As I went though my 4th graders math book, I couldn't find definitions for the rules of Algebra
that was clearly stated and didn't have variables in the examples.

After perusing a few sites I found one that I thought would be good.
Even so, I wasn't to pleased with their examples and removed the
variables from the examples, keeping only a, b, c for simplicity.
Then I just substituted different numbers for each either 1, 2, 3
or 2, 3, 4. I would explain these are simple substitutions
so that the 4th grader would learn variables could be anything.

I've included the Algebra Properties pdf with the information, an education link,
and my source for the definition of the algebra properties. I made a table, then
as you will see I had and issue with it. Finally a summary of
what I've concluded. I would appreciate any thoughts you might have.

Thanks.

 

You seem surprised that 14 doesn't equal 20. Are you saying that we should be teaching kids that it does?

The distribute property is sometimes described as saying that the product of the sums is equal to the sum of the products.

That a(b+c) is not the same as (a+b)c should not strike you as unreasonable.

Let's look at a couple of physical examples.

You have rugs, both of which are a = 2 ft wide. One of them is b = 3 ft long and the other is c = 4 ft long.

They are laid out end to end to cover an area that is 2 ft wide and a total of 7 ft long. What is the total area covered?

Area1 = (2 ft)(3 ft + 4 ft) = (2 ft)(7 ft) = 14 sq ft

Now you take another two rugs, both of which are c = 4 ft long but one is a = 2 ft wide and the other is b = 3 ft wide.

These are laid out side-to-side to cover an area that is 4 ft long and a total of 5 ft wide. What is the total area covered?

Area2 = (2 ft + 3 ft)(4 ft) = (5 ft)(4 ft) = 20 sq ft

Let's confirm this by adding up the areas of the individual rugs involved.

In the first case, rug #1 is 2 ft x 3 ft and rug #2 is 2 ft x 4 ft. The first has an area of 6 sq ft and the second has an area of 8 sq ft for a total of 14 sq ft.

In the second case, rug #3 is 2 ft x 4 ft and rug #4 is 3 ft x 4 ft. The first has an area of 8 sq ft and the second has an area of 12 sq ft for a total of 20 sq ft.

 

As I went though my 4th graders math book, I couldn't find definitions for the rules of Algebra
that was clearly stated and didn't have variables in the examples.

After perusing a few sites I found one that I thought would be good.
Even so, I wasn't to pleased with their examples and removed the
variables from the examples, keeping only a, b, c for simplicity.
Then I just substituted different numbers for each either 1, 2, 3
or 2, 3, 4. I would explain these are simple substitutions
so that the 4th grader would learn variables could be anything.

I've included the Algebra Properties pdf with the information, an education link,
and my source for the definition of the algebra properties. I made a table, then
as you will see I had and issue with it. Finally a summary of
what I've concluded. I would appreciate any thoughts you might have.

Thanks.

I'm not sure what you mean by "definitions for rules". IMHO rules don't have definitions. It sounds like you're having difficulty understanding basic concepts expressed in plain English. I don't if there is any help for that. It is also obvious that you are unaware that there is more than one kind of algebra and are similarly unaware that all of the algebras that you will ever see besides all the ones that you won't ALL follow the same pattern of rules.

Before throwing stones at the material, it might be a good idea to try to understand it before trying to help a fourth grader with the problem. If you don't understand it, then you're just making the problem worse. Fourth graders actually have pretty good BS detectors and seem to know instinctively when they are being instructed by someone who is not familiar with the material. Don't pretend to be knowledgeable when you are not. You can however admit that you're uncertain about it and work through it together.

You are correct that you don't need variables represented by letters to explain what is going on. You can stick with single digit numbers and the four basic operations of arithmetic. You explore each of the properties with examples of how they work with addition and multiplication and counter examples of how they don't work with subtraction and division.

If you want to help your 4th grader start by having a conference with the teacher and listen to the kid.

 

You seem to have missed that the second example of the distributive property IS IDENTICAL to the first example but with different numbers and swapping the variables a & c.

