This video illustrates the use of manipulatives to help students integrate the concept of counting by ones with skill in grouping by tens.
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This video demonstrates how to use fraction tiles to explore how fractions such as 4/4 are equivalent to 1. Before fractions are introduced in the curriculum, students use integers, which only have one value associated with the numeral or number word. Fractions may be the first time that students are introduced to the possibility that the same quantity can be represented with different representations, such as one whole and four fourths. Using models allows students to practice finding equivalent fractions, which is a prerequisite skill for performing computation with fractions.
This video shows how to use the set model to represent the fraction 3/4 with two-colored counting chips and clips. Individual chips within the set, represent the fractional parts. It is important that students be exposed to the set model because fractions in real-world settings are often represented this way.
This video demonstrates how to use fraction circles to help students compare the value of several fractions with different numerators and denominators. The use of direct modeling with concrete manipulatives, such as fractions circles, allows students to develop conceptual understanding of fractions before they attempt to compare fractions without concrete manipulatives or pictorial representations. After students have had multiple opportunities to practice comparing fractions with concrete manipulatives, they may be ready to use other strategies such as mental images and reasoning strategies.
This video shows how to use the traditional division algorithm. Unlike other traditional algorithms used with addition, subtraction, and multiplication, the traditional algorithm used for division requires that students move left to right. The traditional division algorithm is very efficient to use and can be used with numbers of varying digit length. Although efficient, correct use of the traditional algorithm requires that students have strong basic fact recall (i.e., with multiplication facts and subtraction) and that students have a firm understanding of place value. Related Resources View other videos in this series.
This video demonstrates how to use the lattice division strategy. The lattice division strategy eliminates the requirement to use automatic recall of facts, such as in the partial quotient strategy, but this strategy requires that students follow a very specific set of steps. Careful use of the lattice is required. The lattice strategy partitions numbers into smaller parts and it may not be an efficient strategy for students to use if they do not understand how division works. To use this strategy, students should have a solid understanding of place value and dividing large quantities in equal groups.
In this video, Dr. Sharon Vaughn, Senior Advisor to the National Center on Intensive Intervention and the Executive Director of The Meadows Center for Preventing Educational Risk, discusses intensive academic interventions and supplies up to date information about the status of research studies on the subject.
In this article, Drs. Ketterlin Geller, Lembke, and Powell discuss how they are supporting educators to implement (1) the process of data-based individualization (DBI), (2) the principles of explicit and systematic instruction, and (3) key components of algebra readiness as part of Project STAIR (Supporting Teaching of Algebra: Individual Readiness).
The purpose of this guide is to provide brief explanations of key practices that can be implemented when working with students in need of intensive intervention in mathematics. Special education instructors, math interventionists, and others working with students who struggle with mathematics may find this guide helpful. Strategies presented in this guide should be used in conjunction with teaching guides developed for specific mathematical concepts.