Unit 3: Reasoning and Explaining (MP2 and MP3)

# 3.1 Beginning to Reason: Definitions and Conjectures

**The Difference between a Mathematical Argument and a Proof **

The CCSS for mathematical practices do not use the word “proof”. This is because many people are familiar with a narrow definition of proof (e.g., a two-column geometry proof). The term “argument” is intended to be more general in form but ultimately has the same purpose of constructing a logical sequence of steps that justify and communicate a given conclusion from a set of agreed premises.

As stated in California’s CCSS for Mathematics (p.1):

Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments."

When students begin to reason, they need to establish definitions (e.g., clear and logical descriptions of what they are reasoning about). They also may need to make conjectures — informed guesses of what is true — that they then set out to explain through reasoning.