AoPS newbie here! What is good pace for AoPS Pre-Algebra? How to use Alcumus?

[matrips]

I bought AoPS pre-algebra over Christmas after toying with the idea for awhile. So now what?

 

Is there a standard pace that 'most' kids should work at? So far my kids have just taken it this week to read and work out problems in their head, or explain a few to me. Should they be writing stuff down? Will that be more obvious as they get further? 'Should' they watch the Alcumus videos? Do they go along with the book or are they extra problems? Do you teach it or can they just read it and work through it? Does it depend on the kid?

 

Background: they completed Singapore EB-6B including all IP and CWP. Completed an online Prealgebra last year and went halfway through an online Algebra this year. They're only 6th grade though, so I'd rather slow them down and cement concepts really well. AoPS sounded different enough to do this without being a repeat of their previous books. Plus my one kid would enjoy math competitions and AoPS seems good for that.

[daijobu]

I don't know what most kids are doing, so I'll tell what I did with my daughters.  

 

We did one section of the chapter each day.  (Usually, there are rare cases where we spread it out over 2 days.)  We work through the problems together, with me writing out the solutions, demonstrating good documentation.  By that I mean having the equal signs lined up, using arrows to mean "implies" and avoiding other notation errors such as stream of consciousness equalities.  Building these habits now, will help in solving more complicated problems in the years to come.  

 

Then my students do the exercises at the end of the sections on their own, checking their answers in the solutions manual and checking with me if they don't understand anything.  At the end of each chapter they spend roughly 2-3 days each on the review problems and chapter problems.  

 

My kids didn't care for Alcumus.  We watched some of the videos (don't miss the LCM one!), but didn't watch many of them.  

 

I agree with taking your time and making sure everything is solid before moving on.   Avoid doing anything in your head; write every step down even if your student already knows how to do it.  You never know if they don't.  If they forget something like what negative exponents mean, resist the urge to just tell them the answer.  Go back to that section of the book and go over again the motivation and or the derivation.  It's a good idea for students to keep some "back of the envelope" quickie derivations for stuff they forget.  Forgotten the quadratic formula?  Begin with ax^2 + bx + c = 0 and complete the square.  Every time.  

 

Now is a great time to lay down those good habits!  I remember those years fondly.  

 

ETA: cleaned up my writing.

Edited December 31, 2016 by daijobu

[Lilaclady]

I think t is very important for the students to be able to show their work. It helps them/ you see their reasoning and helps then when they need to proof their work.

 

I assign a specific time usually an hour and they work until the time is up. We have supplemented with alcumus but that is done outside of school time or when I am occupied and they need to be engaged doing something.

We do watch the videos at the beginning of each chapter unless there are lots of videos then we will do a few and spread them out.

We have typically finished a book in a year doing this.