makes no sense. I would rather have a kid who can multiply 64 x 25 mentally (by halving 64 twice and doubling 25 twice, to see that it's equal to 16 x 100 = 1600) than a kid who can sit down and carry out the long multiplication with pencil and paper, by rote.

I feel that we need to consider several things when it comes to calculators. It's best when the kids can do mental calculations and do paper-and-pencil methods, including understanding why they work. Calculators should be used judiciously, but used. Like she mentions, number sense is of paramount importance so that kids can estimate their answers and tell if the calculator "got it wrong" (e.g. they punched wrong buttons).

On spiraling curricula:

Steve is right that a spiral curriculum can lead to a lax attitude of "it's ok if they don't master this now, because they'll see it again later" that goes on ad infinitum, and the kid never masters anything. This is clearly no good. But the solution isn't necessarily to take away the spiraling for those who need it, IMO. The solution is to have limits - for example, it's ok if they don't completely "get" long multiplication when it's previewed in 3rd grade, or even when it's introduced more formally in 4th, but they have to get it when it's reviewed in 5th, or they shouldn't move on.

This sounds like a really sane approach.

She also talks about including non-routine problems for ALL students to solve. I definitely recommend this practice and have written about it before! MathMom gives several good reasons for this:

1. First, it provides a fabulous way of helping students to appreciate the uses of the procedures and skills they have learned or are learning.

2. Second, this is the kind of thing that "real mathematicians" do! ... A "mathematician" does not sit down and solve 25 ratio and percent word problems, knowing exactly which skills are required to perform the computations. Instead, she investigates "puzzles", looks for interesting patterns makes new discoveries, generalizes results.

3. Third, it develops self esteem and confidence.

4. Fourth, it builds transferrable problem solving skills.

Read it all at Ramblings of a math mom: Math wars.

Carnival of math

You might not have heard about it, but there exists a blog carnival for math, too. I submitted my rainbow entry into the latest one.

Not all of the entries there are higher math, by the way, such as MathMom's Calculator rant or Puzzler puzzled from JD2718.

If interested, go check it out: Carnival of math, edition 17!

Carnival of math

You might not have heard about it, but there exists a blog carnival for math, too. I submitted my rainbow entry into the latest one.

Not all of the entries there are higher math, by the way, such as MathMom's Calculator rant or Puzzler puzzled from JD2718.

If interested, go check it out: Carnival of math, edition 17!

Calculator activitity for 2nd grade

I would like to know a simple activity that i could do with a grade 2 student, which involves using the calculator.

Here are a few ideas. Hopefully they are of help.

Add or subtract the same number repeated times.

For example, start with 10, subtract 1 repeated times and see how it goes to the negative numbers.

Start with any 2-digit number and add 100 repeated times. Or start with a 3-digit number and subtract 50 or 100 repeated times.

Here's a game: Player 1 chooses a 2-digit number. Player 2 predicts how many times you can subtract 10 before the number becomes negative. Then this is checked with calculator. If player 2 was right, he gets a point. Play till a predetermined amount of points.

Or, use adding. Player 1 chooses a three-digit number, and player 2 has to predict how many times you can add 100 to it before the result is more than 1000. Then check with calculator.

Readers, feel free to submit more ideas in the comments.

Calculator activitity for 2nd grade

I would like to know a simple activity that i could do with a grade 2 student, which involves using the calculator.

Here are a few ideas. Hopefully they are of help.

Add or subtract the same number repeated times.

For example, start with 10, subtract 1 repeated times and see how it goes to the negative numbers.

Start with any 2-digit number and add 100 repeated times. Or start with a 3-digit number and subtract 50 or 100 repeated times.

Here's a game: Player 1 chooses a 2-digit number. Player 2 predicts how many times you can subtract 10 before the number becomes negative. Then this is checked with calculator. If player 2 was right, he gets a point. Play till a predetermined amount of points.

Or, use adding. Player 1 chooses a three-digit number, and player 2 has to predict how many times you can add 100 to it before the result is more than 1000. Then check with calculator.

