Addition With Regrouping and Subtraction With Regrouping Trainer’s Guide developed by Bradley J. Kaffar and Susan P. Miller Strategic Math Series: Level 2 2011 The University of Kansas Center for Research on Learning Lawrence, Kansas University of Kansas Center for Research on Learning 2002

Overview of the Strategic Math Series Level 1 Addition Facts 0-9 Subtraction Facts 0-9 Place Value: Discovering Ones & Tens Addition Facts 10-18 Subtraction Facts 10-18 Multiplication Facts 0-81 Division Facts 0-81 Level 2 Addition With Regrouping Subtraction With Regrouping University of Kansas Center for Research on Learning 2011 University of Kansas Center for Research on Learning 2002

Purpose of the Series (Level 2) To provide students with: the skills needed to solve complex computation and word problems. a foundation for solving more advanced problems in the future. University of Kansas Center for Research on Learning 2011

Rationales for the Series Students need: manipulative and pictorial models to promote conceptual understanding of algorithms and place value. strategies for solving math problems at the abstract level. skills to discriminate between problems that require regrouping and problems that do not require regrouping. University of Kansas Center for Research on Learning 2011

Rationales for the Series Students need: fluency-building practice to master and retain complex computation and regrouping skills. strategies for solving word problems. successful experiences in math. University of Kansas Center for Research on Learning 2011

Guiding Principles The Concrete-Representational-Abstract (C-R-A) Teaching Method Concrete: use objects (e.g., base-ten blocks) Representational: use drawings (e.g., squares, lines) and tallies Abstract: use numbers (e.g., 42, 317) University of Kansas Center for Research on Learning 2011

Guiding Principles Mastery Learning Procedural processes become fluent Fluency assists retention Students then ready to advance to more complex problems University of Kansas Center for Research on Learning 2011

Guiding Principles Use of Mnemonics Enables students to actively engage in the problem-solving process Enables students to apply this process independently University of Kansas Center for Research on Learning 2011

Instructional Phases Phase 1 Pretest Phase 2 Teach Concrete Application Phase 3 Teach Representational Application Phase 4 Introduce the “RENAME” Strategy Phase 5 Teach Abstract Application Phase 6 Posttest Phase 7 Practice to Fluency University of Kansas Center for Research on Learning 2011

Concrete Level Lessons 1 - 3 Use three-dimensional objects (e.g., base-ten blocks) and a place-value mat to represent and solve computation problems. Ones blocks Tens strips Hundreds flats University of Kansas Center for Research on Learning 2011

Representational Level Lessons 4 and 5 Use drawings to solve computation problems. Horizontal tallies represent ones Vertical lines represent tens Squares represent hundreds University of Kansas Center for Research on Learning 2011

Representational Level Addition With Regrouping University of Kansas Center for Research on Learning 2011

Representational Level Subtraction With Regrouping University of Kansas Center for Research on Learning 2011

E Examine the ones column: 10 or more, go next door. The “RENAME” Strategy (used to solve addition with regrouping problems) R Read the problem. E Examine the ones column: 10 or more, go next door. N Note the ones in the ones column. A Address the tens column: 10 or more, go next door. M Mark tens in the tens column. E Examine and note hundreds; exit with a quick check. University of Kansas Center for Research on Learning 2011

“10 or More” Sentences Adding the Ones: If adding the numbers in the ones column results in 10 or more, regroup to form a ten (10 or more, go next door). Adding the Tens: If adding the numbers in the tens column results in 10 or more, regroup to form a hundred (10 or more, go next door). University of Kansas Center for Research on Learning 2011

Addition With Regouping West Region Update Conference for SIM Professional Developers Read the problem. 3 5 7 + 2 8 4 University of Kansas Center for Research on Learning 2011 Copyright © 2009 by Susan P. Miller and Bradley J. Kaffar

Examine the ones column: 10 or more, go next door. 3 5 7 + 2 8 4 If adding the numbers in the ones column results in 10 or more, regroup to form a ten (10 or more, go next door). University of Kansas Center for Research on Learning 2011

Note ones in the ones column. 1 3 5 7 + 2 8 4 University of Kansas Center for Research on Learning 2011

Address the tens column: 10 or more, go next door. 3 5 7 + 2 8 4 If adding the numbers in the tens column results in 10 or more, regroup to form a hundred (10 or more, go next door). University of Kansas Center for Research on Learning 2011

Mark tens in the tens column. 1 3 5 7 + 2 8 4 University of Kansas Center for Research on Learning 2011

Examine and note hundreds; exit with a quick check. Addition With Regouping West Region Update Conference for SIM Professional Developers Examine and note hundreds; exit with a quick check. 1 3 5 7 + 2 8 4 6 University of Kansas Center for Research on Learning 2011 Copyright © 2009 by Susan P. Miller and Bradley J. Kaffar

