# Mathematics Strategies to Support Intensifying Interventions

NCII developed a series of mathematics lessons and guidance documents to support special education instructors, mathematics specialists, and others working with students who struggle with mathematics. These lessons and activities are organized around six mathematics skill areas that are aligned to college– and career-ready standards, and incorporate several instructional principles that may help intensify and individualize mathematics instruction to assist teachers and interventionists working with students who have difficulty with mathematics. The lessons may be used to supplement mathematics interventions, programs, or curricula that are currently in place. However, these lessons by themselves would not constitute an effective mathematics intervention.

### Implementing the Lessons to Support Continuity of Learning During COVID-19

These video examples and tips illustrate how the sample lessons can be used during COVID-19 to provide additional practice opportunities for students. Examples include information for educators using the lessons through virtual learning and for parents or other family members in implementing them at home.

In this video, Dr. Sarah Powell shares considerations for teaching students with math difficulty.

The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics.

Click on the skill areas below to explore resources and lessons related to each area.

## Select a Skill to Explore

Need Help Determining What to Target?

### Number System/Counting

 Within college- and career-ready standards, place value, numeracy, and counting are taught in Grades 1 and 2. Counting skills cover knowing number names and the counting sequence, counting to tell the number of objects, comparing numbers, extending the counting sequence, and adding and subtracting within 20. Students who struggle with counting often have difficulty with counting principles and understanding numbers and what they represent. These resources may be used as these concepts are introduced or with students in higher grade levels who continue to struggle with the concepts.

#### Example

View an example of how standards-aligned instruction for counting may be taught across the continuum of the multi-tiered system of support (MTSS) framework.

#### Lessons and Activities

The following lessons and activities may be used to develop and customize mathematics instruction and interventions to meet student needs. Each provides considerations for instruction, sample activities with embedded instructional principles, worksheets, and supplemental materials. Instructional videos highlighting these practices also are available.

Teaching Counting Guide (508 compliant version)

### Basic Facts

 Within college- and career-ready standards, basic facts are taught in Grades K–4. Basic facts cover addition and subtraction concepts, adding and subtracting, multiplication and division concepts, and multiplying and dividing. Students who struggle with basic facts may not have mastered prerequisite skills, such as counting, knowledge of numbers, and understanding what numbers represent. In addition, they may struggle with specific basic fact skills, such as understanding symbols, fluency with facts, and selecting strategies to calculate answers. These resources may be used as these concepts are introduced, or with students in higher grade levels who continue to struggle with the concepts.

#### Example

View an example of how standards-aligned instruction for basic facts may be taught across the continuum of the MTSS framework.

#### Lessons and Activities

The following lessons and activities may be used to develop and customize mathematics instruction and interventions to meet student needs. Each provides considerations for instruction, sample activities with embedded instructional principles, worksheets, and supplemental materials. Instructional videos highlighting these practices also are available.

### Place Value Concepts

 Within college- and career-ready standards, place value concepts are taught in Grades K–5. Place value concepts cover such skills as extending the counting sequence and understanding place value. Students who struggle with place value concepts may not have mastered prerequisite skills, such as knowledge or understanding of numbers. In addition, they may struggle with specific place value skills, such as zero, reading numbers, and understanding place value. These resources may be used as these concepts are introduced or with students in higher grade levels who continue to struggle with the concepts.

#### Example

View an example of how standards-aligned instruction for place value concepts may be taught across the continuum of the MTSS framework.

#### Lessons and Activities

The following lessons and activities can be used to develop and customize math instruction and intervention to meet student needs. Each provides a standard aligned lesson, with a clear objective, embedded instructional principles and sample activities.

### Place Value Computation

 Within college- and career-ready standards, place value computation is typically taught in Grades 1–5. Place value computation covers such skills as adding and subtracting (including multi-digit addition and subtraction as well as fluently adding two-digit and multi-digit numbers) and multiplying and dividing (including multiplying and dividing whole numbers of varying digits and multiplying and dividing decimals to the hundredths). Students who struggle with place value computation may not have mastered prerequisite skills, such as basic fact retrieval. In addition, they may struggle with specific computation skills, such as understanding place value, regrouping, and estimating. These resources may be used as these concepts are introduced or with students in higher grade levels who continue to struggle with the concepts.

#### Example

View an example of how standards-aligned instruction for place value may be taught across the continuum of the MTSS framework.

#### Lessons and Activities

The following lessons and activities can be used to develop and customize math instruction and intervention to meet student needs. Each provides a standard aligned lesson, with a clear objective, embedded instructional principles and sample activities.

### Fractions as Numbers

 Within college- and career-ready standards, fractions are typically taught in Grades 3–5. Developing an understanding of fractions as numbers includes part/whole relationship, number on the number line, equivalent fractions, whole numbers as fractions, and comparing fractions. Students who struggle with fractions may not have mastered prerequisite skills, such as whole number understanding and operations. In addition, they may struggle with specific fraction skills, such as reading fractions, writing fractions, understanding that the larger the denominator the smaller the value of each part, poor understanding of multiples, and understanding the four models of fractions and when to use them (area, sets, measurement, and division). These resources may be used as these concepts are introduced or with students in higher grade levels who continue to struggle with the concepts.

#### Example

View an example of how fractions as numbers may be taught across the continuum of the MTSS framework.

#### Lessons and Activities

The following lessons and activities can be used to develop and customize math instruction and intervention to meet student needs. Each provides a standard aligned lesson, with a clear objective, embedded instructional principles and sample activities.

### Computation of Fraction

 Within college- and career-ready standards, fractions are typically taught in Grades 3–5. Computation of fractions covers skills focused on building fractions from unit fractions—applying and extending operations of whole numbers. This includes: Adding and subtracting fractions Decomposing fractions in more than one way Adding and subtracting mixed numbers with like denominators Solving word problems involving addition or subtraction Multiplying fractions Solving word problems involving multiplication Using equivalent fractions Adding and subtracting fractions with unlike denominators Solving word problems involving addition or subtracting of unlike denominators Dividing fractions Solving word problems involving division of fractions Students who struggle with fractions may not have mastered prerequisite skills, such as whole number understanding and operations. In addition, they may struggle with specific fraction skills, such as reading fractions, writing fractions, understanding that the larger the denominator the smaller the value of each part, poor understanding of multiples, and understanding the four models of fractions and when to use them (area, sets, measurement, and division). These resources may be used as these concepts are introduced or with students in higher grade levels who continue to struggle with the concepts.

#### Example

View an example of how computation of fractions may be taught across the continuum of the MTSS framework.

#### Lessons and Activities

The following lessons and activities can be used to develop and customize math instruction and intervention to meet student needs. Each provides a standard aligned lesson, with a clear objective, embedded instructional principles and sample activities.

Subject
Mathematics

### Related Resources

#### Course Content

Intensive Intervention in Mathematics Course Content

#### Webinar

Making Fractions Make Sense: Considerations for Secondary and Intensive Intervention

#### Training Modules

Supporting Mathematics Intervention in Middle School

#### Training Modules

Supporting Mathematics Intervention in Elementary School

TIP FROM THE FIELD

Using multiple representations to teach mathematics allows students to understand mathematics conceptually, often as a result of developing or “seeing” an algorithm or strategy on their own. By building strong conceptual understanding, students are able to better generalize skills and understand algorithms (Gersten et al., 2009; Jones, Inglis, Gilmore, & Evans, 2013; Miller & Hudson, 2007)