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:
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:
Later, we had this solution:
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:
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.
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.