Apples and Oranges: Hands-on writing equations from word problems with variables.

For some people, writing an equation from a word problem comes easily and for others it is a struggle.  So, when we started working on these equations, I found that hands on was just one way to access it.  We started with fairly simple problems that involved fruit.  For example:

Greenie and Honey each go to the farmer's market.  Greenie comes home with 3 bags of fruit plus 4 pieces of fruit.  Honey comes home with 2 bags of fruit plus 7 pieces of fruit.  Each bag of fruit contains the same number of pieces of fruit.

(Here the students put together some representation of fruit and bags of fruit.  For the first problem, I had the bags loaded already with a solution.  We used coins to represent fruit but you could use pictures of fruit, actual fruit, colored counters, etc.)

Step 1: Write an equation for the amount of fruit Greenie has:

4 + 3B = G

Step 2:  Write an equation for the amount of fruit Honey has:

7 + 2B = H

(At this point, most of the kids were able to not only write an equation but represent the equation with the manipulatives, in this case, coins.  For example, they laid out 4 coins and 3 bags to equal Greenie)

Step 3: If Greenie and Honey came home with the same amount of fruit each, how many pieces of fruit are in each bag?

So, here's the cool part.  The kids set up the two groupings to equal each other, and then by taking away parts from each side equally, they come to the answer.

I also showed it graphically with dots (fruit) and squares (bags).

And finally, with pencil and paper:
7 + 2B = 4 + 3B
(7-4) + 2B = (4-4) + 3B
3 + 2B = 0+3B
3 + (2B-2B) = 0 + (3B-2B)
3 = 1B

We did some more practice with similar problems and then the kids wrote their own problems for a partner and had the partner solve it.  They really loved this part!  They even set up the manipulatives for their partners.  It was a solid way to play with writing equations from word problems.