Addition, Subtraction, Multiplication, Division - McGraw-Hill Australia

More documents

Recommendations

Info

DivisionThe division operation is first introduced forsingle-digit divisor problems. Students underlinethe part of the dividend that is at least as big asthe divisor. Next, they work the underlinedproblem and find the remainder for that part.Then, they bring down the next digit and workthe new problem in the same way. Theycontinue in this manner until they have written anumber above the last digit of the dividend. Thissignals that the problem is finished.The single-digit divisor strategy is first shownwith problems that have 1- and 2-digit answers.Early problems do not have answers with zeros.Later problems present 3-digit answers,answers with zero in the middle, and answerswith zero as the final digit. Special exercisesfocus on these troublesome types of divisionproblems.For 2-digit divisors, the procedure is the sameas that for single-digit divisors, except thestudents round off the divisor and theunderlined part of the problem to the nearesttens number. For example, if the problem is63 483, students write the rounded-off problemas 6 48 . The rounding-off sometimes leads totrial answers that are either too large or toosmall. Students are taught to determine whetherthe remainder is too large, and if it is, to makethe answer larger. If the remainder is too small(a negative number), students make the answersmaller. By the end of the module, students cansolve problems of these types:44 5900 24 216534 3618 75 3052Problem-Solving RoutinesThe most important feature of the operationsportions of these modules is that the problemsolvingroutines are introduced only after youhave taught all preskills necessary for errorlessstudent performance. For the students, theroutines are simply procedural chains of familiardiscriminations and responses, and success isensured.The care with which each necessary preskill isintroduced is well demonstrated by theoperations activities in the Subtraction module.Before the students learn the routine forsubtracting with borrowing in one column, theymaster these preskills:• Rewriting numbers by borrowing. Given anumber with one digit slashed, the studentslearn to borrow from the slashed digit. Thestudents write the borrowed amount in frontof the digit immediately to the right of theslashed digit.Given 35722Students write 3 1 572• Subtracting multidigit numbers withoutborrowing. Given a multidigit subtractionproblem, the students learn to subtract thebottom digit from the top digit in eachcolumn, starting with the ones column.GivenStudents begin with the ones column andwrite 841 410431• Minusing zero when zero is not written.Given a subtraction problem in whichthe minuend has more digits than thesubtrahend, the students learn that theabsence of a digit in the subtrahend meansthey must subtract zero.Given841 410348 7Students write 348 7341Corrective Math ©2005©Copyright SRA/McGraw-Hill. All rights reserved.Series Guide/◆ Addition ◆ Subtraction ◆ Multiplication ◆ Division 9
• Determining when and where to borrow.Given a partial subtraction problem, thestudents learn that “if you’re minusing morethan you start with, you have to borrow.” Thestudents use a slash to indicate the positionof the digit they would borrow from.GivenStudents write• Subtracting when borrowing has beendone. Given a problem in which borrowinghas been done for the students, thestudents learn to subtract accurately.GivenStudents write23 1 4 1823 1 4 18• Practice borrowing. Given a problemrequiring borrowing, students learn torewrite the digits in the minuend.GivenStudents write2 72 71652 3645 1 2 365 35 3Only after the students have mastered all sixpreskills are they introduced to the borrowingroutine.1. The students read the problem in the onescolumn.2. The students determine whether they haveto borrow.3. If borrowing is necessary, theyA. Determine which number to borrow from.B. Slash that number, and write the numberthat is left.C. Write a 1 in front of the number to theright of the number borrowed from.D. Reread the problem in the ones column,and subtract.The same care is taken later in the Subtractionmodule when teaching the preskills required forborrowing from consecutive columns andborrowing from zero. The same care is alsotaken in Addition, Multiplication, and Divisionmodules. In every case, all necessary preskillsare taught before problem-solving routines areintroduced.Story Problems TrackOne of the major strengths of the CorrectiveMathematics program is that CorrectiveMathematics teaches a precise strategy fordetermining which mathematics operation isrequired by a given story problem—a featurenot typically shared by other mathematicsprograms.Story problems are introduced in the Additionmodule through three major exercises:working with pictures, working with sentencesin columns, and working with sentences inparagraphs.Addition story problems include distracters,numbers that appear but are not used incomputing the answer. Two types of distractersare presented: distracters that involve the wrongclass of object and those that involve the wrongverb. Here is an example of a story problemwith a distracter that is from the “wrong class ofobjects” (rosebushes).There are 528 apple trees. There are4108 cherry trees. There are 180rosebushes. There are 600 oak trees.How many trees are there?Corrective Math ©2005©Copyright SRA/McGraw-Hill. All rights reserved.10 Series Guide/◆ Addition ◆ Subtraction ◆ Multiplication ◆ Division
Page 1: ◆ Addition ◆ Subtraction ◆ Mu
Page 7 and 8: There are 9 books on each shelf. Th
Page 9 and 10: Scope and Sequence ChartSubtraction
Page 11: Scope and Sequence ChartDivision1 5

Addition, Subtraction, Multiplication, Division - McGraw-Hill Australia

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?