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Common Core In Action - Solving Difficult Math Problems

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The writer lost me in the first paragraph, "As the daughter of a musician and a psychotherapist, she's actually one of the lucky ones. There is no pressure to perform, academically or otherwise, in this house. We believe in creativity, low stress, and happiness."

So that stuck in my mind throughout reading.

 

Kids need to be pushed along, even from a young age. Kids need to have some kind of sense of urgency to get things accomplished, even from a young age. This can be done lovingly with chores and other basic daily tasks.

 

Go ahead and push them in school, and if you feel your child is overwhelmed, talk to the teacher and figure out a way to tone it down in manageable chunks for your kid.

 

But for the rest of the kids that are thriving on the frequent tests, and it's forcing them to pay attention and get busy, well that's a good thing.

 

Thank God that my 3 older ones were pushed, and pushed hard! They are succeeding on so many levels and they are well adjusted and normal. If the expectations were any less, they would not have achieved all that they have.

Edited by hoops5

Some of what is part of CC math is just 'short-cuts'. Anyone who does enough math will develop the shortcuts naturally. Like tipping - 15%-18% is your target usually. Take total bill and take 10% - oh that is simply moving decimal one place. Then take 50% or half of that - and finally add together and bingo - you have your tip without knowing or using percentages at all. BTW, that will result in a greater than 15% tip since tax is in the total and usually not to be tipped on. So leaving the tax in helps round it up.

 

 

For the above I would this shortcut:

 

Original 325-38 = ?

 

Get to nearest 100s resulting in this modified equation:

 

(325-25) - (38-25) =

 

300 - 13 =

 

Now get to nearest 10

 

(300-10) - (13-10)

 

290 - 3

 

Now its real easy - 287.

 

No carries, no columns....

 

The thing is these are all just shortcuts (using acceptable math methods). Its really more advanced algebra - and understand the underlying rules should be part of the learning or understanding - not just showing some 'neat tricks'.

This is exactly how I approach mental subtraction.
I think it's funny you have to drag politics into everything. But sense you did, I know democrat liberal teachers that absolutely hate it.

 

On paper - its not really 'quicker' or shorter. Granted.

 

That would be more an 'in the head short-cut' to avoid using pencil, paper or scratchpad.

 

Dragonfire captured the value and concept in his post at #33.

On paper - its not really 'quicker' or shorter. Granted.

 

That would be more an 'in the head short-cut' to avoid using pencil, paper or scratchpad.

 

Dragonfire captured the value and concept in his post at #33.

The value of good mental shortcuts and extended practice using them is that it frees your mind to focus on solving problems without slowing down to reach for a calculator to perform basic math operations.

 

Mastering mental math skills is no different than mastering skills in sports. If students don't engage in long hours of practicing basic concepts, then their ultimate potential for achievement is limited.

The value of good mental shortcuts and extended practice using them is that it frees your mind to focus on solving problems without slowing down to reach for a calculator to perform basic math operations.

 

Mastering mental math skills is no different than mastering skills in sports. If students don't engage in long hours of practicing basic concepts, then their ultimate potential for achievement is limited.

 

 

Word.

No, it's utterly pointless for real world use. Companies and employers are results oriented. They care about the solution to the problem, not how you get there.

 

Isn't the above something people promoting CORE would say as well. Why does it matter how you get there? Why does it matter if you "anchor" or "memorize" as long as you get there?

My youngest is 21 so I'm not overly familiar with any of the "new new math."

 

I will say this. Memorization has value but so does thinking of numbers in a relational manner. Yes, it seems strange to go to a method to figure 9 + 6 when we can EASILY (key) memorize the answer. But what if it's 478 + 72? Now what? Well, most of us that can do calcualtions without pencils are now going to the relational method and there are different ways to get there.

 

What if it's 14% of 70? Again, everybody starts reaching for a calculator. I learned at a young age to use the "divide by 10" to simplify it. 14% is 10% + 4%. 10% is easy. So I've got "7" to start with. Now I say that 4% is 4 X 1%. 1% is also easy because , again, I divide by 10 and get .7. 4 * .7 is 2.8(because I memorized that 4*7=28 and , again, divide by 10). Now I've got 7 + 2.8 = 9.8. 14% of 70 = 9.8. No calculators needed despite not having 14% of 70 memorized.

 

We should encourage all critical thinking in math rather than poo poo-ing and saying "in my day...."

Some of what is part of CC math is just 'short-cuts'. Anyone who does enough math will develop the shortcuts naturally. Like tipping - 15%-18% is your target usually. Take total bill and take 10% - oh that is simply moving decimal one place. Then take 50% or half of that - and finally add together and bingo - you have your tip without knowing or using percentages at all. BTW, that will result in a greater than 15% tip since tax is in the total and usually not to be tipped on. So leaving the tax in helps round it up.

 

 

For the above I would this shortcut:

 

Original 325-38 = ?

 

Get to nearest 100s resulting in this modified equation:

 

(325-25) - (38-25) =

 

300 - 13 =

 

Now get to nearest 10

 

(300-10) - (13-10)

 

290 - 3

 

Now its real easy - 287.

 

No carries, no columns....

 

The thing is these are all just shortcuts (using acceptable math methods). Its really more advanced algebra - and understand the underlying rules should be part of the learning or understanding - not just showing some 'neat tricks'.

 

Similar concept but different relations used for me.

 

I simply say 325 - 38 is 328 - 40 + 2. Minus 40 part is easy to do in the brain and then I just add 2 since I only needed to take off 38 and not 40.

I understand this method a little better.

 

I round up in my head all the time to do this type of problem.

I round the bigger number down to the nearest 10 and the smaller number up to the nearest 10 and remember the total I adjusted (in this case 7)

Then subtract the two numbers and add back the left over amount.

 

325-38, becomes

320-40 (7 left over)

280 + 7 = 287

 

 

And if 320-40 isn't immediately obvious, just drop the 0 and 32-4=28. then add back the 0 for 280

We are on the same page Clyde :thumb:

My youngest is 21 so I'm not overly familiar with any of the "new new math."

 

I will say this. Memorization has value but so does thinking of numbers in a relational manner. Yes, it seems strange to go to a method to figure 9 + 6 when we can EASILY (key) memorize the answer. But what if it's 478 + 72? Now what? Well, most of us that can do calcualtions without pencils are now going to the relational method and there are different ways to get there.

 

What if it's 14% of 70? Again, everybody starts reaching for a calculator. I learned at a young age to use the "divide by 10" to simplify it. 14% is 10% + 4%. 10% is easy. So I've got "7" to start with. Now I say that 4% is 4 X 1%. 1% is also easy because , again, I divide by 10 and get .7. 4 * .7 is 2.8(because I memorized that 4*7=28 and , again, divide by 10). Now I've got 7 + 2.8 = 9.8. 14% of 70 = 9.8. No calculators needed despite not having 14% of 70 memorized.

 

We should encourage all critical thinking in math rather than poo poo-ing and saying "in my day...."

This!!! A thousand likes for this.
We are on the same page Clyde :thumb:

 

Essentially, we're using some sort of anchor number calculation like in the first example.

Essentially, we're using some sort of anchor number calculation like in the first example.
Right, and it doesn't matter the "anchor" you use, as long as it is consistent and you can apply it to varying problems accurately.
No, it's utterly pointless for real world use. Companies and employers are results oriented. They care about the solution to the problem, not how you get there.

 

If Common Core promotes better understanding, and helps more kids master higher level math skills, more people will be able to get the solution. That's our issue right now, not enough people can actually solve the problem. If you really care about results, more people that can get you those results is a good thing.

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