DECIMAL LONG DIVISION LEVELS I-VI
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2 DECIMAL LONG DIVISION LEVELS I-VI Single and Double-Digit Divisors Table of Contents IMPORTANT NOTE TO TEACHER v LEVEL I Single-digit Divisors: 1-step Double-digit Divisors: 1-step Single-digit Divisors: 2-step Double-digit Divisors: 2-step Single-digit Divisors: 3-step Double-digit Divisors: 3-step LEVEL II Single-digit Divisors: whole number and decimal quotients with 1, 2, or 3 decimal places. 16 Double-digit Divisors: whole number and decimal quotients with 1, 2, or 3 decimal places. 21 Levels I and II Single and Double-digit Divisors LEVEL III Single-digit Divisors: basic Single-digit Divisors: 0 place holder in the quotient ones place Single-digit Divisors: 0 place holder in the quotient ones and tenths places Single-digit Divisors: multiple 0 place holders in the quotient Single-digit Divisors: dividends requiring extended dividing until obtaining a remainder of 0. 34
3 LEVEL III (Continued) Double-digit Divisors: basic Double-digit Divisors: 0 place holder in the quotient ones place Double-digit Divisors: 0 place holder in the quotient ones and tenths places Double-digit Divisors: multiple 0 place holders in the quotient Double-digit Divisors: dividends requiring extended dividing until obtaining a remainder of Levels I, II and II Single and Double-digit Divisors LEVEL IV Pre-Level IV: transforming decimal divisors to whole number divisors Single-digit Divisors (after transformation): basic Single-digit Divisors (after transformation): Level I style Single-digit Divisors (after transformation): Level II style Single-digit Divisors (after transformation): Level III style Single-digit Divisors (after transformation): Level III style: dividends requiring extended dividing until obtaining remainder of Double-digit Divisors (after transformation): basic Double-digit Divisors (after transformation): Level I style Double-digit Divisors (after transformation): Level II style Double-digit Divisors (after transformation): Level III style Double-digit Divisors (after transformation): Level III style: dividends requiring extended dividing until obtaining remainder of Levels I, II, III and IV Single and Double-digit Divisors
4 LEVEL V Single-digit Divisors: basic: single digit repeating Single-digit Divisors: single digit repeating following non-repeating value(s) Single-digit Divisors: single digit repeating: level II style Single-digit Divisors: single digit repeating: level III style Single-digit Divisors: single digit repeating: level IV style Double-digit Divisors: basic: single digit repeating Double-digit Divisors: single digit repeating following non-repeating value(s) Double-digit Divisors: basic: double digits repeating Double-digit Divisors: double digits repeating following non-repeating value(s) Double-digit Divisors: basic: triple digits repeating Double-digit Divisors: single digit repeating: level II style Double-digit Divisors: single digit repeating: level III style Double-digit Divisors: single digit repeating: level IV style Levels I, II, III, IV and V Single and Double-digit Divisors LEVEL VI Single-digit Divisors: rounding quotients to nearest whole number: level I style Single-digit Divisors: rounding quotients to nearest whole number: level II style Single-digit Divisors: rounding quotients to nearest whole number: level III style Single-digit Divisors: rounding quotients to nearest whole number: level IV style Single-digit Divisors: rounding quotients to nearest whole number: level V style Single-digit Divisors: rounding quotients to nearest tenth: level I style Single-digit Divisors: rounding quotients to nearest tenth: level II style Single-digit Divisors: rounding quotients to nearest tenth: level III style Single-digit Divisors: rounding quotients to nearest tenth: level IV style Single-digit Divisors: rounding quotients to nearest tenth: level V style
5 LEVEL VI (Continued) Single-digit Divisors: rounding quotients to nearest hundredth: level I style Single-digit Divisors: rounding quotients to nearest hundredth: level II style Single-digit Divisors: rounding quotients to nearest hundredth: level III style Single-digit Divisors: rounding quotients to nearest hundredth: level IV style Single-digit Divisors: rounding quotients to nearest hundredth: level V style Double-digit Divisors: rounding quotients to nearest whole number: level II style Double-digit Divisors: rounding quotients to nearest whole number: level III style Double-digit Divisors: rounding quotients to nearest whole number: level IV style Double-digit Divisors: rounding quotients to nearest whole number: level V style Double-digit Divisors: rounding quotients to nearest tenth: level I style Double-digit Divisors: rounding quotients to nearest tenth: level II style Double-digit Divisors: rounding quotients to nearest tenth: level III style Double-digit Divisors: rounding quotients to nearest tenth: level IV style Double-digit Divisors: rounding quotients to nearest tenth: level V style Double-digit Divisors: rounding quotients to nearest hundredth: level I style Double-digit Divisors: rounding quotients to nearest hundredth: level II style Double-digit Divisors: rounding quotients to nearest hundredth: level III style Double-digit Divisors: rounding quotients to nearest hundredth: level IV style Double-digit Divisors: rounding quotients to nearest hundredth: level V style NOTE TO THE TEACHER SYNTHESIS Levels I, II, III, IV and V Single and Double-digit Divisors: repeating decimal quotients and exact quotients Levels I, II, III, IV, V and VI Single and Double-digit Divisors: rounding quotients to the nearest hundredth Teacher answer pages
6 IMPORTANT NOTE TO THE TEACHER ABOUT THE DEVELOPMENTALLY APPROPRIATE USE OF THIS BOOK There are a number of fundamental prerequisite developments required for student readiness to begin decimal long division: Students must have successfully integrated Levels I VIII of whole number long division prior to starting decimal long division. All six levels of decimal long division require the application of all eight levels of whole number long division. If students have not yet fully integrated whole number long division, IT IS NEVER APPROPRIATE TO ATTEMPT THE CON- CEPT-PROCEDURE INTEGRATION OF LONG DIVISION THROUGH THE TEACHING OF DECIMAL LONG DIVISION. Levels I-VIII of whole number long division are taught in Making Math Real: The Four Operations and the 400 Math facts. Students must have integrated decoding and encoding the decimal code through the thousandths place and beyond taught in Making Math Real: Fractions, Decimals, and Advanced Place Value. Students must have integrated rounding decimals to the nearest hundredth place taught in Making Math Real: Fractions, Decimals, and Advanced Place Value. Students must have integrated the complete unit of increasing and decreasing decimals by powers of 10 taught in Making Math Real: Fractions, Decimals, and Advanced Place Value. The extensive volume of incremental practice in this book is intended to enable the educator to be prescriptive for students indicated areas of practice not to assign pages of unstructured drill. USING THIS BOOK DISASSOCIATED FROM ITS DESIGN AND INTENT WILL NOT HELP STUDENTS LEARN DECIMAL LONG DIVISION. Furthermore, it is NOT intended that students complete every page of this book unless indicated by their processing needs.
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