Tuesday, May 1, 2012

Commutative Property With Dominos


Domino Math –
One math concept that really helps kids with using math facts quickly is that of the "turn around fact or pair". The concept uses the commutative property which basically says that a+b will always equal b+a.  It is not important that the child know the name of the property, what is important is that she/he encounter examples of it enough to see a pattern and use it to his/her advantage.

For example if the child is very familiar with the result of the commutative property, then if she/he knows that 13 + 8 = 21 then when he/she has to calculate 8 + 13 on a timed test, she/he can speed things up because he/she already knows the answer rather than having to calculate it.  Unfortunately, most kids do not make this connection until much later in school.  Young children usually see math problems as distinct from one another and only begin to understand and use "the rules" for themselves after they've seen the pattern form many times.  They WON'T just take the teacher's word for it.  Many courses teach the concept in one or two lessons, but don't spend enough time with it to make it truly helpful or useful to the elementary mathematician.  

This activity helps kids put a "picture" in their minds of what addition looks like, and makes it a simpler challenge because they are not also concentrating on reading number symbols, or writing number symbols that are probably relatively new. It allows them to concentrate on the concept of addition only.  After they get the hang of the activity shown in the video, it is even easy to turn the whole thing into a game.  If you'd like to do the activity my daughter is doing in the video on this page with your own child here are the instructions for what we are doing:

1. When we started, I pulled out all the dominoes that added up to 10 or less. This way the activity is not overwhelming and remains appropriate for early mathematicians. 
video

2. My daughter was asked to add the dots from one side to the other side and place the dominoes in piles according to what they add up to in ascending order.

3. While doing the first couple of tiles, I taught my daughter how to "read" the domino in a math sentence - i.e. "2 dots + 3 dots = 5 dots". I then asked her to do the same with some of the dominoes she picked.  We did each domino both ways so she also read "3 dots + 2 dots = 5 dots".  Eventually, they get the idea that it doesn't really matter which number you start with in an addition problem.

4. After she was done sorting we looked at the relationship between how high the number is and the increasing number of ways to "add up to" that number.

5. After knowing she understood she could start with any number she desired I encouraged Alice to "count on" by stating the higher number of dots first and starting her counting from there, "7 + 3" would be counted "seven, eight, nine, ten." As I modeled this for her, she will used this technique more and more. Once your child is confident with his or her facts to ten, go ahead and work on facts to twenty.  Once they are comfortable with this, start giving them a third domino (with no dots on one side).  They then begin adding three addends.  Continue adding challenge this way until they've grown out of the activity and you've replaced it with other methods for practicing math.

By the time we were done with one round of this game, she realized that "0's" add nothing and to check her idea said, "mommy, if I add 0 to 12 is it 12?" She was also asking me about higher numbers plus one that whole afternoon. 

Interest won't last long with this activity because it becomes repetitive even for younger kids fairly quickly. Continue the activity until your child loses interest and then don't push. They are very likely to be interested again another day whereas, if you push, they'll lose interest all-together.  


Once they've gotten the hang of it, you can turn it into a game for more than one player.  


1.  Pull out 20 or more dominos that are appropriately "spotted" for the age and ability of each child.  For example, for a group of Kindergartners, you might use mostly dominoes with one side dotted and the other blank and make sure no sets of dots add to higher than 8 or 12 etc.  For more experienced mathematicians you might skew the domino set to higher numbers and make sure there are not any "zeros".  I do not suggest using the entire box because then the game becomes tedious for all its players and your children will not want to play it.

2.  With your child or children, flip all the dominos over so none of the dots can be seen and mix them up.  Each player pulls a domino and adds both sides together.  Each player must state their domino's identity using two "math sentences" that are accurate (3 dots plus one dot equals four and one dot plus three dots equals four) The person with the domino with the highest sum wins everyone else's dominos.  Play continues until all the dominos are taken from the middle and a winner is established based on who won the most dominos.

When this game is played frequently, those playing are getting a lot of practice with their math facts as well as examples of the commutative property.  If a child is having trouble coming up with a second "math sentence" simply turn the domino around to illustrate the new "problem".  This game is simple and quick enough to be as much fun as Hi Ho Cheerio was when she/he was first learning to count, but more suited for the slightly older child.

Intermediate
Add another level to your domino math practice with dice.  Pull out a selection of 20 or so dominos.  you'll probably want to skew the dominos you pull out toward the higher end of the spectrum of sums you can get from the dominos.  Have your child pull a domino, add the two ends and then roll the die and subtract the amount on the die.  Take turns doing this and when everyone has one domino sum compare.  The person with the highest sum wins all the dominos.  Play until all the dominos are gone and declare a winner based on who collected the most dominos.  Since multiplication is really the addition of sets of numbers, commutative property also works with multiplication so if you have a child working on his/her multiplication tables this can be played using multiplication as well.

If you wanted to add a board game element, you could move a piece around a board game (such as chutes and ladders) instead of "keeping" dominos for scoring. for correct answers they can move forward by the numbers added or just by one.  The winner then becomes whoever gets to the finish first.  Be creative with it and have some fun.

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