Student: 6th Period Mathematics Class, JS, TK, ER, RG, MQ

Initiator: Jami Shlensky

Context for Instruction:

Instruction will take place at Jefferson Middle School in a self-contained cross

categorical classroom. It will occur between the hours of 11:20 and 12:07. The skill will be

taught during math class so it will be a part of the naturally occurring routine after the daily

bellringer (warm-up). The classroom teacher as well as a teacher’s aide is in the room.

Materials for instruction will include the smart board, white boards, dry erase markers,

notebooks, and worksheets. Students will be seated at their desk and I will teach them

using the Smart Board. I will float around the room during independent work and

assessment.

Program Objective:

When presented with a division problem, students will complete the long division

problem and write the correct answer to the equation on 4 out of 5 consecutive probe

trials.

Generalization:

The generalization that is most concerning when it comes to division is when it is

not presented on a sheet of paper with a pencil. As a result of this, the program is

structured to have the students convert the division problem to a long division problem,

themselves. This will allow them to learn how to use long division to complete any type of

division problem. This generalizes to money math, dividing a recipe, or sharing with

friends. I will monitor whether generalization strategies are successful by presenting them,

during instruction, with multiple forms of division problems; word problems, long division

problems, money problems, manipulatives, etc. The informal assessments of whether or not

they can complete these problems will allow me to see if the skill is being generalized. I will

also monitor their AIMS Web testing to see their success with division on said probes.

Rationale:

It is necessary for these five students to master long division skills so that they are

able to move to higher mathematical thinking. The students are struggling in our current

curriculum due to the fact that they cannot perform basic mathematical functions. If I can

create a program to help mitigate that problem then the students can progress in their

development and mathematical skills to a level of higher thinking. Division is a skill that is

required for basic real-world functioning when it comes to money and sharing. In order for

the students to be successful independently, not only in academics but in life, they need to

learn how to divide.

Assessment Procedures:

During baseline and instructional procedures I will assess the students by

presenting them with a single long division problem on a white piece of paper that says

"Complete the following problem". They will have two minutes to complete the problem

with no assistance. In order to grade the assessment students will be graded based upon

the following 9-step process for long division.

● Rewrite program for long division

● How many times does the outside number go into the first digit of the inside

number? (Division-D)

○ If the outside number is greater than the first digit, borrow one (ten)

from the second digit

● Write the number, for how many times the divisor goes into the first digit

above the line

● Multiply the number on top of the line by the divisor (Multiply-M)

● Write the product below the number, under the line

● Subtract (S)

● If there is a remainder, bring down the second digit of the dividend

● Repeat this Division, Multiply, Subtract (DMS) process until finished

**No reinforcement is to be provided during assessment**

Assessment Schedule:

Assessment, during baseline and instruction, should occur once every Friday during

math class from 11:20-12:07. Students will complete one division problem every Friday.

The assessment is a self created blank sheet of paper with the division problem on it. An

example can be seen, attached.

Instructional Procedures:

Forward chaining will be used to teach how to use long division. One step will be

introduced at a time to reduce the amount of time required for an instructional session, and

increase probability of correct student responses. For the steps not yet instructed upon, the

instructor should assist the students in complementing these steps by doing them for the

students on the SMART board, explaining each step verbally as it is completed. Each step

should be instructed upon for three consecutive sessions. After the three instructional days

and the assessment, the next step in the process should be instructed upon.

The process follows these steps:

● Rewrite program for long division

● How many times does the outside number go into the first digit of the inside

number? (Division-D)

○ If the outside number is greater than the first digit, borrow one (ten)

from the second digit

● Write the number, for how many times the divisor goes into the first digit

above the line

● Multiply the number on top of the line by the divisor (Multiply-M)

● Write the product below the number, under the line

● Subtract (S)

● If there is a remainder, bring down the second digit of the dividend

● Repeat this Division, Multiply, Subtract (DMS) process until finished

● Stimulus Prompts

o No stimulus prompts are introduced at the beginning of instructing upon

a target procedure but if error patterns are noted, highlighting the error,

as followed, may be used to prevent errors.

▪ Provide student with a note card with the target step on it written

in black and the error highlighted. For example if student is

struggling with how to bring the number down to continue the

division process I would provide them with a note card that has an

example problem, highlighting the correct procedure.

● Response Prompts

o With chaining, the previous step becomes the response prompt. No

additional response prompts are provided

Reinforcement:

Within group instruction, if a student offers the correct response they will receive

specific, direct verbal praise such as “Nice T, that’s the right step! First we need to convert

the problem to long division form.” After three days of instruction on a specific chain, it will

no longer be positively reinforced. If at any time performance falls, reinforcement of

previous steps can be returned to and faded again until performance is stabilized.

Maintenance:

Once criterion for mastery has been met and the material has been generalized, a

maintenance probe will be taken every two weeks. The presence of proper long division

skills will also be monitored within other math activities completed in the classroom.