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 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 demonstrates how to use lattice multiplication. Although the lattice multiplication strategy eliminates regrouping while solving the problem, it requires careful construction of the lattice (it needs to be the correct size), correct placement of the numbers (above or below the lattice line), and a solid understanding of place value. The lattice strategy uses place value by partitioning multi-digit numbers into smaller parts and it may not be an efficient strategy for students to use if they do not understand how multiplication works. However, learning this strategy with whole numbers may benefit students as they begin to multiply decimals as lattice multiplication is an efficient tool to use with decimals.
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 video demonstrates how to use the lattice division strategy. The lattice division strategy eliminates the requirement to use automatic recall of facts, such as in the partial quotient strategy, but this strategy requires that students follow a very specific set of steps. Careful use of the lattice is required. The lattice strategy partitions numbers into smaller parts and it may not be an efficient strategy for students to use if they do not understand how division works. To use this strategy, students should have a solid understanding of place value and dividing large quantities in equal groups.
This video illustrates the use of manipulatives to help students develop fluency in counting by tens and ones.
This video illustrates the use of manipulatives to help students integrate the concept of counting by ones with skill in grouping by tens.
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 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.