The Division Process: Division with Remainders : Concrete Level

More Teaching Plans on this topic: Representational, Abstract

PHASE 2: Practice Strategies

Receptive/Recognition Level

*The student practice strategies described below can be used for all skills taught during initial acquisition through Teacher Directed Instruction. A detailed description for providing practice for one of the skills is provided below:

Purpose: to provide students with many opportunities to determine which examples provided reflect the appropriate remainder.

Learning Objective 4: Divide with remainders using concrete materials in measurement/”separating into equal groups” and partitive/”sharing” situations.

Structured Language Experiences

Materials:

Teacher -

• Concrete examples of solutions to various division equations with and without remainders.
• “Choice” cards (three for each concrete example) that represent possible solutions to each concrete example. One card includes the appropriate solution. Appropriate language is used to represent the solutions (e.g. “four groups of five with two left over” would represent the solution to “22 ¸ 5 = ___.”).
• Response sheet with correct solutions for answer key.

Students -

• Response sheet numbered according to number of examples provided.
• Pencil for writing

*Appropriate accommodations for students with significant writing problems are to have them tape record their responses or have a letter written at the top of each “choice” card. Students can write the letter of the card they choose instead of writing the phrase.

*An appropriate accommodation for students with reading difficulties is to pair them with a classmate who has the ability to read the language “choice” cards.

Description:

Activity:

Students work at a center where there are laid out a variety of concrete examples showing solutions to division equations (For example, the concrete solution to the division equation, “16 ¸ 5 = __” would be three groups of five counting objects and one counting object left over. *It is important to group the counting objects in a distinct fashion so that the “remainder” can be clearly identified.). Above each concrete example are three cards with possible solutions written on them (For example, cards might read, “three groups of five with two left over,” three groups of five with one left over,” “three groups of five with zero left over.”. One card is the correct solution (with remainder). Students select which solution is appropriate and writes it down beside the appropriate number on their response sheet.

“Structured Language Experience” Steps:

1) Review directions for completing structured language experiences/peer tutoring activity and relevant classroom rules.

2) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model both how to decide an appropriate choice and model how to write the solution on the response sheet.

3) Provide time for student questions.

4) Signal students to begin.

Monitor students as they work. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate behavior. Also provide corrective feedback and modeling as needed.

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Expressive Level

Purpose: to provide students with multiple opportunities to solve division equations involving solutions “with remainders” and to describe the meaning of their concrete representations.

Learning Objective 4: Divide with remainders using concrete materials in measurement/”separating into equal groups” and partitive/”sharing” situations.

Structured Language Experiences/Structured Peer Tutoring

Materials:

Teacher -

• Develop learning sheets – Each learning sheet includes division equations involving solutions “with remainders.” With each equation, the following questions structure student responding: How many total chips (or other appropriate concrete object)? How many plates (or other appropriate container)? How many chips on one plate? How many chips are left over?
• Appropriate number of counting/discrete concrete objects and containers (e.g. counting chips, unifix cubes and paper plates.)
• Master answer key for learning sheet.

Students -

• Learning sheets
• Appropriate counting/discrete concrete objects and containers
• An answer key

Description:

Activity:

Students work in pairs, responding to the learning sheet. The student practice period is separated into two equal time periods. The coach presents the division equation by pointing to it and saying the equation aloud (e.g. points to the equation, 8 ¸ 3 = __, and says, “eight divided by three.”). Then the coach asks each question that follows. The player responds to each question using the appropriate concrete objects and then saying the answer. The coach writes the answer in the appropriate space, checks the answer key and provides appropriate feedback (e.g. positive verbal reinforcement for accurate responses and corrective feedback for inaccurate responses.) For inaccurate responses, the coach provides feedback and the player attempts the question a second time. The first response is crossed out and the second response is recorded. The coach provides appropriate feedback as appropriate. The teacher signals students to “switch roles” at the appropriate time.

“Structured Language Experiences/Structured Peer Tutoring” Steps:

1) Select pair groups and assign each pair a place to practice (try to match students of varying achievement levels if possible).

2) Review directions for completing structured language experiences/peer tutoring activity and relevant classroom rules. Practice specific peer tutoring procedures as needed (see step #4).

3) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model both what the coach does (e.g. reads aloud the division equation) and how the player responds (e.g. using concrete materials).

4) Divide the practice period into two equal segments of time. One student in each pair will be the player, or “talker/describer” and will solve the division equation using concrete materials and then describe their solution. The other student will be the coach, or “listener/evaluator” and will point to and then say aloud each problem. The coach will then write the response in the appropriate space, check the answer key, and provide feedback regarding the player’s response (e.g. positive verbal reinforcement for accurate responses and corrective feedback for inaccurate responses.) For inaccurate responses, the coach provides feedback and the player attempts the question a second time. The first response is crossed out and the second response is recorded. The “listener/describer” will also tally corrects and incorrects based on the player's responses.

5) Provide time for student questions.

• Signal students to begin.
• Signal students when it is time to switch roles.
• Monitor students as they work in pairs. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate tutoring behaviors. Also provide corrective feedback and modeling as needed.

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