I’m trying a new approach, called array cards, I stumbled across the other day with Emily to help her be able to memorize multiplication facts easier.  I’m making them more visual for her. 

This was my first version.  I cut graph paper that I printed off from here into the shapes of multiplication problems and labeled them but then I didn’t end up liking the way they looked.

Then I tried to make it more visual for her by showing the addition way along with the multiplication way.  Didn’t really like that either.

I finally found a way to do it that liked.  I had her cut out squares and rectangles of any size and then she counted the number of squares inside the shape and wrote it down.  We then cut 2 more identical shapes and labeled them.  We wrote the multiplication sentence one way when turned one direction (6 x 3 = ) and we wrote it the other way (3 x 6 = ) on the shape that was oriented the other way.  Make sense?  See the picture to make my jumbled talk more understandable.

This way makes sense to her and now I can use these as flashcard.  She gets the connection between the shape and the number sentence.

Here are the multiples of 3 done.

This led to her finally understanding what square numbers were.  The shape that a number multiplied by itself makes is a square while the rest of the shapes are all rectangles.  See the squares at the bottom.  It was an a-ha moment!

This led us to a better understanding of what division really means and why the division sign looks the way it does.

15 divided by 3 really means that if we have 15 blocks and arrange them in rows of 3 then we will have on the left side of the division bar and how many blocks go across the row at the top? 

Get it?  I first learned this explanation from the guy on Math-U-See.  Makes the division sign make so much more sense when you know this, right?

And for 15 divided by 5, we just turn the block in the middle or make a new one the same size but oriented differently and so the same thing. 

Square roots work the same way...the sign just has a funny little tail :)

link to printable graph paper site I used.

I thought these two “make math easier” videos were good, too.

I sure wish I would have taught my kids this way.  It makes way more sense and prepares them for moving over a space when learning how to multiply two-digits numbers

This sure does make multiplying by 11 so much easier...strange robot voice though