Whenever I feel like I have nothing to wear (yet a closet full of clothes!), I like to dig through my closet and wear old pieces in new ways. Yesterday, I posed this real-life dilemma to our students:
In my closet, I have three kinds of tops: tank tops, t-shirts, and sweaters. For bottoms, I have shorts, skirts, slacks, and jeans. How many different outfits can I make using one top and one bottom?
Some students, like Morgan, chose to approach this problem using pictures:
We agreed this was a good start, but then realized we were missing combinations because we were just guessing and checking. Some students, like Shawn, tried making combinations in order, for example, finding all the possible combinations with a tank top before moving on to combinations for a t-shirt:
Dylan showed us how to make an organized list to show all the possibilities.
Here's another variation of an organized list Ben shared:
And one from Devin:
When Luis showed us his picture and organized list, he also explained that he used repeated addition to find the number of combinations:
Since repeated addition is multiplication, we saw a connection.
Now we can multiply to solve combination problems!
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