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.
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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 reviews to how use the traditional algorithm to solve multiplication with regrouping.
This video describes how to use the partial products strategy with multiplication.
This video illustrates how to use the partial quotient strategy to divide. To correctly use the partial quotient strategy, students need to have strong recall skills in division and multiplication facts. Students rely on this knowledge to partition the larger quantity that is being divided, into smaller and more manageable numbers. The partial quotient strategy is an alternative strategy for students who have not yet mastered the steps of the traditional algorithm.
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 module was adapted from a series of training modules developed by the National Center on Intensive Intervention (NCII) and is aimed at district or school teams involved in the initial planning for using data-based individualization (DBI) as a framework for providing intensive intervention in academics and behavior. The audience for this module may include school teams supporting academic intervention and progress monitoring in middle school mathematics.
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.
The first module in the Intensive Intervention Math Course Content focuses on the mathematics content necessary to include within intensive intervention. This includes matching decisions about instruction and assessment to the mathematics content.
This video describes how to use the partial differences strategy to solve multi-digit subtraction.