E Examine the ones column: use the BBB Sentence for ones. The “RENAME” Strategy (used to solve subtraction with regrouping problems) R Read the problem. E Examine the ones column: use the BBB Sentence for ones. N Note the ones in the ones column. A Address the tens column: use the BBB Sentence for tens. M Mark tens in the tens column. E Examine and note hundreds; exit with a quick check. 22 University of Kansas Center for Research on Learning 2011

BBB Sentences BBB Sentence for Ones: Bigger number on Bottom means Break down a ten and trade. BBB Sentence for Tens: Bigger number on Bottom means Break down a hundred and trade. University of Kansas Center for Research on Learning 2011

Subtraction With Regrouping West Region Update Conference for SIM Professional Developers Read the problem. 4 5 7 - 2 6 8 University of Kansas Center for Research on Learning 2011 Copyright © 2009 by Susan P. Miller and Bradley J. Kaffar

Examine the ones column: use the BBB Sentence for ones. 4 17 5 7 - 2 6 8 Bigger number on Bottom means Break down a ten and trade. University of Kansas Center for Research on Learning 2011

Note ones in the ones column. 4 17 5 7 - 2 6 8 9 University of Kansas Center for Research on Learning 2011

Address the tens column: use the BBB Sentence for tens. 3 14 17 4 5 7 - 2 6 8 9 Bigger number on Bottom means Break down a hundred and trade. University of Kansas Center for Research on Learning 2011

Mark tens in the tens column. 3 14 17 4 5 7 - 2 6 8 9 University of Kansas Center for Research on Learning 2011

Examine and note hundreds; exit with a quick check. Subtraction With Regrouping West Region Update Conference for SIM Professional Developers Examine and note hundreds; exit with a quick check. 3 14 17 4 5 7 - 2 6 8 1 9 1 8 9 + 2 6 4 5 7 University of Kansas Center for Research on Learning 2011 Copyright © 2009 by Susan P. Miller and Bradley J. Kaffar

Instructional Procedures Give an Advance Organizer Describe and Model Conduct Guided Practice Conduct Independent Practice Conduct Problem-Solving Practice Administer Regrouping Probe Administer Review Probe Conduct Pig Game Practice Provide Feedback University of Kansas Center for Research on Learning 2011

Feedback Sequence for Individuals 1. Score each student’s product for correct and incorrect responses. 2. Meet with student; plot score on the Progress Chart. 3. Specify incorrect responses and error patterns if they exist. 4. Demonstrate the task. 5. Ask student to practice the application. 6. Close the feedback session with positive statement. University of Kansas Center for Research on Learning 2011

Feedback Sequence for Groups 1. Score the student products. 2. Provide positive feedback to the group. 3. Specify incorrect responses and corresponding error patterns if they exist. 4. Show the students how to avoid the error pattern. 5. Ask the students to practice the application. 6. Close the feedback session with positive statement. University of Kansas Center for Research on Learning 2011

Field Test Results Addition With Regrouping: Study 1 Computation Mean Pretest Mean Posttest Treatment Group 49% 90% Comparison Group 66% 72% Word Problems 41% 89% 51% 69% Addition With Regrouping Minute* 3.22 8.11 6.00 *Problems correct per minute University of Kansas Center for Research on Learning 2011

Field Test Results Addition With Regrouping: Study 2 Mean Baseline Treatment Maintenance Generalization Triad 1 23.33% 92.74% 93.33% 90.00% Triad 2 22.50% 94.43% 96.67% Triad 3 5.00% 91.29% Participants were nine elementary students with learning disabilities. All nine participants increased their performance level only after introduction of treatment. Maintenance occurred seven days after instruction ceased. Generalization occurred 14 days after instruction in the general education classroom. Percentage of non-overlapping data (PND) was 97.83% (i.e., a large effect size). University of Kansas Center for Research on Learning 2011

Field Test Results Subtraction With Regrouping: Study 1 Computation Mean Pretest Mean Posttest Treatment Group 60% 86% Comparison Group 76% 78% Word Problems 45% 77% 62% 57% University of Kansas Center for Research on Learning 2011

Field Test Results Subtraction With Regrouping: Study 2 Mean Baseline Mean Treatment Mean Maintenance 10.95% 87.20% 86.00% Participants were five fifth grade students with learning disabilities. All five participants increased their performance level only after introduction of treatment. Maintenance occurred seven days after instruction ceased. Percentage of non-overlapping data (PNP) was 90.20% (i.e., a large effect size). University of Kansas Center for Research on Learning 2011

Materials to Obtain Base-ten blocks Whiteboard and display equipment Stopwatch or clock with a second hand All other materials are contained in manuals. Pig dice accompany each manual. University of Kansas Center for Research on Learning 2011

Student Notebook Contents Learning Contract Progress Chart Place-Value Mats: Hundreds, Tens, and Ones Learning Sheets Regrouping Minute(s) Review Minute(s) Pig Game Sheets Celebrate your accomplishments! University of Kansas Center for Research on Learning 2011