Table of Contents

Unit 5: Seeing Structure and Generalizing (MP7 and MP8)

5.4.1 Making Connections

By examining students’ efforts to see structure and generalize, you also examined their ability to communicate their thinking and construct viable arguments to support their claims. This experience connects directly to the writing standards in the CCSS for English Language Arts.

Time to Read

Differentiating Instruction

Consider how you would assist students in developing strategies for seeking visual and numerical structure and developing generalizations, whether verbal, symbolic, or numeric. The following strategies support students, especially English learners and students with special needs, in communicating their thinking effectively. Note that these strategies are only examples:

  • Allow students to write responses in their native language.
  • Allow student responses to a task be a draft only. In class, examine some student work that needs revision and some that is acceptable or exemplary. Have students discuss these sample student works in small groups and then debrief with the whole class, focusing on how to improve explanations that need revision. Then allow students to revise their first draft on the task individually.
  • Construct questions about student explanations that help the student focus on what is missing or is not clear. Use sticky notes so that the student can revise the work.
  • Possible scaffolding questions to help students develop and articulate structure for a given pattern include:

How might you extend this pattern? Why extend it that way?

What stays the same and what changes in your pattern?

Is there another way to extend the pattern? How so?

Time to Extend

Consider the following activities to expand your knowledge of the two structure and generalizing practices:

  • Examine the patterning examples across the grades. Reflect on how expectations for students grow as students develop mathematically.
  • Select the task appropriate for your grade level and share with grade level colleagues at your school site. Devise a plan with fellow teachers to give the problem and review student work. Discuss the similarities and differences among the students’ papers as well as in the student work presented in Section 5.4.

What strategies are your students using to develop generalizations?

What next steps would you consider to support students or challenge their thinking?