Sharing With the Distributive Property

Sharing With the Distributive Property

     Sharing can be a difficult procedure for a young preschooler. When I first encountered the distributive property two years ago, I found the same difficulty in learning how to “share” the number outside of the parenthesis with the numbers inside the parenthesis. I had been away from college since 1995 and many of the math concepts were foreign to me. Thankfully, I was introduced to an explanation like the one here from http://www.northstarmath.com/sitemap/DistributiveProperty.html:

 Definition of Distributive Property

• Distributive property states that the product of a number  and a sum is equal to the sum of the individual products of addends and the number.

                     That is: a(b + c) = ab + ac

At first, I copied down this definition and simply applied it to every problem I needed to solve for the assignment. After working with the property, I started to make other connections that helped me understand this property.

    Look at the problem 4 (9 + 5) = x.  Imagine that 9 and 5 are friends of our dear number 4. Let's imagine that number 4 wants to spend time equally with both friends. Number 4 will visit number 9 and multiply. Then, number 4 will visit number 5 and multiplies. Like the example in Danica McKellar's book, the number outside of the parenthesis, 4, needs to split it's time fairly with number 9 and number 5 in terms of multiplication. Here is the solution:

            4 (9 + 5) = x

            36 + 20 = x

             56 = x

           

Here is a video that also addresses the distributive property:

     

     After tackling problems in algebra that utilized the distributive property, I was glad I had a good understanding of the basic concept. I happen to be someone who loves to share, so this helped solidify this concept in my mind. Teaching this concept may also require some creativity:

It may also require some stories concerning sharing and fairness that I have learned from the preschoolers in my life. After all, fairness is very important to a preschooler as well as to the distributive property!

Here are some additional resources and games:

http://www.freemathhelp.com/distributive-property.html

http://www.quia.com/ba/15357.html

http://www.glencoe.com/sec/math/brainpops/00112041/00112041.html

Playing Along a Number Line

Here it is… the best board game I ever played on family game night.

 

http://www.geekalerts.com/taking-pac-man-tetris-to-the-next-dimension/

This is Pac- Man, the board game. I remember not only trying to outwit the ghosts that my siblings controlled but also strategically gobbling up marbles. With the roll of the two dice, I moved my Pac-Man along the rows as well as the ghost of my choosing. Despite the fact that my brother loved to win and coulddn't stand losing, we always had a great time gobbling up marbles. Not only did the fate of my brothers rested in the luck of my roll, but I was also learning an important strategy in adding and subtracting.

     This game and other board games that use movement in terms of counting and moving pieces a specific number of spaces have a cousin in the number line. When I first encountered the number line in college, it felt like an old friend. In terms of board games, if my starting point is 5 and I am moving (adding) 6 spaces, I end up at 11. If I was unfortunate enough to move 3 spaces back from 5, I know that I will end at the number 2. 

http://www.youtube.com/watch?v=wzEZ1m9GUgM

The number line also helps students see the addition and/ or subtraction in action. Here is a video that addresses addition along a number line.

 

     This strategy not only assists students by providing a neat activity, but also helps students with mental math as they see the spaces traveled between numbers. Students can also move along a number line taped to the floor and "feel" the number of spaces moved. Moving from the number 5 to the number 11 as we add 6 spaces feels very different as we manipulate tokens or our feet along the number line. Playing with the number line has been fun for me as a college student and I see how students benefit from working with it. Here are some additional resources and games:

Resources:

http://www.math-aids.com/Number_Lines/

http://www.math.com/school/subject1/lessons/S1U1L11GL.html

 

 Games:

http://www.funbrain.com/linejump/

http://www.brainpop.com/games/battleshipnumberline/

http://www.sheppardsoftware.com/mathgames/earlymath/fruit_shoot_NumberLine.htm