## Week 7 Assignment – Video Analysis

Overview:
Mathematical justification: Is the process where students support their mathematical claims and choices when solving problems or explaining why their claims or answers make mathematical sense (Staples & Bieda, 2020).

Adaptive reasoning: Is the reasoning that supports students navigate through the many facts, procedures, concepts, and solution methods and to see that they all fit together in some way that they make sense (Kilpatrick et al., 2001, p. 129).  It is logical reasoning essential to doing mathematics and to supporting students learning mathematical ideas that they can use across grade level and math domains (e.g., number operations and algebra). Adaptive reasoning includes many forms of reasoning including inductive, deductive and analogical (using metaphors and mental and physical representations) reasoning that are tools to think with to advance learning.

Math Task 1 [Grades K-8]: Compare and order the following fractions: 1/2, 1/3, 1/4, and placing them on a number line segment with endpoints 0 and 1. Where would you mark the position for each of these fractions? Where would you position 1/10? How would you justify the position of each of these fractions?

Identify three more non-unit fractions (fractions without one in the numerator) to place on the number line that you will ask a peer to place without finding a common denominator or numerator.  Develop a justification that explains why the placement is true that relates the three fractions to one another.

Math Task 2 [Grades 10-12]: Compare and order the following logarithms on a number line, log base 2 of , , 1, 2.  Construct an argument for how your number line shows why the number placement is true.

Video Case [Grades K-8]: Watch clips 1-4 from the link below. Clips 5 and 6 are optional:
https://rucore.libraries.rutgers.edu/rutgers-lib/46919/emap/1/standalone

SMPs Resource: http://www.corestandards.org/Math/Practice/

QUESTIONS THAT NEED TO BE ANSWERED USING THE RESOURCES: