The Division Process: Division with Remainders: Abstract Level

More Teaching Plans on this topic: Concrete, Representational

PHASE 2: Practice Strategies

Receptive/Recognition Level

*The student practice strategies described below can be used both for 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 multiple opportunities to choose accurate solutions to division problems when give several choices.

Learning Objective 1: Solve division story problems/equations without the use of concrete objects or drawings – Solving division equations.

A. Self-Correcting Materials – Clothespin Division (adapted from Mercer & Mercer, 1998)

Materials:

Teacher -

• Develop a variety of Clothespin Division Cards – Each card is separated into eight regions on the front and back. On the front of the card, a division equation is written in each region. On the back of the card, one of eight different symbols is written in each region (e.g. § ¨ © ª · ƒ * #). Cards can reflect certain division fact families, especially problematic division problems, or random division problems/facts dependent on the needs of your students. Each card is numbered, “1, 2, 3, …”)
• A set of eight clothespins for each Clothespin Division Card. Each clothespin has the correct answer of one division problem on one side and the corresponding symbol of the division equation it answers on the other side.
• Zip lock bags to store each card and set of clothespins. *Each bag can be numbered by card number to store corresponding clothespins while cards are kept altogether in a separate bag or other container.
• Answer Key that lists the problems and answers for each Clothespin Division Card.

Students -

• Clothespin Division Cards and corresponding clothespins.
• A response sheet (sheet of paper)
• A scratch sheet of paper for working out problems if needed
• Pencil

Description:

Activity:

Students work with square or rectangular shaped cards divided into eight regions. On the front side of the card, division problems are written in each region. On the back of each card are eight different symbols with one symbol written in each region. Each card is numbered at in the center or in one of the corners in an alternate color. Students right the number of each card they respond to on their response sheets. Each Clothespin Division Card has a set of eight clothespins. Every clothespin has the correct answer to one division equation written on one side and the corresponding symbol from the back of the card written on the other side of the clothespin. Students choose the clothespins that “answer” each division equation and clip them to the card in the appropriate region. When students have answered all of the equations, they flip the card over. If the symbol on a clothespin matches the symbol on the back of each card, then the student knows they solved the equation correctly. As students finish a card and check their answers, they record the number they got correct on their response sheet next to the card number. The teacher circulates the room and monitors students as they work, providing positive reinforcement, providing specific corrective feedback, and answering questions as appropriate. Students can exchange cards as they finish. The teacher evaluates student performance by reviewing their response sheets.

Idea for Monitoring Student Performance

You and your students can keep track of how they do with each numbered card by writing the number correct on an individual chart that lists the different card numbers (e.g. graph paper can be used where each column represents a different card and the card’s number is written at the top or bottom of a column). Each row represents days the student practices with the Division Clothesline Cards. Dates can be written to indicate the day of practice. Each time a student responds to a card, he/she (or you) can record the total number correct on their chart for each card they respond to. When the student gets eight correct three days in a row, they can put a star next the number that represents that card. Students can “visualize” their progress and this process can be an efficient way for you to quickly monitor student progress, particularly if each “card number” represents particular division facts/problems. You can quickly see which fact families students are becoming proficient with at the receptive/recognition level.

Self-correcting Materials Steps:

1) Introduce self-correction material.

2) Distribute materials.

3.) Provide directions for self-correcting material, what you will do, what students will do, and reinforce any behavioral expectations for the activity.

4) Provide time for students to ask questions.

5) Model responding/performing skill within context of the self-correcting material.

6) Model how students can check their responses.

7) Have students practice one time so they can apply what you have modeled. Provide specific feedback/answer any additional questions as needed.

8) Monitor students as they work.

9) Provide ample amounts of positive reinforcement as students play.

10) Provide specific corrective feedback/ re-model skill as needed.

11) Encourage students to review their individual response sheets.

12) Review individual student performance record sheets.

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Expressive Level

Purpose: to provide students multiple practice opportunities to solve division problems in a motivating format.

Learning Objective 1: Solve division story problems/equations without the use of concrete objects or drawings – Solving division equations.

Instructional Game – Division Basketball

Materials:

Teacher -

• Sets of cards that represent division problems with increasing levels of difficulty. Lay up cards have the easiest problems, 10 foot jump shot cards have more difficult problems, and 3 point shot cards are the most difficult. The front side of each card has the type of shot written on it, the problem the offensive player answers, and the problem(s) the defensive player answers to “block.” The answer to each problem is written on the back of each card. Two “block” problems are written for “lay up” cards. One “block” problem is written for “10 foot jump shots.” No “block” problems are written on “3 point shot” cards. (*One set of problems for each type of shot can be made on sheets of paper so that problems and answers for each card can be cut out to fit the size of a 4x5 note-card. The master sheets can then be copied to make as many sets as needed. Problems and answers are glued to the front and back of a each note-card and a letter is written (a-z). Note-cards can be laminated to protect them.

For Example:

• Response sheets that have three columns labeled “Lay-Up,” “10 foot jump shot,” and “3 point shot.”
• Drawing of basketball court on chalkboard/dry-erase board or poster board posted in front of room.

Students -

• Three decks of Division Basketball cards (Lay-Up, 10 foot jump shot, 3 point shot).
• Response sheet
• Scratch piece of paper for solving problems
• Pencil

Description:

Activity:

Students work in pairs or small groups. Each pair or small group has a drawing of a basketball court on tag board (a larger basketball court could be drawn on the chalkboard/dry-erase board or on a poster-board and placed in the front of the room as an alternative to providing a smaller version for each student pair). Additionally, each student pair or small group has three sets of cards. Each set represents division problems that increase in difficulty (See description of cards under “Materials.”) The easiest set of cards are for “lay-ups.” The next most difficult set of cards are “10 foot” jump shots. The most difficult set of cards are “3 point shots.” Students take turns pulling a card from one of the three sets of cards. The student who “has the ball” chooses whether to shoot a “lay up” for one point, a “10 foot jump shot” for two points, or a “3 point shot” for three points. The player “shoots” by answering the division problem on the card. The player receives the appropriate number of points if they answer the problem correctly. The player or team on defense has the opportunity to “block” a lay-up or 10 foot jump shot by responding to the “block” division problem(s) also on the front of side of those cards. If the “defense” answers the “block” division problem(s) correctly, then the offensive player does not receive points for their shot. If a player chooses to answer a “3 point shot” card, the defense cannot block that shot. After both the player on offense and the player on defense answer their problems, they check their answers by turning the card over. Each player records the letter of the card they answered under the column labeled “lay-up,” “10 foot jump shot,” or “3 point shot” along with the points they made (both offensive shots and block attempts). Teacher monitors students and provides positive reinforcement, specific corrective feedback and answers questions as appropriate. Teacher reviews individual student response sheets to evaluate student performance.

Instructional Game Steps:

1) Introduce game.

2) Distribute materials.

3) Provide directions for game, what you will do, what students will do, and reinforce any behavioral expectations for the game.

4) Provide time for students to ask questions.

5) Model how to respond to the card prompts.

6) Provide time for students to ask questions about how to respond.

7) Model how students can keep track of their responses.

8) Play one practice round so students can apply what you have modeled. Provide specific feedback/answer any additional questions as needed.

9) Monitor students as they practice by circulating the room, providing ample amounts of positive reinforcement as students play, providing specific corrective feedback/ re-modeling skill as needed.

10) Play game.

11) Encourage students to review their individual response sheets.

12) Review individual student response sheets to determine level of understanding/proficiency and to determine whether additional modeling from you is needed.

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