Whole Number Content for Intensive Intervention

Whole Number Content for Intensive Intervention

Intensive Intervention in Mathematics Course: Module 6 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 6, we focus on whole number concepts and computation. In this module, educators will learn about:

  • How to explain the meanings of addition, subtraction, multiplication, and division
  • Different computational algorithms for the four operations
  • How effective whole-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


This video introduces Module 6 and provides an overview of the module content and related activities.


Related Videos

Video Question: Mr. Flores asks how to help students understand the concepts and procedures of whole numbers.
(Associated with PowerPoint Slide 2 and 90)


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

Part 1 reviews the different conceptual meanings of the four operations. Teachers learn addition as total and join; subtraction as separate and compare; multiplication as equal groups and comparison; and division as partitive and measurement. These concepts relate closely to the word-problem schemas of Module 5.



Worksheets & Activities

Activity 1 - Describe Addition and Subtraction

Activity 2 - Describe How a Student Thinks About Addition and Subtraction

Activity 3 - Describe Multiplication and Division

Activity 4 - Describe Concepts within Multiplicative Word Problems


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

Part 2 emphasizes place value and computation. Teachers review appropriate place value language. Teachers also learn various algorithms students can use to solve addition, subtraction, multiplication, and division computation problems.



Worksheets & Activities

Activity 5 - Solve Addition and Subtraction Problems with Two Different Algorithms

Activity 6 - Solve Multiplication and Division Problems with Two Different Algorithms

Activity 7 - Use Two Different Schemas to Describe a Multiplicative Word Problem

Discussion Board – Teach a Multi-Digit Operation


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

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



Worksheets & Activities

Activity 8 - Identify Components of an Intervention Lesson on Computation

Discussion Board – Non-Standard Algorithms


Related Videos

Video Example: A tutor works on multiplication with a student and uses manipulatives to model problems.
(Associated with PowerPoint Slide 69)

Video Example: A tutor works on subtraction with a student and uses manipulatives to model problems.
(Associated with PowerPoint Slide 71)

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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 Whole Number Concepts and Procedures


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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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