Rational-Number Content (Intensive Intervention in Mathematics: Module 7)

Rational-Number Content (Intensive Intervention in Mathematics: Module 7)

Module Overview

In Modules 4 and 5, we emphasized important instructional delivery methods and strategies to include when providing instruction within intensive intervention. Modules 6 and 7 focus on important concepts and procedures for whole numbers (Module 6) and rational numbers (Module 7) teachers may find important for being able to explain mathematics to students. In Module 7, we focus on rational number concepts and computation. In this module, educators will learn about:

  • Different models to explain fraction and decimal concepts
  • How to explain computation with fractions and decimals in a conceptual way
  • How effective rational-number instruction looks within intensive intervention

This module is divided into three parts, with an introduction and closing. A 508 compliant version of the full PowerPoint presentation across all parts of the module is available below.

Complete Slide Deck (508 compliant)

Workbook (508 compliant)

For questions related to course content, please contact ncii@air.org

Introduction

This video introduces Module 7 and provides an overview of the module content and related activities.

 

 

Related Videos

Video Question: Mr. Flores asks how to help students understand fraction concepts.
(Associated with PowerPoint Slide 2 and 100)

 

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Part 1: What rational-number core concepts should be emphasized in intensive intervention?

Part 1 explains the concepts of fractions and decimals. Teachers learn to use the length, area, and set models to explain fractions. Teachers also learn how decimals and percentages relate to fractions.

 

 

Worksheets & Activities

Activity 1 - Using the Length Model with a Student

Activity 2 - Using the Area Model with a Student

Activity 3 - Using the Set Model with a Student

Discussion Board – Favorite Fraction Tools

 

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Part 2: What rational-number procedures should be emphasized in intensive intervention?

Part 2 reviews addition, subtraction, multiplication, and division with fractions and decimals. Teachers learn how to model finding common denominators. We also review how to explain fraction computation conceptually. We conclude with a brief example of using concrete manipulatives to demonstrate computation with decimals.

 

 

Worksheets & Activities

Activity 4 - Modeling Addition and Subtraction of Fractions

Activity 5 - Modeling Multiplication and Division of Fractions

Activity 6 - Using CRA to Teach Decimals

Discussion Board – Application to Ratio and Proportion Problems

 

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Part 3: What does DBI look like with intensive interventions that focus on conceptual and procedural understanding of rational numbers?

Part 3 provides video and intervention examples of intensive intervention on rational-number content. Teachers review several videos to see how teachers use explicit instruction, multiple representations, and concise language to teach about rational numbers. Teachers also read an excerpt from an evidence-based intervention focused on rational numbers to identify how instructional delivery (Module 4) and strategies (Module 5) work together within intensive intervention.

 

 

 

Worksheets & Activities

Activity 7 - Identify and Analyze Components of an Intervention Lesson on Fractions

Discussion Board – Teaching Fractions, Decimals, or Percentages

 

Related Videos

Video Example: A tutor uses fraction tiles to demonstrate showing the denominator and numerator of a fraction.
(Associated with PowerPoint Slide 79)

Video Example: A tutor work with a student to add fractions with unlike denominators.
(Associated with PowerPoint Slide 81)

Video Example: A tutor asks a student to find common denominators with manipulatives.
(Associated with PowerPoint Slide 82)

Video Example: A student independently solves an addition problem with fractions and unlike denominators.
(Associated with PowerPoint Slide 83)

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Closing: What are the next steps?

The closing video reviews the content covered in the module and concludes with a classroom application activity.

 

Worksheets & Activities

Classroom Application: Modeling Rational Number Concepts and Procedures

 

Related Videos

Video Question: Mr. Flores asks how to help students understand fraction concepts.
(Associated with PowerPoint Slide 2 and 100)

 

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Coaching Materials and Facilitation Guide

"Coaching/Facilitator Guide" helps facilitate implementation, reflection, and feedback. It is intended for use by external (i.e., SEA or LEA staff, faculty, project-based coaches) or internal (i.e., school-based instructional coaches) coaches working directly with in-service educators who are learning and practicing the course content. Additionally, materials within the coaching/facilitator guide can be adapted by faculty as they prepare pre-service educators. The goal for coaching/facilitation is to ensure that educators are practicing the content they are learning and receiving feedback to improve their instruction. Included in this guide are: (a) sample communication emails, (b) a master checklist, (c) a discussion guide with important talking points, and (d) a fidelity form that can be completed by a coach/facilitator when observing classroom instruction.

Coaching/Facilitator Guide

 

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