Unit 3: Reasoning and Explaining (MP2 and MP3)

3.5 Summary

In this unit, you witnessed a 5^th-grade classroom in which the students learned to use the two reasoning and explaining practices (MP2 and MP3). Review the summary of key concepts within these two practices below:

Reasoning Abstractly and Quantitatively

• Make sense of quantities and their relationships in problem situations
• Decontextualize — to abstract a given situation and represent it symbolically
• Contextualize — to probe into the referents for the symbols involved
• Create a coherent representation of the problem at hand
• Consider the units involved
• Attend to the meaning of quantities, not just how to compute them
• Know and flexibly use different properties of operations

Constructing Viable Arguments and Critiquing the Reasoning of Others

• Use stated assumptions, definitions, and previously established results in constructing arguments
• Make conjectures
• Build a logical progression of statements
• Analyze situations by breaking them into cases
• Recognize and use counterexamples
• Justify their conclusion, communicate them to others, and respond to the arguments of others
• Distinguish correct logic or reasoning from that which is flawed

As demonstrated in this unit, elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.