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.
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Implementation Guidance and Considerations
These lessons were developed as part of a National Center on Intensive Intervention Community of Practice with educators focused on implementing intervention virtually during Spring 2020 in response to COVID-19. Participating educators represented Colorado, Oregon, Rhode Island, Texas, and Washington. These activities were developed by practitioners and are intended to showcase example strategies that educators have used to deliver intervention in a virtual environment during the pandemic.
What Does the Literature Say? Research and Journal Articles Focused on Intensive Intervention and Data-Based Individualization
This collection highlights a sampling of articles focused on intensive intervention and data-based individualization (DBI). Although there is a wealth of research on key components of the DBI process (e.g., progress monitoring, validated intervention programs), this list is not intended to include articles that focus on specific steps in the DBI process, nor is it an exhaustive review of all available literature. In the list below, we highlight seminal research on DBI and articles published since 2011, when NCII was first funded.
These resources were created by Patricia Maxwell from Coventry Public Schools in Rhode Island to help with virtual mathematics instruction and intervention. The long-term goal is for students to fluently and automatically know addition facts. Manipulatives, including fingers, help students to be accurate, which is a precursor of fluency and automaticity. To meet this goal, students use manipulatives and learn strategies on how to put together numbers, which improves their “number sense.” The handouts below cover the use of ten frames, number lines, and rekenreks. Example videos are linked in the resource.
This video reviews key vocabulary related to fractions. It is important that teachers model the use of precise mathematical language so that students understand how to use correct vocabulary and can accurately communicate their ideas and solutions strategies related to fractions.
This guide was developed by Melanie Kowalick an MTSS Curriculum Specialist in Wichita Falls Independent School District. This planning guide may be used for planning short intervention activities, review and practice activities, or progress monitoring checks. During school closures, we learned that virtual intervention does not look the same as face-to-face intervention. Parent support and planning are going to be the key to helping our students who have difficulties with reading and mathematics. For educators or parents, part of this support includes simple ways to monitor student progress.
This unit of study includes a tip sheet, slides with activities, and supplemental materials that are associated with finding the area of various polygons, the area of circles, and the relationship between the area formulas, as well as a final activity exploring the area of a parallelogram and the area of a circle. This presentation is not intended to be used in one virtual session but as guidance for a unit of study related to the area of polygons. This unit was created by Robert Stroud from Westerly Public Schools in Rhode Island to support making the connections between various polygons and their areas rather than just providing formulas to compute.
This video demonstrates how to use fraction tiles and the set model to convert mixed numbers to improper fractions. It is important that students have the opportunity to convert fractions using both models of representation.
This video demonstrates how to use the set model to convert mixed numbers to improper fractions. It is important that students are exposed to converting fractions using this model because it is often how fractions are represented in the real world. Beginners and students who struggle may find the set model difficult to understand because the whole (1) is represented by a set of chips (4 chips in this example); therefore, students will benefit from explicit modeling and several opportunities to engage in guided and independent practice.
This video demonstrates different partitioning strategies that students can use to multiply fractions. Partitioning refers to dividing a shape, such as a rectangle, into equal pieces. In area models and length models, the total number of equally partitioned pieces represents the denominator of the product. Students can practice multiplying nonequivalent fractions using an area model without concrete materials, such as by creating a grid using paper and pencil, or with concrete materials such as fraction grids. Students should also have the opportunity to practice multiplication using fraction tiles and length model.