Readers, feel free to submit more ideas in the comments.

Square root of 11

Is square root of 11 an irrational number? How do you know from using a calculator? Thank you.

Well, I happen to know that if the square root of a natural number is NOT a whole number, then it is an irrational number. There are no other possibilities.

Of course you can't tell by the calculator. The calculator will show you 8 or 10 decimals, but you won't know from that if it's going to continue or not, or if it is periodical or not.

But pure mathematics and established, proven theorems will tell you that! : )

A proof that the square root of 2 is irrational

Lots of proofs of the same... plus one proving that any root is irrational if it's not a whole number

Proof that the square root of any prime is irrational

Square root of 11

Is square root of 11 an irrational number? How do you know from using a calculator? Thank you.

Well, I happen to know that if the square root of a natural number is NOT a whole number, then it is an irrational number. There are no other possibilities.

Of course you can't tell by the calculator. The calculator will show you 8 or 10 decimals, but you won't know from that if it's going to continue or not, or if it is periodical or not.

But pure mathematics and established, proven theorems will tell you that! : )

A proof that the square root of 2 is irrational

Lots of proofs of the same... plus one proving that any root is irrational if it's not a whole number

Proof that the square root of any prime is irrational

Finding values of sine without a calculator

How do I find the sin or inverse sin of 46 degrees (or any degree) without using a calculator?
Thanks.
Jackie

Finding an "inverse sin" doesn't apply to degrees by the way. We take sine of an angle and get a number; inverse sine is taken from a number and gives back an angle.

So is it possible to find values of sine without a calculator? I am sure there are various methods, but these two came to my mind.

1) We can go back to the definition of sine in a right triangle and using a protractor, DRAW a right triangle with that angle. Draw as accurately as you can.



Then from the picture again, we need to measure the two sides: the opposite side and the hypotenuse and then calculate their ratio (paper and pencil). Again, measure as accurately as you can.

Now, as far as the opposite problem, let's say you know that the sine of some angle is 0.86 or some other number (between -1 and 1). Can we find the angle without the calculator?

Draw a right triangle with hypotenuse 1, opposite side 0.86 (or some multiple of those), and measure the angle in degrees.

This method, I feel, is a good one for demonstration and teaching purposes when first learning about sine.

2) Another possibility is to use the Taylor series of sine. Hopefully you don't need to take too many terms from it to get the desirable accuracy. This will include calculations that you'd need to do on paper.

Let's say we use Taylor series in origin and take the first four terms:

sin(x) ≈ x - x³/3! + x⁵/5! - x⁷/7!

To use this, you need to first change the 46 degrees or whatever to radians. Obviously all the calculations involved will take some time without a calculator... Auch! But an approximative method such as this that only involves the four basic operations is what your calculator probably uses, too.

Here you will find the Taylor series for inverse of sine.

3) Using sine addition formula and a known value.

Sine addition formula says:
sin(a + b) = sin a cos b + cos a sin b.

So... if you're interested in finding, say, sin(46°) and we do already happen to know sin(45°) and cos(45°)... but we need to work in radians to use the formula. So convert 46 and 45 degrees to radians (without a calculator? I'm going to cheat now...) and get 45° is Pi/4 or 0.785398, 46° is about 0.80285.

sin(Pi/4 + 0.01745) = sin(Pi/4) cos(0.01745) + cos(Pi/4) sin(0.01745).

It just so happens that for small values of x (near zero), sin x ≈ x. (You learn that in calculus, I think). So sin(0.01745) is about 0.01745. Cos(0.01745) should be pretty near 1 somewhere.

sin(Pi/4) or sin 45° is 1/√2, and cos(Pi/4) is the same. Plugging those in,

sin(Pi/4 + 0.01745) = 1/√2 * 1 + 1/√2 *0.01745.

I'm going to cheat again and do this with a calculator... to get 0.71945.

Did I get close? Well, sin46° is about 0.7193398. Got three decimals right; that's okay I guess.

