Math Focal Points
Table Of Contents
Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers.
Students apply their understanding of models for division, place value, properties, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends. They select appropriate methods and apply them accurately to estimate quotients or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for dividing whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems. They consider the context in which a problem is situated to select the most useful form of the quotient for the solution, and they interpret it appropriately (NCTM, 2006, p.17).
This list of resources begins with interactive activities that emphasize the connection between multiplication and division. Other resources deal directly with long division and offer lessons in that skill.
In this interactive activity, students learn about division through building rectangular arrays on a grid. Each array represents the factorization of a number (ranging from 1 through 50). Students represent the product of two factors of the number as the area of a rectangle on a grid, an important representation of multiplication and division. The challenge is to find all possible divisors of the number.
MSP full record
An excellent online game, easily adapted to a paper-and-pencil format, exercises skills with factors and multiples. The activity offers practice with multiplication of numbers from 1 through 9 and with division of their products.
(From Illuminations — MSP full record)
With this virtual manipulative, students use rectangular models to explore and practice division. From picture and equation, the learner sees that the dividend equals the divisor times another number plus a remainder. In a “Test Me” option, users are given division problems to solve. They can create a picture representing the division problem, then fill in the text boxes to give the equation and check their answer.
(From National Library of Virtual Manipulatives — MSP full record)
Using this online activity, the student practices division by finding remainders for a given number and clicking the appropriate numbers in Pascal's triangle to form a colored number pattern. The applet guides the student in finding all possible remainders, starting with zero, and will not allow an incorrect number to be colored.
MSP full record
Many, many division topics are addressed here through short lessons and practice problems. In particular, instructions on how to perform long division are presented through well-set out examples.
(From AAA Math — MSP full record)
Pages, called “factsheets,” emphasize the meaning of place value in division and the concept of division as repeated subtraction, with well-explained examples of both short and long division. A game as well as worksheets and quizzes are available for practice.
MSP full record
Worked examples of short- and long-division problems. For long division, an applet gives a step-by-step demonstration of the procedure; the pace at which the student views each step is controlled by the student.
MSP full record
Reference
NCTM. (2006).
Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author
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Copyright
March 2008 — The Ohio State University. This material is based upon work
supported by the National Science Foundation under Grant No. 0424671. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation.
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