Reasoning & Constructing Arguments

Practices # 2 & 3 for KINDERGARTEN

How do we help students make sense of mathematics?

The focus of our training this year is to help teachers create the conditions that will help us build mathematically proficient students. We have spent the first half of the year building your understanding of Problem Solving and Number Talks. These two practices are the pillars of mathematical thinking. All of the rest of the Standards for Mathematical Practice serve to support and deepen those practices.

When teachers create the opportunities for students to experience mathematics through The Standards for Mathematical Practice, our students will build a deeper understanding of the skills and concepts that will help them make sense of mathematical ideas.

This month we will consider the following 2 practices:

Practice # 2: Reason Abstractly and Quantitatively

Practice # 3: Construct Viable Arguments and Critique the Reasoning of others.

These two practice serve as pathways that allow students to become effective problem solvers and effectively communicate their mathematical ideas.


  • It is through reasoning that children learn that math makes sense
  • Reasoning and sense making are intertwined
  • Effective questioning helps students see the connections between ideas without telling them too much
  • Conjecturing, generalizing, and justification are fancy terms that are really practices that students must use to make sense through reasoning
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Practice # 2: Reason Abstractly and Quantitatively

Mathematically proficient students are able to make sense of quantities or symbols for quantities. This allows them to move back and forth between real life problems and symbolic representations of mathematical problems so that they can manipulate the ideas to find solutions.
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Practice # 3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students are able to not only figure out the correct answer, but they can also defend the reasons why they chose a certain process to solve it as well as prove why their answer makes sense. They are also capable of entering into discussions with others to agree, disagree and support the mathematical thinking of others.
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Resources for Number Talk topics:

If you need to deepen your background knowledge of Mathematical Reasoning click below:

The link below has short video explanations of each of the 8 Mathematical Practices.

Click on this link and take a minute to listen to the 2 videos on today's topics: Practice # 2 Reasoning and Practice # 3 Constructing Arguments

This website has videos of students using each standard to solve a problem

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