# Grades 6ā8: Cultivating Integer Fluency

Professional Learning Workshop

## Boost your integer knowledge

Investigate commonly used rules that impede the deeper conceptual understanding underlying fluency with integer operations. Model integer operations with number lines, two-color counters, and algebra tiles to develop procedural fluency.

## Explore a key question during each segment of learning

#### How can we build on existing student understanding of addition and subtraction to develop their understanding of these operations with integers?

• Explain how to represent whole numbers in a variety of ways to support understanding of addition and subtraction.
• Make sense of and create authentic real-world contexts modeled with addition and subtraction.
• Articulate and apply strategies to transition from addition and subtraction with whole numbers to integers.

#### How can the meaning of addition and subtraction persist when we extend the number system to include integers?

• Explain integer addition and subtraction with the construct of zero pairs modeled with number lines and two-color counters (or algebra tiles).
• Develop studentsā conceptual understanding of integer addition and subtraction using number lines and two-color counters (or algebra tiles).
• Teach integer addition and subtraction in authentic real-world contexts using number lines and two-color counters (or algebra tiles).

#### How does a conceptual understanding of integer addition and subtraction support fluency?

• Explain what it means to be fluent with integer addition and subtraction.
• Support students to build procedural fluency through a conceptual understanding of integer addition and subtraction.
• Provide authentic real-world contexts that create a need for adding and subtracting with integers.

#### How can we build on existing student understanding of multiplication and division to develop their understanding of these operations with integers?

• Explain how to represent whole numbers in a variety of ways to support understanding of multiplication and division.
• Make sense of and create authentic real-world contexts modeled with multiplication and division of integers.
• Articulate and apply strategies to transition from multiplication and division with whole numbers to integers.

#### How can the meaning of multiplication and division persist when we extend the number system to include integers?

• Use and explain integer multiplication and division modeled with number lines and two-color counters (or algebra tiles).
• Plan to develop studentsā conceptual understanding of integer multiplication and division using number lines and two-color counters (or algebra tiles).
• Teach integer multiplication and division in authentic real-world contexts using number lines and two-color counters (or algebra tiles).

#### How does a conceptual understanding of integer multiplication and division support fluency?

• Explain what it means to be fluent with integer multiplication and division.
• Plan to support students to build procedural fluency through a conceptual understanding of integer multiplication and division.
• Provide authentic real-world contexts that create a need for multiplying and dividing with integers.

## Designed with you in mind

This offering is divided into two 3-hour parts. It is recommended that the parts be completed in order, within a reasonable time frame. Your NWEA representative will help determine the best on-site or virtual delivery option to meet your needs.

### On-site learning

Face-to-face session with a consultant

### Virtual learning

Live instruction through our online portal