Distributive Property and Combining LIke Terms

Thanks to Julie and Nora, I was inspired to introduce combining like terms and the distributive property to my students using some manipulatives.

I started with a grocery bag (one of the ubiquitous freebies emblazoned with a company logo), a dozen ziplocs, some buttons, some paper clips, and some cap erasers.

Like Nora suggested, I set up some ziploc bags with a few items and I made several identical ziplocs.  To make it easy for my students to differentiate between the bags from a distance, I placed a piece of colored card stock in each bag.  The set up is illustrated on the ISN page below. 

Students volunteered to come up one at a time to place items in the grocery bag or remove them from the bag.  They could only touch one kind of item per turn (so Ziplocs with yellow paper, loose buttons, Ziplocs with red paper, etc).  We started with combining like terms using just the loose items and tried three practice rounds.  Each time, I asked the students how many of each item were in the bag before we showed how to write the answer algebraically.

Then I introduced the Ziplocs to the activity.  We discussed how parentheses group items in math just like the clear bag was grouping the items.   Some of my students erroneously thought that we could show multiple identical bags by using an exponent but with some follow up questions they decided that multiplication was what they really needed.  Again, as we wrote our expressions, I had students predict the simplified expression before we wrote the work algebraically.

The real magic happened when they had a homework problem like 9[5 + 2(x + 3)].  I asked, "if the parentheses are represented by the ziploc bag, what would the brackets represent?"  They told me the brackets were modeled by the grocery bag.  "How many grocery bags would we need?"  They decided they would need nine grocery bags.

I wish I had done this activity using pennies as well.  If I had, I would have made them each worth 1 instead of assigning them a variable.  One point of confusion I saw after this activity was what to do with an expression like 12 + 5x.  Many of my students tried to make that 17x and I think we would have done well to have constants in the original lesson.


Thanks to Julie and Nora for the inspiration.  I was so excited about this lesson that I immediately shared it with my colleagues.  This is the best part of the MTBoS- great lesson ideas at your fingertips, tried out by real teachers!  

Mathematically yours,
Miss B