A twist on multiplication flash cards.

I read a short ebook this week by Renee Ellison called Teach Math Faster.  (Quick read, only $0.99 on Amazon Kindle.)  She has some very good hands-on ideas for helping children with math basics.  One of them was a twist on the tried-and-true multiplication flash cards, in which she added a visual representation of each quantity instead of simply writing the numerals.

Why is this helpful?  Because the more often a child can use concrete ideas when learning math, the better he will understand what the numbers are doing. Math educators call this "number sense."  For example, instead of rotely memorizing the words and symbols of
6 x 4 = 24,  the child using Ellison's flash card design sees an array of 24 blocks, arranged in four rows of six blocks each.

This is the front of a
Teach Math Faster flash card.

Now of course, children who are old enough to learn multiplication will have long mastered the concept of number symbols standing for quantities.  However, many children have only a shallow understanding of what multiplication actually means.  They will use "times" as a verb-- "I can times six an three"-- in the same way that my children used to think that verse was a verb meaning "to defeat"-- as in, Godzilla versus ("verses") Megalon.  (They would say, "I'm going to verse those bad guys!")  But when the front of the flash card shows a graphic representation of what  "six times four" means, the concept is reinforced at the same time that the memorization is taking place.

An added dimension of concept reinforcement occurs when a range of multiplication facts is studied-- while "8x7=56" uses the same number of digits as "2x5=10," there is a clear difference between the space occupied by ten squares compared to fifty-six squares.  The child's number sense increases when she sees just how much bigger 56 is than 10.

On the back of the flash card, Mrs. Ellison repeats the array, this time without the numbers, and provides the product:

This is the back of a Teach Math Faster flash card.

So when the child is using this flash card, he is reading the numbers on the front and multiplying them in his head just like a traditional flash card.  He checks for the correct answer on the back, just like a traditional flash card.  But his brain is experiencing something totally new: the abstract symbols are gone, replaced by a picture of what's happening in the problem.

Genius!

Now for the bad news:  as far as I know, this style of flash cards is not commercially available.  Like the other manipulatives in Mrs. Ellison's little book, they have to be home made.  She recommends using graph paper to keep the size of the squares consistent-- otherwise, there is less visual impact in the size difference that I explained above.  So you-- or your child-- write the numbers in the squares and cut the arrays out, then glue them onto index cards.

One suggestion I would make:  if you are using color-coded math manipulatives such as Cuisenaire rods or Math-U-See blocks, match the flash cards to whichever set you're using.  It's as simple as adding lines of the appropriate colors to the edges of the array on the front side of the card, like this:

This array matches Cuisenaire rods, with
forest green for 6 and magenta for 4.
Math-U-See would use purple and yellow.

Cuisenaire rods and Math-U-See blocks
use different colors to signify quantities.

Be sure not to color-code the back side of the card, however, because that would too quickly give away the numbers that the student is supposed to be memorizing.  The array itself already shows the answer if the student counts the blocks, but he still has to work for it. Color-coding the front side makes sense because the number symbols are also written in, so nothing is being given away.

As mentioned in a previous post, adding color provides one more level of connection for the brain.  If your child already associates certain quantities with specific colors, tapping into this association will increase his number sense as he learns his multiplication facts.