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.
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In Module 7 of the Intensive Intervention in Mathematics Course Content we focus on rational number concepts and computation. 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.
It is important that the instructional practices and interventions delivered within a school’s multi-tiered system of support (MTSS) be grounded in evidence. However, the “practice” that happens within each tier is different; therefore, the type of evidence that is required for each tier also must be different. A useful way to think about evidence-based practices in MTSS is to think about levels of evidence that vary and correspond to the different levels of intervention intensity at each tier. In the tables below, find resources to support the selection and evaluation of Tier 1, Tier 2, and Tier 3 or intensive interventions.
In Module 6 of the Intensive Intervention in Mathematics Course Content we focus on whole number concepts and computation. 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.
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.
The purpose of this module is to review how to implement the Early Numeracy Intervention, a validated intervention program that can be used for Tier 2 math intervention, or as an intensive intervention platform within DBI.
This module discusses approaches to intensifying academic interventions for students with severe and persistent learning needs. The module describes how intensification fits into DBI process and introduces four categories of intensification practices. It uses examples to illustrate concepts and provides activities to support development of teams’ understanding of these practices, and how they might be used to design effective individualized programs for students with intensive needs.
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 video shows how manipulatives can be used to explain division problems that have a fair-share or equal partition problem structure. This example demonstrates how manipulatives can be used to show how repeated subtraction (i.e., when the whole is decreased iteratively by equal sets) can be used in division to determine the size of the equal set. When students have many practice opportunities to solve division problems with strategies such as repeated subtraction, they develop a solid conceptual understanding that division represents partitioning a quality into groups of equivalent sets.
This video shows how manipulatives can be used to explain division problems that have a fair-share or equal partition problem structure. This example demonstrates how manipulatives can be used to show how repeated subtraction (i.e., when the whole is decreased iteratively by equal sets) can be used in division to determine the size of the equal set. When students have many practice opportunities to solve division problems with strategies such as repeated subtraction, they develop a solid conceptual understanding that division represents partitioning a quality into groups of equivalent sets.