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The Division Process: Division with Remainders : Concrete Level

More Teaching Plans on this topic: Representational, Abstract


Phase 1

Initial Acquisition of Skill

Phase 2

Practice Strategies

Phase 3


Phase 4


Download printable version of this teaching plan, with additional detailed descriptions


Math Skill/Concept: Division process and division with remainders using concrete materials.

Prerequisite Skills:

  • Multiplication process & facts
  • Grouping objects

Learning Objectives:

1) Divide without remainders using concrete materials.

2) Divide without remainders using concrete materials within a story problem context - measurement/”separating into groups” situations.

3) Divide without remainders using concrete materials within a story problem context - partitive/”sharing” situations.

4) Divide with remainders using concrete materials in measurement/”separating into equal groups” and partitive/”sharing” situations

Important Ideas for Implementation:

1) This teaching plan describes how you might teach both the division process as well as division with remainders using concrete materials. Depending on your grade level and your students’ prior knowledge/experiences, you might teach both of the concepts/skills or you may only want to teach one of the two concepts/skills.

2) If you are teaching the division process and division with remainders, students should achieve mastery of the division process at the concrete, representational/drawing, and the abstract levels of understanding before beginning instruction for division with remainders.

3) If you are teaching only division with remainders and find your students are having difficulty, you might consider re-teaching the division process using the strategies described.

4) At the concrete level of instruction, two division situations are taught including: 1.) Measurement/”Separating into Equal Groups” situations that require division by separating a set of objects into groups that contain a specified number of objects for the purpose of determining how many groups one can make; 2.) Partative/”Sharing” that require division by “sharing” a total set of objects equally among a specified number individuals and determining how many objects each individual gets. These two “division situations” are both naturally occurring/authentic situations that require division.

5) While this teaching plan incorporates the use of discrete counting objects, you might consider modeling and providing practice by using base-ten materials after students demonstrate understanding and mastery of basic division (e.g. one digit/two digit dividends divided by one/two digit divisors) through the abstract level. Base-ten materials can be very helpful when dealing with division problems that involve larger values (e.g. three digit dividends) and help reinforce understanding of place value.

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