Me trying to complete the completing the square pages. I hope you can see that part of this is showing you repetitive lessons that get the students ready for "advanced" mathematics, but it's not advanced if the various parts are easily understood.
Basic concepts like understanding the equals sign means SAME dividing by two, what a square number is and what square root means need to be understood and internalized WHILE we learn concepts in algebra. Being able to write an expression different ways but have it be the same just in different forms need to be understood too.
Just playing with square numbers at an early age teaches so much, and more importantly makes life easier later. This page takes you from lessons with toddlers to lessons with high school students all centering around completing the square.
From things as simple as multiplying and dividing by two, building and knowing square numbers, how to square numbers that end in 5, square numbers whose roots we call radicals--so many fun things we can do with with square numbers including delve into the imaginary.Don't worry we won't go there this time around, but we will head down the road to understanding where the quadratic formula comes from and how to derive it.
But we get there in baby steps. Understanding basic concepts along the way.
So I have added a little to the basic completing the square page. Now when you go there you can end up
which is the entrance page to a nice little page chock full of lessons on completing the square and square numbers. It even contains a link to this blog that you may have missed because it's a few years old, driving home the point that the posts get old but not the lessons on those posts. The page has videos that very few people have seen according to their hit count on youtube because they are not public (I'm talking to you Shalynn). Start at the top and work your way down. Now that you know where you are going maybe you will look at those early videos differently.
The password you need is the sitewide password. Those that have a lifetime pass just got ye more value for money already spent. You won't find the videos on these pages anywhere else. They don't come up in searches, you have to know the link. Here is a much more detailed tour of what you get on this page. I could make a PDF on this one topic alone like Supremely Simple Subtraction or Divinely Dandy non Difficult Division--but it's going to be awhile.
Please come back and leave a comment for others.