Download Understanding Division: Interpretations, Properties, Algorithms, and Mental Methods and more Study notes Elementary Mathematics in PDF only on Docsity! Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion MATH 112 Section 3.4: Understanding Division Prof. Jonathan Duncan Walla Walla College Fall Quarter, 2006 Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion Outline 1 Interpretations of Division 2 Properties of Division 3 Division Algorithms 4 Mental Division Methods 5 Conclusion Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion Repeated Subtraction Model A model that ties in well with the “repeated addition” model of multiplication is the “repeated subtraction” model for division. Example You are making miniature apple pies. Each pie requires 6 ounces of apples. You have 18 total ounces of apples. How many pies can you make? Take 6 away from 18 repeatedly until you no longer have 6 to take away. Since we can take away 3 groups of six, the answer is 3. The Repeated Subtraction Model To divide a whole number a by another whole number b, divide the quantity a into portions of size b. The number of resulting portions is the quotient, and anything left over is the remainder. Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion Comparing the Two Models To see how the two models we have examined differ, lets solve the following problem in two different ways. Example Divide the number 10 by 2. Start with a train of 10 blocks. Divide it into two equal trains. Each train is five units long, so the quotient is five. Using a train of 10 blocks as our starting point, divide the train into smaller trains of length two. Since we get five trains of length two, the quotient is five. Other Models Other models of division include the “missing factor” and “number line” models. Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion Properties of the Four Operations The following table describes the properties of each of the four operations we have examined. Property Summaries Commutative Associative Identity Inverses + yes yes yes yes − no no no no × yes yes yes yes ÷ no no no no Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion The Standard Algorithm As with previous operations, we assume that you know the “standard” long division algorithm Example Use the standard division algorithm to solve the following problem: 14948÷ 71 Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion Scaffolding Division Another interesting algorithm makes use of “guess-and-check” methods and breaks division problems down into smaller pieces. Example Use scaffolding to solve each division problem. 576÷ 8 6371÷ 24 Interpretations of Division Properties of Division Division Algorithms Mental Division Methods Conclusion Algorithms for Mental Division There are a few tricks that can make division easier to do mentally. Example Find each product mentally as quickly as possible. 1 6000÷ 20 2 20000÷ 400 3 152÷ 8 4 882÷ 9
