### Description

**What is the Mathematical Generalizing?**

Develop a clear enough understanding of the characteristics of mathematical generalizing to be able to explain your understanding to others.

### Time To Complete

### I Can Statements

I will know my exploration of the mathematical generalizing is of high quality when:

- I can identify the specific key elements that define mathematical generalizing, such as figures, givens, steps, deductions. (Note: This will vary depending on the type of generalizing students will undertake, such as geometric proofs.)

**Suggestions for Assessing Student Readiness to Move Forward:**

- Confer with students to check their understanding of the elements of mathematical generalizing,
- Provide students an anchor or model and ask them to code or otherwise identify the elements of the task.

Conduct a mini-lesson on mathematical generalizing, describing the key organizational structure, form, and approach of the exemplars. Provide models closely related to the specific format in which students will be working.

Provide several exemplars and ask students to select two or three to examine and create a list of similarities in structure, craft, and form. Or use a jigsaw format, where students work in groups and each group reads texts about mathematical generalizing and examines a different exemplar. Then reorganize the groups so that the new groups each have one representative from the former group, and each representative shares their learning with the others in this new group to create a collective understanding of the genre.

- Coding the Text—Ask students to examine two exemplars and code the elements they discover. For example, students use the following:
- F: figures
- I: interpretation
- G: given
- V: validation of conclusions

- Coding the Text—Ask students to examine two exemplars and code the elements they discover. For example, students use the following:

### Resources

Examinations of geometric proofs:

- http://www.sparknotes.com/math/geometry3/geometricproofs/section1.rhtml
- http://www.regentsprep.org/regents/math/geometry/gp3/WhatPrf.HTM

Examples of mathematical induction:

- http://www.themathpage.com/aprecalc/mathematical-induction.htm
- http://www.analyzemath.com/math_induction/mathematical_induction.html
- http://www.purplemath.com/modules/inductn3.htm

Sample Mathematical Generalizations: