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.
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This video describes how to use the partial products strategy with multiplication.
This video illustrates the use of an efficient counting on strategy that students may practice to solve simple addition problems without the use of manipulatives. When students use a counting on strategy to solve an addition problem, they must be able to hold one number in working memory; however, an important working memory strategy to teach students and allow students to practice includes using fingers to track counting. Counting on is an efficient strategy that students may use to quickly determine the solution to an addition problem. With enough practice opportunities students will soon be able to perform simple arithmetic without the use of working memory strategies such as finger counting.
This video illustrates the use of an efficient counting on strategy that students may practice to solve simple subtraction problems without the use of manipulatives.
This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance.
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.
In Module 8 of the Intensive Intervention in Mathematics Course Content we highlight the necessity for implementing evidence-based practices with fidelity. We also explain how to make adaptations to the instructional platform when students demonstrate inadequate progress. We finish this module by putting all the information learned across modules together with the intensive intervention framework.
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.