instructional program: teaching addition and subtraction

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Context for Instruction: Instruction will occur at a side table in a pull-out resource room during 3 rd hour math class. Student D will be pulled into the hallway for all assessments. There will be up to eight other students present in the resource room during the instruction, and they will be working with the teacher and classroom aide while I work one-on-one with Student D. Program Objective: During math instruction, Student D will independently solve 5 one-step addition and subtraction word problems with up to 3-digit numerals with 5 out of 5 problems correct on 4 out of 5 trials. Generalization: I am concerned that Student D will only be able to perform this skill in a highly structured one-on-one “pull out” setting. To address this, I will use the “teach in the natural setting” strategy by having him complete problems in a small group once a week during instruction in the resource room. This setting is more natural and realistic to how he will be completing the task once the instructional program is over. It is also the context in which students typically perform this skill. I will check his work, and if there is significant discrepency between his performance during one- on-one instruction and small group instruction, this issue will be addressed through additional assessment and analysis. Rationale: Student D is currently unable to consistently solve one-step addition and subtraction word problems correctly. This is a skill that will be necessary for him to continue his academic career, because more complex math skills tend to build off more basic ones. He will not be able to successfully progress to harder material if he has not mastered these more basic skills first. In addition, the skills gained from learning these word problems are

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Instructional Program: teaching addition and subtraction

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Context for Instruction:Instruction will occur at a side table in a pull-out resource room during 3rd hour math class. Student D will be pulled into the hallway for all assessments. There will be up to eight other students present in the resource room during the instruction, and they will be working with the teacher and classroom aide while I work one-on-one with Student D.

Program Objective:During math instruction, Student D will independently solve 5 one-step addition and subtraction word problems with up to 3-digit numerals with 5 out of 5 problems correct on 4 out of 5 trials.

Generalization:I am concerned that Student D will only be able to perform this skill in a highly structured one-on-one pull out setting. To address this, I will use the teach in the natural setting strategy by having him complete problems in a small group once a week during instruction in the resource room. This setting is more natural and realistic to how he will be completing the task once the instructional program is over. It is also the context in which students typically perform this skill. I will check his work, and if there is significant discrepency between his performance during one-on-one instruction and small group instruction, this issue will be addressed through additional assessment and analysis.

Rationale: Student D is currently unable to consistently solve one-step addition and subtraction word problems correctly. This is a skill that will be necessary for him to continue his academic career, because more complex math skills tend to build off more basic ones. He will not be able to successfully progress to harder material if he has not mastered these more basic skills first. In addition, the skills gained from learning these word problems are applicable in real-life contexts as well, such as knowing whether he has gotten the correct amount of money back at the grocery store.

Assessment Procedures:Assessment will occur at the table in the hallway directly outside of the resource room. Student D should not have any materials, and he will complete the assessment without any teacher assistance or prompting. Assessment should be given according to the following procedures:1. Teacher will give Student D a worksheet of 5 word problems (addition and subtraction, mixed randomly).2. Teacher will tell Student D that this is a quiz and to complete the problems independently. If he asks for assistance, teacher will tell him that this is meant to test what he is able to do on his own.3. After he has completed all of the problems, the percentage correct can be determined by dividing the number of correct answers by the total number of problems. Since accuracy is determined based only on whether the answer is correct, it is okay if Student D does not use all of the steps of the cognitive strategy during assessment. The only thing that is assessed for accuracy is the answer.4. For each problem that Student D has completely correctly, mark a (+) in the corresponding box on the data sheet. For each problem that was completed incorrectly, mark a () in corresponding box. Fill in the corresponding bar on the bar graph up to line that indicates the number of problems that were completed correctly.

Assessment Schedule:The baseline data will be taken one time. Student D will complete five math word problems (addition and subtraction, mixed randomly). After baseline data has been taken and instruction has started, I will assess Student D every other day at the beginning of the class period. He will complete five problems at this time. Since he typically will complete six problems on each day of instruction, this means the ratio of instruction to assessment will be about 12:5.

