Classroom Sneak Peek #2 - Reason abstractly and quantitatively

Last week I started a blog regarding CCSS Mathematical Practice #1 - Make Sense of problems and persevere in solving them.  I addressed what this looks like in the classroom, what students will be doing, what teachers will be doing, and the most important, the type of questions teachers will be asking.  This week, I'm addressing these same issues with a focus on CCSS Mathematical Practice # 2 - Reason abstractly and quantitatively. 

2. Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

So what does this really look like?  The chart below is a work in progress.  I've designed this with the expertise of many classroom teachers.  If you have other ideas, please don't hesitate to email me and share your expertise as well. 

If you are interested in this process to facilitate this discussion with your staff, read What Do the Common Core Standards Look Like in the Classroom. 

Mathematical Practice: Reason abstractly and quantitatively

Student Actions:	Teacher Actions:	Open-Ended Questions:
Act out and solve story problems. Represent the problem with visuals or math tools. Asks themselves how do these tools represent the problem. Consistently thinks about how the problem and the solution fit together. Explains their answers, not just how they arrived at it. Reflect on their thinking. Uses references and prior knowledge to solve the problem Check for patterns or properties of operations they know to solve. Understands and explains properties: (4 + 3 = 3 + 4) or 42 x 8 = (40 x 8) + (2 x 8) Use symbols to represent the problem Visualize what the problem is asking.	Provide story problems and real-world problems for students to solve. Encourage use of a variety of tools and strategies. Manipulatives and other math tools need to be on hand for students to pick up and use at anytime. Monitor the thinking of the students. Question students about patterns and properties of operation. Facilitate discussion about solutions, strategies, patterns, and properties.	How does your picture/model represent the problem? Where are the 15 chocolate bars? What does this part represent? Have you solved a problem like this before? What did you do then to model or represent the problem? How did you know you could break 42 into a 40 and a 2 and then multiply each by 8? What does the x represent? What does it stand for in the problem? How might visualizing the problem in your head help you solve the problem? What patterns do you see? How might that pattern help you figure out for the 20th term? Why does that strategy make sense to you? What did __________ say that helped you clarify in your mind the problem?