Someone on a message board asked for some helpful ideas to teach their child about place values and borrowing.  I posted a reply, but then thought that it may be good to share that information here as well.  After I posted my reply I saw that there were other suggestions that were very similar to mine.  I'm not a math major, but the process that I, and others, shared can be helpful in creating a picture in a child's mind or giving them something concrete to base the math problem on.  There are lots of great manipulatives on the market, and there are also lots of great math manipulatives right in your own home.  If you have dried beans, buttons, paper clips, popcicle sticks, game pieces, a rock collection, markers, crayons, or practically anything else you can use it as a math manipulative to help your child "see" the math problem.  This can apply to all sorts of math problems, but is very helpful with teaching place value and borrowing in a subtraction problem.   So, if you are looking for a new way to explain the math concepts of place value and borrowing here are a couple of suggestions.

Click 10 plastic blocks together as a "10 group" and then have 10 loose blocks beside it.  Talk about how it takes 10 loose blocks to "make up" or equal the block of 10.  If you are using buttons you can string 10 buttons on a piece of yarn or thread to make a group of 10.  If you are using dried beans place 10 beans in a small bowl.    Another mom posted a suggestion that said you could take 10 popcicle sticks and rubber band them together to make a group of 10.  You get the idea.  You may have to come up with a creative way to make a group of 10, but make the group so that you can explain that 10 loose beans are equal to the group of 10 beans in this bowl. 

You can do the same thing with pennies and dimes, You might try this process. Get as many pennies as you can possibly find (real or play money). Make a math problemlike 25 - 8 = ___. Write it really big on a large piece of paper and lay it on the table. Tell your child to count out 25 pennies and place them above the number 25, then 8 pennies above the number 8. (Or you can stack the problem and place 2 sets of 10 and 5 one's above the number 25.)  Then take him through the process of borrowing using the pennies to borrow from the tens to add to the ones. You may need to use a red permanent marker and color one side of the pennies in either the 10's or the 1's pile so that when he borrows he can distinguish between the original coins in the pile and the ones he borrowed.  This may create a visual picture within his mind that will help him process the concept.  If this works have him make up some problems of his own where he would need to borrow, then have him use the same process with the pennies to work those problems until it is cemented.  I suggest beginning with one's and ten's and not moving on to hundred's or higher until he gets the smaller place values so you won't create any confusion in his mind.

I hope these suggestions are helpful.  Sometimes we need to get creative in our own thought processes in order to meet our children's needs.  One mom suggested that you only work on this for about 15 minutes a day so that your child will not become frustrated.  I think that is good advice.  If your child is getting it and wants to continue, then do continue on a little longer, but be careful not to let it get to a point of frustration before stopping.  Small steps in learning are much better than working long periods of time to understand a concept if your child is frustrated.

Blessings!

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