Base Ten Blocks Make Algebra Child's Play

Base Ten Blocks Make Advanced Algebra Child's Play. For those of you wondering if the work I do with younger kids makes a difference when they are older...that picture was taken with some very young students (8 and 9 years) who at the time were learning much more about 8 + 8 and 8 x 8, and that 64 is square, than they were about algebra.

This post will eventually be on one of the password protected pages (Advanced Algebra) but you are getting these videos here for FREE. Eventually, this post will get buried on this blog and people will have a hard time finding it. As I have often said these posts get old but they don't get out dated...use the methods you find here on your students. They work.

And again if they work on little kids they will work on high school kids and college students too. The idea is to introduce CONCEPTS in stages and get comfortable with them THEN add more and a little more. It is good to start with something easy and familiar so they get the grasp of it..."it" being the concept or idea rather than deluge them with a huge amount of unfamiliar math all at once. This is what textbooks do. They put too much together at once and it becomes overwhelming and confusing.

Start with completing the square. I have lots of vids and pages devoted to that, making it easy and using it to teach children more than just algebra but also counting and dividing by two and addends and multiplication. But when the time comes they are quite familiar with completing the square and factoring. Being thus grounded, it's easy to add new concepts and more understanding. So lets begin with this:


This video is not listed so please don't share it unless you are sharing this whole post.

Being able to count by square numbers all the way to 25 is also a good skill to have...

Note that I start off with lessons on making squares and square numbers. Imagine that.
Being able to square numbers quickly and easily makes this vastly simpler for understanding because that part is out of the way as it were. So when we want to take half of the x and square it it's no problem (get it?) even if the amount of x is odd...as Forrest would say: "That's good, that's one less thing." [To worry about.]

Being able to square numbers that end in 5 is a good skill to have but rather than memorize some rule I show them where the rule comes from and math is less mysterious.

You may also note that using base ten blocks to make algebra easy has benefits where kids can see the relationship between squaring 35 and getting 1225, and taking half of 7 and squaring that and getting 12.25...a lot of older students just go, "OH! Well then that's easy..." Usually they hate any of the ones that have fractions in them...but that's easy too. I find fractions are almost universally a stumbling block.

After you've watched the first one up there lets go back and really get the concepts down.

So lets back up, keep it easy and start with something REALLY familiar and focus:



And then a little practice.



And a little more:



And now they look like the little geniuses they are and are ready to play with the quadratic:

This video is not listed so please don't share it unless you are sharing this whole post.

I spent another class where instead of dividing by "a" we multiply by "4a" to make it easier but that video is lost. You can see a stale presentation of it here though:



With the DBoyz I some questions and really got into why we complete the square with b²...

And now we are ready to start playing with ones that have more negatives...and instead of real roots imaginary ones and so on...what do you think? By the time they are in high school will this stuff be easy or hard for them?

And it all started with taking x² + 2x + 1, taking the x and putting them on the sides and putting the one in the corner...then moving on to 4x and 6x and 10x...with base 10 blocks they can see what they are doing get their hands on it and then when we move to mostly symbols it makes sense. 

This is one of they key differences we find with kids who learn math using base ten blocks they can see the relations ships and math isn't a confused segmented set of mysterious rules. And then completing the square and vertex form are much more easily understood and relate-able, the students see how it all goes together. I have found that using base ten blocks makes things like distance formula, Pythagorean theorem, and the first trig identity go together in the students heads too...instead of being completely separate things.

Using base ten blocks in a step by step approach can make math child's play for your students too. Manipulatives make math easy and fun, it's just counting. I've tried to give a detailed explanation via the videos here but if I left something out or you have further questions please comment below...