Resource/examples for how to write out math work?

[Allearia]

My son is doing AOPS Algebra, and I am trying to help him learn to write out the solutions properly. I don't know how much detail I should require. For example, should they be similar to how they are written in the solutions manual? They seem to be more detailed than he needs. At this point I just want him to be able to write the answers neatly in his notebook so I can see the steps he took and how he solved the problem. It seems as though it would be obvious but for some reason I am not figuring out how to explain it to him. I am planning to go through some of the problems and write out answers as an example but if anyone has any tips that would be great.

[Kathy in Richmond]

Here's some help from AoPS:

 

How to Write a Solution

 

Kids taking the AoPS online courses will be gently nudged to follow these guidelines as the class progresses. If you're doing AoPS at home, try to implement a bit of this each week. When I taught middle schoolers in CTY, I gave the kids (mostly 11 and 12 year old boys) one goal per weekly homework, starting with legibility and working up to these rules.

[regentrude]

The solution manual includes verbal explanations for the students - the student does not need to write those.

I expect my student to:

-write down given information, expression, initial equation

- for a word problem: make a drawing, give symbol names to all quantities, write down relationships between them in the form of mathematical equations

-show all steps he makes while manipulating the equation

- have only one equation per line - no run-on equations

- have equal signs neatly aligned underneath each other

-double- underline or box his final answer

 

 

I prefer a beginning algebra student to put a vertical line behind the equation and to indicate which operation he is going to perform to both sides. Students in my home country are routinely taught this procedure, and it cuts down on errors.

For example: Let the problem be "Solve the following equation for x:  2x-5=-8x", the solution should look like this:

2x-5= - 8x   | +5

2x   = - 8x +5   | +8x

10x = 5  | :10

x    = 5/10

x=1/2

 

I have been teaching it to both my students as an initial tool; advanced students will no longer show this, but simply perform the operation. But for beginners, it is a good reminder. For an advanced student, the solution to the above equation would more look like:

2x-5=- 8x

10x=5

x=1/2

 

 

[daijobu]

- have equal signs neatly aligned underneath each other

 

 

 

 

I'm a huge fan of lining up my equal signs!  I picked this up from our high school math teacher years ago.  I also like to underline terms as they are combined or rearranged, so we don't lose any along the way.  

 

While I'm on the subject, I find it helpful when dealing with 2-3 equations at once is to number them, and keep them labeled as I use them.  

[regentrude]

While I'm on the subject, I find it helpful when dealing with 2-3 equations at once is to number them, and keep them labeled as I use them.  

 

Absolutely! I teach my children to do this as well.

[Twigs]

:bigear:

[Allearia]

Just wanted to come back with a belated thank you. We've been working on it, although we are also going through some remedial handwriting practice that will help a lot. I also did have been working through some problems myself and showing them to him, I will have to do the lining up equal signs thing, thanks! He has also been trying graph paper, but the paper I got i think the lines are too dark so it hasn't helped the readability so much.

[kiana]

A general comment on math work:

 

Please make sure that your son knows that '=' should only be written between quantities that are actually equal. It is very common that people will write '=' to mean 'and my next step is', which really hurts when students are required to use the transitive property of equality.

 

To give a very simple example -- make sure that work for 1 + 2 + 3 + 4 isn't shown as something like '1 + 2 = 3 + 3 = 6 + 4 = 10'