What is 24?
I project one of each level (the dots in the corners represent the levels) and students work on a level of their choice. They record their solutions in their journals.
So Much Good Math!
This one's kind of a no-brainer. We discuss order of operations a LOT during 24's. Here's an exampe from today. In our level 3 problem, a student gave the following solution: (21+9)/(3+14) We solved...it wasn't correct...so I asked her what steps she wanted to take to solve and she quickly realized the second set of grouping symbols were actually making it not equal 24. |
In our level 1 problem, one student gave the following solution: 17-(4+3)+14 Later, we had this solution: 17+4-3-4 Here's the (edited) dialogue that happened in class: Me: Is this a unique solution or is it the same as one we already have? (spattering of responses..."same", "different") Student 1: I think they're different because in the first one we're adding 3 and in the second one we're subtracting 3. Student 2: I think they're the same because in the 1st one we're adding 3 to 4 and then subtracting so we're actually subtracting 3 and 4. Student 1: Oh yeah, I see. We are taking away 3 so, yeah...they're the same. Me: Does anyone know which property this is showing? (1 student raises their hand...shocker) Student 3: (shyly)......Distributive???..... And the conversation takes a side track about how we should be confident in our guesses.... Anyway, we are constantly pointing out how different solutions are the same based on Commutative, Associate and Distributive properties. |
How about this answer for level 1: 17-4=13-3=10+14=24 It kinda makes me wanna hide in a corner and cry because...yes...I still get solutions like this. And we continue talking about why this doesn't make sense. We'll get there eventually. |
Since we're always looking for an end solution of 24, students are starting to notice patterns in the 4 numbers.
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Starting next week we're going to bring in integer 24's so students can start solidifying their understanding of integers. Fractions will come a bit later. |