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BUT FIRST...WHAT DO WE KNOW ABOUT THE ANSWER?

I apologize for the oversight. Here's the revised version without changing your words:

This simple question has made a huge difference in my classroom. It's like those seven words "What do we know about the answer?" helped my students realize how they should be thinking when solving a problem.


I always tell my students "Practice like a Mathematician using (some Mathematical Practice)." In this particular case, especially MP. 7 and MP. 8. I always tell them to ask themselves "Does My Answer Make Sense?" Many of my students listened, but some did not. In group collaboration or discourse AFTER solving problems, students would catch their mistake and agree that their answer "didn't make sense."


While reading the book "Beyond Invert and Multiply" prior to students solving a problem, they asked the students to think about what they knew about the answer. I knew I needed to apply that ASAP. At the time, I was building my students' conceptual understanding of fractions before our actual fraction lessons. I asked them what do we know about the answer in more of a scaling fractions way while adding fractions with unlike denominators. I loved the result.


Sooo...I decided to ask my students "What do we know about the answer?" after they completed their "Find Three Ways" and had gotten different answers with various strategies. I was so amazed at some things that they said. I also demonstrated how to be more specific about things I would know about the answer.


For example, in the problem 34 x 38 students would say:

1. I know my answer will have a 2 in the ones place because 8 x 4 = 32.

2. I know my answer will be more than 900 because 30 x 30 = 900.


One thing a few of my students would say is:


I know my answer will have a 9 in the highest place because 3 x 3 is 9. At that moment, I let students discourse about why starting in the front (highest place) might not be the best way to get to know something about the answer in multiplication or addition problems. They discussed how 4 x 8 equals 32, so the three tens needed to be bundled and added to the tens column.


This practice was so helpful; I actually turned it into a discourse routine. Getting students to apply their knowledge before actually working their problems was exactly what my students needed. I have personally seen so much improvement in my students just by simply asking the question "What do we know about the answer?"

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