This video illustrates how manipulatives can be used to explain the commutative property of addition to students. Understanding that the order in which two numbers are added does not change the result supports basic fact fluency and students’ thinking related to problem solving. For example, when students understand how the commutative property works and if they have mastered a basic fact such as “3 + 1” then they have also mastered the basic fact of “1 + 3.”
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This video demonstrates two subtraction problem structures that students must understand to master basic facts. Each problem structure has three numbers, with one number missing.
This video shows how manipulatives can be used to explain subtraction using a part-part-whole structure.
This video illustrates how manipulatives can be used to show the relation between strategies for subtraction and addition.
This video shows how manipulatives can be used to explain multiplicative problem structures to students who are just beginning to use multiplication strategies.
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.
This video shows how manipulatives can be used to explain that multiplication represents groups of equal sets of numbers.
This video illustrates the use of scaffolding with manipulatives to teach students to group objects by tens with counting by ones.
Providing more explicit instruction, captured within the comprehensiveness domain of the Taxonomy of Intervention Intensity, is critical within intensive intervention. The Recognizing Effective Special Education Teachers (RESET) project, funded by U.S. Department of Education Institute for Education Sciences (IES) and led by Evelyn Johnson at Boise State University, developed a series of rubrics based on evidence-based practices for students with high incidence disabilities. One set of rubrics focuses on explicit instruction. Based on the main ideas of Explicit Instruction, the Explicit Instruction Rubric was designed for use by supervisors and administrators to reliably evaluate explicit instructional practice, to provide specific, accurate, and actionable feedback to special education teachers about the quality of their explicit instruction, and ultimately, improve the outcomes for students with disabilities.