I need something More in math

[Karen in CO]

We're currently using LoF Percents and NEM 1 for math which we've recently started. Yesterday we had a math crisis. My dd gets how to use the distributive property and can even demonstrate how it relates to real things like the area of rectangles, BUT she wanted to know WHY it works.

 

All of the explanations I've found fall into the what and how categories. We spent some time yesterday looking into the history of the distributive property (law), but it seriously highlighted that we're going to have a problem in math (again). I can see it on the horizon coming at me like giant snowball rolling downhill. She wants to understand how all of these mathematical properties came into being and why they work.

 

I'm certain that I need a theoretical mathematician to move in next door to me which isn't likely to happen. I also topped out at math after my Differential Equations class (and changed majors from physics to Comp.Sci. to escape more math). I am much more comfortable with procedures in math and don't really care for in depth discussion over the why's.

 

Help me find a math book or program that covers math starting with axioms and has a fully worked solutions manual. Is there also a set of math books that covers the history of math showing how it matured from tabulating crops to its modern incarnation?

 

Thanks

Edited October 19, 2011 by Karen in CO

[obsidian]

AoPS sounds like it would be a very good fit.:001_smile: they just came out with a Prealgebra book.

[wapiti]

On that note, you might see if this video on the distributive property or this sample section has the flavor of what you're looking for.

Edited October 19, 2011 by wapiti

[Crimson Wife]

Russian Math 6 from Perpendicular Press is supposed to be proof-heavy but it doesn't have a complete answer key. Could you maybe use the explanations in the RM6 text with the problem sets in NEM?

[Ray]

Mathmatics 6, Nurk (russian math 6) for the grit, and Mathematical Thinking, Tanton for the 'something else';)

 

http://www.jamestanton.com/?category_name=think-math

[kiana]

For a response to her specific question: If the geometric applications don't tickle her 'a-ha' buttons, an arithmetic answer could be:

 

With integers, we can view multiplication as repeated addition. If she is (for example) trying to do 4(2+3), we could do (2+3) + (2+3) + (2+3) + (2+3), which is just 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 when you remove the parentheses.

 

Using the commutative and associative properties of addition, we can rewrite this as 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3. But what's 2 + 2 + 2 + 2? Why, it's 4x2! And similarly, 3 + 3 + 3 + 3 is 4x3. So it's 4x2 + 4x3, which is what the distributive law says it should be.

 

Others already recommended AOPS, which is all I can think of for her level :P

[Emerald Stoker]

nm

[5 Hikers]

We're currently using LoF Percents and NEM 1 for math which we've recently started. Yesterday we had a math crisis. My dd gets how to use the distributive property and can even demonstrate how it relates to real things like the area of rectangles, BUT she wanted to know WHY it works.

 

All of the explanations I've found fall into the what and how categories. We spent some time yesterday looking into the history of the distributive property (law), but it seriously highlighted that we're going to have a problem in math (again). I can see it on the horizon coming at me like giant snowball rolling downhill. She wants to understand how all of these mathematical properties came into being and why they work.

 

I'm certain that I need a theoretical mathematician to move in next door to me which isn't likely to happen. I also topped out at math after my Differential Equations class (and changed majors from physics to Comp.Sci. to escape more math). I am much more comfortable with procedures in math and don't really care for in depth discussion over the why's.

 

Help me find a math book or program that covers math starting with axioms and has a fully worked solutions manual. Is there also a set of math books that covers the history of math showing how it matured from tabulating crops to its modern incarnation?

 

Thanks

 

Your daughter is going to do so awesome in college! She needs a field that requires Calculus based Physics. A good read for her would be John Hudson Tiner's book on Exploring Mathematics. It gives the history behind it.