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).
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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 addition algorithm with regrouping.
This video shows how manipulatives can be used to explain how different combinations of numbers make 10. When students practice putting together and taking apart numbers with manipulatives in different ways they develop a conceptual understanding for composing and decomposing and how numbers are related to one another. Understanding number combinations allows students to develop fluency skills with other operations and assists students with problem solving.
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.”
In this video, Dr. Devin Kearns, an Assistant Professor of Special Education in the Department of Education Psychology at the Neag School of Education at the University of Connecticut and NCII Trainer & Coach, discusses importance of consistency when selecting, administering, and scoring progress monitoring tools.
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.