The Division Process: Division with Remainders: Abstract Level

More Teaching Plans on this topic: Concrete, Representational

PHASE 4: Maintenance

*Maintenance activities at the abstract level of understanding should include concrete and representational/drawing experiences as well as “abstract” (numbers and symbols only) experiences. By “re-visiting” previous concrete and representational/drawing experiences, students reinforce the conceptual understanding they acquired during those phases of instruction. Including “language experiences” during these maintenance activities, where students describe their solutions, also reinforces conceptual understanding students established during their concrete and representational/drawing experiences.

Purpose: to provide students with opportunities to maintain their level of mastery of solving division story problems and division equations.

1. Instructional Games & Self-Correcting Materials

Materials:

*Dependent on the Instructional Games or Self-Correcting Materials you implement.

Description:

*Periodically provide students opportunities to practice division with and without remainders via self-correcting materials and instructional games. This can be done via “centers,” in small groups, or as a whole class. Include opportunities to solve division problems with concrete materials and by drawing in addition to abstract level practice opportunities. Even though students master a concept/skill at an abstract level, providing maintenance practice opportunities using concrete materials and by drawing reinforce their conceptual understanding. (*See the descriptions for “Instructional Games” and “Self-Correcting Materials” in the Instructional Strategies site for more information of how to implement these student practice strategies.)

2. Problem of the Day

Materials:

Teacher -

• A written prompt on the chalkboard, dry-erase board, or overhead projector (e.g. a division problem or division story problem) or a concrete/drawing example representing a solution to a division equation (e.g. solution to a division problem that includes a remainder).

Students -

• Paper and pencil to record their responses

Description:

Teacher presents a “problem of the day” that focuses on a particular skill or conceptual understanding of solving division story problems and/or division equations. The problem can be written in nature where students solve the problem with concrete materials, by drawing, or at the abstract level only. Students can also be challenged to develop a story problem for an "already solved" division equation. The “problem of the day” is displayed as students enter the room or as the period begins. Students are asked to “solve” the problem and provided necessary directions. After an appropriate amount of time, the teacher and the students “talk through” the problem and its solution. Students can individually describe how they approached the problem. Specific positive verbal reinforcement is provided by the teacher as well as specific feedback regarding misunderstandings students may have. Teacher notes students who seem to be having difficulty for the purpose of reviewing/re-modeling appropriate skills and concepts.

Ideas for Prompts:

1) Display the concrete or drawing representation of an equation as well as its solution and ask students to represent the equation and the solution using only numbers and symbols.

2) Display an equation and ask students to represent the equation and the solution with concrete materials or drawings.

3) Display a concrete, drawing, or abstract representations of an equation and have students develop a story problem for that equation.

4) Display an equation and solution with concrete materials, by drawing, or with only numbers and symbols with one part of equation missing (e.g. one of the mixed numbers being added) and ask students to determine the missing part.

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