(a+b)c
= c(a+b) ‘commutative property of multiplication
= c(b+a) ‘ commutative property of addition

Then, swap the variable names for a & c.
= a(b+c)

And thus I’ve shown that the two examples are identical. There is no problem in what we are teaching our kids.

 

I'm not sure what you mean by "definitions for rules". IMHO rules don't have definitions. It sounds like you're having difficulty understanding basic concepts expressed in plain English. I don't if there is any help for that. It is also obvious that you are unaware that there is more than one kind of algebra and are similarly unaware that all of the algebras that you will ever see besides all the ones that you won't ALL follow the same pattern of rules.

Before throwing stones at the material, it might be a good idea to try to understand it before trying to help a fourth grader with the problem. If you don't understand it, then you're just making the problem worse. Fourth graders actually have pretty good BS detectors and seem to know instinctively when they are being instructed by someone who is not familiar with the material. Don't pretend to be knowledgeable when you are not. You can however admit that you're uncertain about it and work through it together.

You are correct that you don't need variables represented by letters to explain what is going on. You can stick with single digit numbers and the four basic operations of arithmetic. You explore each of the properties with examples of how they work with addition and multiplication and counter examples of how they don't work with subtraction and division.

If you want to help your 4th grader start by having a conference with the teacher and listen to the kid.

Did you bother to go look at the original source material from the henrico.k12 link?
You just can't give a kid these are rules and not explain it to them, you seem to have missed that.
When was the last time you tried to help a 4th grader with math?
When I saw the distributive property...presented by henrico (ibid) it didn't make sense to me.
If it does to you, good for you. However I can't find the list any longer, imagine that.
Cheers

 

However, here is the source document to which I was referring.
It is attached.

 

Does something still not make sense to you?

If so, you need to be pretty explicit about what is still bothering you. If possible, what you think is wrong and what you think it should be.

Do you understand that your prior line of thinking that a(b+c) must produce the same result as (a+b)c was incorrect?

 

Did you bother to go look at the original source material from the henrico.k12 link?
You just can't give a kid these are rules and not explain it to them, you seem to have missed that.
When was the last time you tried to help a 4th grader with math?
When I saw the distributive property...presented by henrico (ibid) it didn't make sense to me.
If it does to you, good for you. However I can't find the list any longer, imagine that.
Cheers

I looked at what you posted, and I looked at the link. Since I am fully familiar with the topic, I did not notice anything unusual. I literally have no idea what you are going on about. I first encountered the material in 1959 as part of a program sponsored by the SMSG (School Mathematics Study Group). It sparked a lifelong interest in science and technology in the aftermath of the large public freakout over the launch of Sputnik (Oct. 4, 1957). You seem like a well-intentioned individual that wants to help your 4th grader. Why don't you spend your time educating yourself so you can do that and quit looking for validation from the great unwashed masses on a public forum.

https://en.wikipedia.org/wiki/School_Mathematics_Study_Group

 

There is nothing inconsistent in your attachment. I suggest instead of questioning it, you take the initiative to understand the material as it is not going to change. It has been taught this way for ages.

 

Something that might help you is to note the following:

The "rules of algebra" that you are referring to are not rules of algebra, but rather rules of arithmetic -- or more precisely, the properties of arithmetic operators.

Moving from arithmetic to algebra does not change these, so if these are what is causing you issues, the answers lie in looking at arithmetic concepts, not algebraic ones.

Then you talked about removing the variables so that they don't confuse the student -- but that defeats the whole point of elementary algebra, which is to move from arithmetic, with its fixed values, to using variables so that ideas and claims can be shown to be true for any and all values that might be used, or to determine the values for which the claim is true, or to establish that the claim is not true for any value that might be used.

As for what you might call the "rules" of algebra, they are pretty basic (and I'm probably going to overlook something).

First and foremost -- if an equation is true, then it remains true as long as you do the same (allowed) thing to both sides. The "allowed" caveat prevents such actions as dividing both sides by zero and then claiming that they are still equal. All bets are off in that case.

If you have an inequality relation, then if you multiply (or divide) both sides by a negative value, the sense of the equality is reversed.

 

I think you can browse khan academy's algebra videos.