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## Adding It Up: Helping Children Learn Mathematics (2001) Center for Education (CFE)

### Citation Manager

. "6 Developing Proficiency with Whole Numbers." Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

 Page 205

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Adding + It Up: Helping Children Learn Mathematics
 Box 6–9 Three Methods for Multidigit Subtraction A Common U.S. Algorithm right to left alternate ungrouping and subtracting Accessible Generalizable Methods left-to-right ungrouping right-to-left ungrouping Do all ungrouping, in any order, until every top number is larger than the bottom number. Then subtract each kind of multiunit, in any order.

the ones place to get 6, a student moves to the left and sees 3 on the top and 6 on the bottom. The answer 3 is generated spontaneously as a subtraction answer, given 6 and 3. It takes extra effort to suppress this answer and think about the direction in which one is subtracting.

Methods B and C are slight variations of Method A in which Step 1 (regrouping) is done for all columns first. For each column in either direction, the student asks the regrouping (borrowing) question, “Can I subtract in this column? Is the top digit as big as or bigger than the bottom digit?”

 Page 205
 Front Matter (R1-R20) Executive Summary (1-14) 1 Looking at Mathematics and Learning (15-30) 2 The State of School Mathematics in the United States (31-70) 3 Number: What Is There to Know? (71-114) 4 The Strands of Mathematical Proficiency (115-156) 5 The Mathematical Knowledge Children Bring to School (157-180) 6 Developing Proficiency with Whole Numbers (181-230) 7 Developing Proficiency with Other Numbers (231-254) 8 Developing Mathematical Proficiency Beyond Number (255-312) 9 Teaching for Mathematical Proficiency (313-368) 10 Developing Proficiency in Teaching Mathematics (369-406) 11 Conclusions and Recommendations (407-432) Biographical Sketches (433-440) Index (441-454)