Instructional Procedures:Instruction will take place during math class at a side table in the resource room. Student D is being taught to solve these problems using the following cognitive strategy:

1. Read the problem.Im going to read the problem. If I dont understand, Ill read it again.

2. Paraphrase the problem.Say the problem in my own words. What is it asking? What am I looking for?

3. Identify the important information.What is important? What information that is given in the problem will be necessary to solve it?

4. Identify the correct operation.Is this an addition or subtraction problem? How do I know?

5. Compute the answer.Do the operations in the right order. Start with solving the ones column, then the tens column, and finally the hundreds column.

6. Label the answer and check that it makes sense.I will label my answer. Does my answer make sense?

Instruction will occur on every scheduled opportunity, which should be every day during math class. All steps of the strategy will be taught simultaneously. A cue card listing key words to identify or suggest addition vs. subtraction will be provided during instruction, but not during assessment. Since Student D will not have access to the cue card during assessment, its use will be naturally faded before he meets the objective. Student D will be instructed according to this lesson routine using a most-to-least prompting technique as follows:1. Model one problem using the think-aloud script for the first five days of instruction.2. Complete one problem with the teacher writing and leading the discussion, but asking student to respond to one question per step. Use this level of assistance for the first ten days of instruction.3. Complete one problem using direct verbal prompts on each step of the strategy. For each step Student D completes correctly, give verbal/social praise such as Good job. If he makes an error, model the step as error correction.4. Complete one problem using indirect/question verbal cues for each step of the strategy. For example, What should we do next? For each step Student D completes correctly, give verbal/social praise such as Good job. If he makes an error, provide direct verbal assistance as error correction.5. Student will complete two problems independently, without any prompting or assistance from the teacher. Once he reaches the computation part of the problem, provide verbal/social praise after each step he completes correctly. If at any point during the problem he begins to write an incorrect response, provide direct verbal assistance as error correction. If Student D completes any step of the strategy correctly on both problems, that step will begin with indirect verbal prompts the following day during instruction. If he makes errors on that step with indirect verbal prompts on subsequent days, move back to direct verbal prompts. For each step of the cognitive strategy, circle the prompt level at which the step was completed successfully on the corresponding data sheet.

Reinforcement (type and schedule):Student D will be given verbal praise as a reinforcer. Verbal/social praise will be given for every correct step of the strategy that Student D completes. Reinforcement is faded separately on each step of the cognitive strategy as it is mastered. Once he performs a step of the strategy without assistance on both of the independent practices for two consecutive days, fade reinforcement to every other opportunity for two days. If his performance is maintained, fade reinforcement to approximately every fourth opportunity and keep it at that level until mastery.

Maintenance:This skill will be naturally maintained because it is included in the general math curriculum and in ongoing math assessments. In addition, new math skills will build off of these skills. I will also test for maintenance by giving Student D a 5-problem worksheet with addition and subtraction word problems once a week.

Instruction Data Sheet:

Date Date Date1. Read the problem.

MDVIVIMDVIVIMDVIVI

2. Paraphrase the problem.

MDVIVIMDVIVIMDVIVI

3. Identify the important information.

MDVIVIMDVIVIMDVIVI

4. Identify the correct operation.

MDVIVIMDVIVIMDVIVI

5. Compute the answer.

MDVIVIMDVIVIMDVIVI

6. Label the answer and check that it makes sense.MDVIVIMDVIVIMDVIVI

Assessment Data Sheet:

ProblemDateDate Date#1(+/-)(+/-)(+/-)

#2(+/-)(+/-)(+/-)

#3(+/-)(+/-)(+/-)

#4(+/-)(+/-)(+/-)

#5(+/-)(+/-)(+/-)

Number Correct/5/5/5

Assessment Bar Graph:

Skill Sequence:

Understand the meaning of addition and subtaction operations (increasing number vs. decreasing number).

Identify key words that distinguish between addition and subtraction (for example: more than, sum, difference, etc.).

Use operations to solve 1-digit addition and subtraction problems.

Use operations to solve 2-digit addition and subtaction problems.

Use operations to solve 3-digit addition and subtaction problems.

Apply knowledge of key words and operations to solve up to 3-digit addition and subtraction word problems.