This video illustrates how to use the traditional addition algorithm with regrouping.
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This video describes how to use the partial sums strategy with addition. The problem in this video requires regrouping; however, the partial sums strategy eliminates the regrouping procedure. The partial sums strategy is typically performed left to right and focuses on adding only part of each multi-digit number at a time (e.g., only adding digits in the hundreds column to determine the partial sum of hundreds, followed by only adding digits in the tens column to determine the partial sum of tens, and so on). It may be especially important for students to know and understand the partial sums strategies if they have not yet developed an understanding for regrouping. This strategy is also efficient when all or most of the numbers have the same number of digits.
This video illustrates how to use the traditional algorithm to solve subtraction with regrouping. The traditional algorithm focuses on digit placement and requires that students move right to left to correctly perform the operation. Before students are introduced to the standard addition algorithm, it is important that they have a conceptual understanding of regrouping. This will allow students to correctly use the algorithm when they exchange 10 ones in the ones place value column with 1 ten in the tens place value column. It is important for students to know and understand how to use the traditional algorithm because it is an efficient strategy to use if regrouping is required, when numbers have varying numbers of digits, and when the numbers included are too large to reasonably use other strategies (e.g., partial differences can become confusing for students who do not understand negative integers).
This video describes how to use the partial differences strategy to solve multi-digit subtraction.
This video reviews to how use the traditional algorithm to solve multiplication with regrouping.
This video describes how to use the partial products strategy with multiplication.
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.
This toolkit provides activities and resources to assist practitioners in designing and delivering intensive interventions in reading and mathematics for K–12 students with significant learning difficulties and disabilities. Grounded in research, this toolkit is based on the Center on Instruction’s Intensive Interventions for Students Struggling in Reading and Mathematics: A Practice Guide, and includes the following resources: