CEC 2014 Convention & Expo

Bradley J. KaffarNancy S. Fitzgerald

Dustin B. ManclMargaret A. Vanderwarn

Evidence-Based Practices to Improve Achievement in Computation With

Regrouping and Word Problems

Advance OrganizerEvidence-Based PracticesAddition With RegroupingSubtraction With RegroupingWord Problems With RegroupingCombined Problem-Solving Methods

Introduction

Mathematics is one of the most challenging aspects of the school curriculum for many students, and a concern is the lack of achievement in multi-digit computation with regrouping and word problems. Specifically, out of 29 mathematics difficulties, special education teachers ranked word problems as the most problematic, multi-step problems as second most problematic, and regrouping as the seventh most problematic area for students with learning disabilities (LD) (Bryant & Bryant, 2008).

Evidence-Based PracticesExplicit InstructionConcrete – Representational – Abstract (CRA)

Teaching SequenceCognitive StrategiesSchema-Based Diagrams

Explicit InstructionAdvance OrganizerDescribe and ModelGuided PracticeIndependent PracticeProblem-Solving PracticeSupplemental Practice to Fluency

The “RENAME” Strategy for Addition With RegroupingRead the problem.

Examine the ones column: 10 or more, go next door.

Note the ones in the ones column.

Address the tens column: 10 or more, go next door.

Mark tens in the tens column.

Examine and note hundreds; exit with a quick check.

“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).

Read the problem.

3 5 7+ 2 8 4

Examine the ones column: 10 or more, go next door.

13 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).

Note ones in the ones column.

13 5 7

+ 2 8 41

Address the tens column: 10 or more, go next door.

1 13 5 7

+ 2 8 41

If adding the numbers in the tens column results in 10 or more, regroup to form a hundred (10 or more, go next door).

Mark tens in the tens column.

1 13 5 7

+ 2 8 44 1

Examine and note hundreds; exit with a quick check.

1 13 5 7

+ 2 8 46 4 1

The “RENAME” Strategy for Subtraction With Regrouping

Read the problem.

Examine the ones column: use the BBB Sentence for ones.

Note the ones in the ones column.

Address the tens column: use the BBB Sentence for tens.

Mark tens in the tens column.

Examine and note hundreds; exit with a quick check.

“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.

Read the problem.

4 5 7- 2 6 8

Examine the ones column: use the BBB Sentence for ones.

4 174 5 7

- 2 6 8

Bigger number on Bottom means Break down a ten and trade.

Note ones in the ones column.

4 174 5 7

- 2 6 89

Address the tens column: use the BBB Sentence for tens.

14

3 4 174 5 7

- 2 6 89

Bigger number on Bottom means Break down a hundred and trade.

Mark tens in the tens column.

14

3 4 174 5 7

- 2 6 88 9

Examine and note hundreds; exit with a quick check.

1 11 8 9

+ 2 6 84 5 7

14

3 4 174 5 7

- 2 6 81 8 9

Word ProblemsJoin ProblemsSeparate ProblemsPart – Part – Whole ProblemsCompare ProblemsExtraneous InformationStudent-Originated Problems

The “FAST RENAME” Strategy for Word Problems With Regrouping

Step 1: Find what you’re solving for.

Step 2: Ask yourself, “What are the parts of the problem?”

Step 3: Set up the numbers.

Step 4: Tie down the sign.

Use the “RENAME” Strategy for computation.

Combined Problem-Solving MethodsExplicit Instruction Concrete – Representational – Abstract (CRA)

Teaching SequenceSchema-Based DiagramsThe “READER” Strategy

Schema-Based Diagrams

Read the problem.

The “READER” Strategy

Step 1: Read the problem.

Step 2: Examine the question.

Step 3: Abandon irrelevant (unneeded) information.

Step 4: Determine the operation using diagrams, if needed.

Step 5: Enter numbers.

Step 6: Record answer.

Juan collects rocks. His sister collects dolls. Juan had fifteen rocks before going to the park. Today, Juan collected five more rocks at the park. How many rocks does Juan have in all?

Examine the question.

Juan collects rocks. His sister collects dolls. Juan had fifteen rocks before going to the park. Today, Juan collected five more rocks at the park. How many rocks does Juan have in all?

The “READER” Strategy

Step 1: Read the problem.

Step 2: Examine the question.

Step 3: Abandon irrelevant (unneeded) information.

Step 4: Determine the operation using diagrams, if needed.

Step 5: Enter numbers.

Step 6: Record answer.

Abandon irrelevant (unneeded) information.

Juan collects rocks. His sister collects dolls. Juan had fifteen rocks before going to the park. Today, Juan collected five more rocks at the park. How many rocks does Juan have in all?

The “READER” Strategy

Step 1: Read the problem.

Step 2: Examine the question.

Step 3: Abandon irrelevant (unneeded) information.

Step 4: Determine the operation using diagrams, if needed.

Step 5: Enter numbers.

Step 6: Record answer.

Determine the operation using diagrams, if needed.

Juan collects rocks. His sister collects dolls. Juan had fifteen rocks before going to the park. Today, Juan collected five more rocks at the park. How many rocks does Juan have in all?

☐

+ ☐

The “READER” Strategy

Step 1: Read the problem.

Step 2: Examine the question.

Step 3: Abandon irrelevant (unneeded) information.

Step 4: Determine the operation using diagrams, if needed.

Step 5: Enter numbers.

Step 6: Record answer.

Enter numbers.

Juan collects rocks. His sister collects dolls. Juan had fifteen rocks before going to the park. Today, Juan collected five more rocks at the park. How many rocks does Juan have in all?

15 + 5

The “READER” Strategy

Step 1: Read the problem.

Step 2: Examine the question.

Step 3: Abandon irrelevant (unneeded) information.

Step 4: Determine the operation using diagrams, if needed.

Step 5: Enter numbers.

Step 6: Record answer.

Record answer.

Juan collects rocks. His sister collects dolls. Juan had fifteen rocks before going to the park. Today, Juan collected five more rocks at the park. How many rocks does Juan have in all?

15 + 5 20 rocks

The “READER” Strategy

Step 1: Read the problem.

Step 2: Examine the question.

Step 3: Abandon irrelevant (unneeded) information.

Step 4: Determine the operation using diagrams, if needed.

Step 5: Enter numbers.

Step 6: Record answer.

Post OrganizerEvidence-Based PracticesAddition With RegroupingSubtraction With RegroupingWord Problems With RegroupingCombined Problem-Solving Methods

Resources:http://bradleyjkaffar.efoliomn.com/CEC2014