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Thanks. I hadn't seen that one. Makes sense they'd use visuals at that age and not straight algebra. I just know my daughters could solve these types of problems early. I never worried about how they did it. I knew Singapore was sound.
As a parent, I loved the no homework thing. Yet my kids learned math and learned it very well. The only thing the middle school could do when we transferred dd this year was move her up in math. The kids in her grade are being remediated to get them ready for algebra and she's already been doing algebra for two years.
A lot of Singapore math is Guess and Check. My daughter used it for 4th and 5th grade and it was very frustrating, since DH and I wanted to teach her basic algebra (we did) to help solve some of these problems, but she was not allowed to use that in class.
I liked the fact that the program didn't spiral, she's now in 6th grade and back in a spiral program, but at an accellerated pace, so what I would consider the "worst of both worlds".
A lot of Singapore math is Guess and Check. My daughter used it for 4th and 5th grade and it was very frustrating, since DH and I wanted to teach her basic algebra (we did) to help solve some of these problems, but she was not allowed to use that in class.
I liked the fact that the program didn't spiral, she's now in 6th grade and back in a spiral program, but at an accellerated pace, so what I would consider the "worst of both worlds".
Oh I agree. Rapid spiraling is also known as a tornado. Tears up a lot of turf and leaves total chaos behind. Fortunately, the standard math track restarts in our district schools in 8th grade so we only had to move dd up a grade to get her in algerbra and avoid the last of the fast spiraling classes.
Everyday Mathematics uses rapid spiraling. It's what drove us to the charter school. Dd just fell off of the table.
Another way to solve this is to use a tug of war scenario. I actually used the same problem today in class as a brain teaser and set it up as it takes 6 first graders to equal 1 sixth grader in tug of war. I drew a sixth grader pulling a rope with 6 first graders on the other end. I had 1 sixth grader also pulling on a rope with 2 dogs. The last clue was 1 first grader plus 36 power points equals one dog. I had one student immediately get the answer and some of the others had to think it through a little. He saw that 6 first graders equal 2 dogs pretty easily, so 3 first graders equal 1 dog. Therefore, 1 first grader + 36 = 3 first graders, so 2 first graders are equal to 36 and 1 first grader equals 18.
This is developing more logical reasoning than anything else. I wish we would teach this stuff more, it would help them when they get to Algebra.
Ivory, I totally consider you a genius for figuring that out. Just one small correction - weight, not mass. Grams is the measurement for mass.
Actually, they're both masses. Grams are one measuremnt for mass in SI. Engilsh uses the pound. Weight would be Newtons in SI or pound force in English. I realize she said weight but most people mean mass when they say weight and I'm just used to correcting that. (students enter my class thinking the two are interchangeable) Note there is a conversion factor for grams to pounds that does not involve the gravitiational constant (as in the pounds we weigh ourselves in). That's because they're both mass. If one were a weight and the other a mass, you'd need that pesky gravitational constant in there. Common practice is to say weight when we measure the mass of something. After all, the scale does work because of gravity so it's more of an academic point than a practical one. It's only an issue if you need to calculate a force like when you're writing specs for elevator cables. You wouldn't want to use a mass as a weight there.
Also, as an ex engineer, I know to assume it's pound mass unless it's called out as pound force. She said pound not pound force so I used the word mass.
Normally, I don't use WIKI because it can be inaccurate but since I know the answer is right, here's what WIKI says
PS. In every day life, it really doesn't matter which term you use. When you "weigh" yourself, what the scale tells you is how much the scale deflected due to gravity acting on what is on it. The dial however, usually, reads in units of mass. But since what we're doing involves gravity, we call it a weight. This stuff only annoys physics teachers and engineers. It's transparent to the general public. It only matters when solving force problems and visiting other planetary bodies where the force of gravity might be different.
Last edited by Ivorytickler; 09-23-2009 at 09:13 PM..
I just want to say that I find this totally interesting. Unfortunately, you confused me quite a bit. Haha. Also, my credentials extend to a couple of entry level physics classes.
I don't want to discuss the difference between mass and weight, because I'm pretty sure we have the same understanding. Mass is how much matter something has. Weight is related to the force of gravity, where as mass is not.
More so I'm interested in the units of measurements. My understanding was that because the two terms mean different things (though related), they require separate units for measurement. Mass is a part of the formula for weight but (and here's where I'm confused), that doesn't make a direct conversion, does it? When you say pound force and pound mass, those aren't the same numbers, are they? If not, and pound force is actually the result of an equation, then that makes more sense to me.
we know that b=2c. We know that c=a+36...so 2c=2a+72=6a.
If 6a=2a+72, we can suctract 2a from both sides, leaving us with 4a=72. 72 divided by 4 is 18, the value of a. Once you have a, you can figure b and c easily enough.
Ivory, I totally consider you a genius for figuring that out. Just one small correction - weight, not mass. Grams is the measurement for mass.
At gravity g, mass and weight are virtually identical. g=earth standard gravity of 9.8 meters per second per second. Weight can change at different gravities, but mass remains constant.
At gravity g, mass and weight are virtually identical. g=earth standard gravity of 9.8 meters per second per second. Weight can change at different gravities, but mass remains constant.
Actually, no. In SI, weight is mass times 9.81 m/s^2. They are not identical. One is measured in grams and the other in newtons. (english gets a factor of 32 point something I'm too lazy to look up (I use SI when I teach this and it's been years since I had to do an english unit problem involving force)
Mass is really a measure of a body's resistance to motion. Weight is the force of gravity acting on a body because of it's mass. If I weigh myself on earth and on the moon, my weight will be 1/6th what it is on earth on the moon but my mass will remain the same. The way a scale workes it gravity pulls down on the mass placed on the scale and is compresses (assuming spring scale here) a certain amount under the force. We are in the habit of stating the mass it takes to get the deflection not the force (and it's really a "who cares?" outside of science and if you stay on earth).
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