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(Teacher note: if students choose numbers strategically and therefore finish quickly, give them extra bars to factor into their problem to see how they deal with the leftovers.) Other students chose the opposite route and strategically picked numbers to make it "harder for themselves." Check out the way these two students showed strong reasoning and perseverance through division of numbers larger than any they've ever worked with.
To me, this demonstrated a lot of sense-making and forethought of what was going to happen in their solution path.
And, as an added bonus, despite being asked to answer only one question, the group answered all three!
This was a great way to formatively assess students' thinking related to fractions before they began that unit. Who would have thought 3rd graders would reason about the leftovers in terms of percentages?
Reflecting on the difference between what students would have done with the original problem versus the reasoning work they did related to the one simple sentence, I'm amazed at the outcomes.
Instead of students thinking about how they're going to solve the problem as they read, they are truly thinking about the situation at hand.
Strategy For Solving Word Problems
It's been an amazing way to give every student entry into a problem and allows me to differentiate for all learners in the classroom.Most importantly, we ask ourselves, how can I help students make sense of what they're reading and to think about the logic of their answer in the context of the problem?If we're lucky, we can identify the student's mathematical misconception and work with that.At the same time, I'm provided insight into my students' mathematical understanding.Recently, I had the opportunity to work with a 3rd grade class.If the answer is correct, we assume the student has a grasp of the concept.However, if it's incorrect, we're left with a laundry list of questions: Do they realize their answer doesn't make sense? Did they simply pull the numbers and operate in order simply to finish or did they truly not know what to do with them?I asked them what questions they could answer if I gave them those pieces of information, and they responded: At this point, I could have given them the information they wanted.However, I thought it would be so much cooler to allow them to choose that information for themselves.Inspired by the wonderful folks at The Math Forum, I do a lot of noticing and wondering with students in this fashion.Most recently, after reading Brian Bushart's awesome blog post, I've started taking the numbers out as well!