Tags: sine, calculator

Finding values of sine without a calculator

How do I find the sin or inverse sin of 46 degrees (or any degree) without using a calculator?
Thanks.
Jackie

Finding an "inverse sin" doesn't apply to degrees by the way. We take sine of an angle and get a number; inverse sine is taken from a number and gives back an angle.

So is it possible to find values of sine without a calculator? I am sure there are various methods, but these two came to my mind.

1) We can go back to the definition of sine in a right triangle and using a protractor, DRAW a right triangle with that angle. Draw as accurately as you can.



Then from the picture again, we need to measure the two sides: the opposite side and the hypotenuse and then calculate their ratio (paper and pencil). Again, measure as accurately as you can.

Now, as far as the opposite problem, let's say you know that the sine of some angle is 0.86 or some other number (between -1 and 1). Can we find the angle without the calculator?

Draw a right triangle with hypotenuse 1, opposite side 0.86 (or some multiple of those), and measure the angle in degrees.

This method, I feel, is a good one for demonstration and teaching purposes when first learning about sine.

2) Another possibility is to use the Taylor series of sine. Hopefully you don't need to take too many terms from it to get the desirable accuracy. This will include calculations that you'd need to do on paper.

Let's say we use Taylor series in origin and take the first four terms:

sin(x) ≈ x - x³/3! + x⁵/5! - x⁷/7!

To use this, you need to first change the 46 degrees or whatever to radians. Obviously all the calculations involved will take some time without a calculator... Auch! But an approximative method such as this that only involves the four basic operations is what your calculator probably uses, too.

Here you will find the Taylor series for inverse of sine.

3) Using sine addition formula and a known value.

Sine addition formula says:
sin(a + b) = sin a cos b + cos a sin b.

So... if you're interested in finding, say, sin(46°) and we do already happen to know sin(45°) and cos(45°)... but we need to work in radians to use the formula. So convert 46 and 45 degrees to radians (without a calculator? I'm going to cheat now...) and get 45° is Pi/4 or 0.785398, 46° is about 0.80285.

sin(Pi/4 + 0.01745) = sin(Pi/4) cos(0.01745) + cos(Pi/4) sin(0.01745).

It just so happens that for small values of x (near zero), sin x ≈ x. (You learn that in calculus, I think). So sin(0.01745) is about 0.01745. Cos(0.01745) should be pretty near 1 somewhere.

sin(Pi/4) or sin 45° is 1/√2, and cos(Pi/4) is the same. Plugging those in,

sin(Pi/4 + 0.01745) = 1/√2 * 1 + 1/√2 *0.01745.

I'm going to cheat again and do this with a calculator... to get 0.71945.

Did I get close? Well, sin46° is about 0.7193398. Got three decimals right; that's okay I guess.

Tags: sine, calculator

Calculator in elementary grades?

There is controversy over how much elementary school kids should be allowed to use the calculator. Some say it's a no-no altogether, some think it should be used almost all the time - and some think it should be balanced.

In my opinion, one should severely restrict the calculator use in early grades - until the student has mastered the basic math facts and can quickly do basic mental calculations. Until then, calculator should be used only for some special projects or illustrations.

Why? Because not knowing those facts by heart is a big hindrance when learning fractions, factoring, etc. And because it helps children develop NUMBER SENSE - to be familiar with our number system.

Also kids need to learn to do multiplication and long division by hand - it is needed later when those same procedures are used in algebra.

Read more at this link: Using calculator in elementary math teaching.

Calculator in elementary grades?

There is controversy over how much elementary school kids should be allowed to use the calculator. Some say it's a no-no altogether, some think it should be used almost all the time - and some think it should be balanced.

In my opinion, one should severely restrict the calculator use in early grades - until the student has mastered the basic math facts and can quickly do basic mental calculations. Until then, calculator should be used only for some special projects or illustrations.

Why? Because not knowing those facts by heart is a big hindrance when learning fractions, factoring, etc. And because it helps children develop NUMBER SENSE - to be familiar with our number system.

Also kids need to learn to do multiplication and long division by hand - it is needed later when those same procedures are used in algebra.

Read more at this link: Using calculator in elementary math teaching.