INSTRUCTIONS AND RESOURCES FOR QUESTIONS: Please read thoroughly.

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.

Mathematics Tasks & Videos:

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:

1. Write up your work for Math Task 1 and Math Task 2. Include all work that you produced, and provide enough detail in your arguments so that the reader can clearly follow your thinking.

2. Across the four video clips, choose two video moments that illustrate students developing adaptive reasoning. Include a timestamp to cite your examples, and describe how this is an example of developing adaptive reasoning. Be sure to highlight specific events in the video and link to the language of the strand in your explanation. For example, One example of students developing adaptive reasoning can be seen from time ____ to ____. During this time, students are saying/ doing ______, which is an example of adaptive reasoning because _____.

3. Across the four video clips, choose two video moments that illustrate students engaging in SMP 3. Include a timestamp to cite your example, and describe how this is an example of SMP 3. Be sure to highlight specific events in the video and link to the language of the SMP in your explanation. For example, One example of students engaging in SMP 3 can be seen from time ____ to ____. During this time, students are saying/doing ______, which is an example of students constructing viable arguments or critiquing the arguments of others because _____.

4. Across the four video clips, choose one video moment that illustrates students engaging in SMP 5. Include a timestamp to cite your example, and describe how this is an example of SMP 5. Be sure to highlight specific events in the video and link to the language of the SMP in your explanation. For example, One example of students engaging in SMP 5 can be seen from time ____ to ____. During this time, students are saying/doing ______, which is an example of using appropriate tools strategically because _____.

5. Finally, across all the clips you selected for questions 2-4, discuss how the moments illustrate students engaging in mathematics justification. Include a timestamp to cite your example, and describe how this is an example of mathematical justification supporting students learning. Discuss any insights or questions you have about the clips supporting equitable instruction. For example, An example of students participation in mathematical justification can be seen from time ___ to ___. During this time, students were saying/doing ______, which is using justification to support learning because _______. I noticed students saying/doing _______ which related to equitable/inequitable learning because________.

6. Find and discuss at least two examples of students engaging in SMP 5; note, these examples should be different than those cited in #2. Include a timestamp to cite your examples, and describe how specific events in the video link to features of SMP 5. Be sure to draw on the language of the SMP in your explanation.

Please number each question.