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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


                                                                                - Monitor/Chart Performance   - Assessment

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


PHASE 3: Evaluation

Monitor/Chart Performance

Purpose: to provide you with continuous data for evaluating student learning and whether your instruction is effective. It also provides students a visual way to “see” their learning.


Teacher -

  • Appropriate prompts if they will be oral prompts
  • Appropriate visual cues when prompting orally

Student -

  • Appropriate response sheet/curriculum slice/probe
  • Graph/chart


Steps for Conducting Continuous Monitoring and Charting of Student Performance:

1) Choose whether students should be evaluated at the receptive/recognition level or the expressive level.

2) Choose an appropriate criteria to indicate mastery.

3) Provide appropriate number of prompts in an appropriate format (receptive/recognition or expressive) so students can respond.

Based on the skill, your students’ learning characteristics, and your preference, the curriculum slice or probe could be written in nature (e.g. a sheet with appropriate prompts; index cards with appropriate prompts), or oral in nature with visual cues (e.g. say aloud the prompt and display it visually with concrete objects, drawings, written language, or numbers and symbols) or a combination of written curriculum slices/probes and oral prompts with visual cues.

4) Distribute to students the curriculum slice/probe/response sheet/concrete materials.

5) Give directions.

6) Conduct evaluation.

7) Count corrects and incorrects/mistakes (you and/or students can do this depending on the type of curriculum slice/probe used – see step #3).

8) You and/or students plot their scores on a suitable graph/chart. A goal line that represents the proficiency (for concrete level skills, this should be 100% – 5 out of 5 corrects) should be visible on each students’ graph/chart).

9) Discuss with children their progress as it relates to the goal line and their previous performance. Prompt them to self-evaluate.

10) Evaluate whether student(s) is ready to move to the next level of understanding or has mastered the skill at the abstract level using the following guide:

Concrete Level: demonstrates 100% accuracy (given 3 to 5 response tasks) over three consecutive days.

Representational Level: demonstrates 100% accuracy of (given 8-10 response tasks) over two to three consecutive days.

Abstract Level: demonstrates near 100% accuracy (two or fewer incorrects/mistakes) and a rate (# of corrects per minute) that will allow them to be successful when using that skill to solve real-life problems and when using the skill for higher level mathematics that require use of that skill.

11) Determine whether you need to alter or modify your instruction based on student performance.


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Flexible Math Interview

Purpose: to evaluate student conceptual understanding of the division process, with and without remainders.


Teacher -

  • A small notepad to write notes regarding particular student’s understanding as you “interview” them.
  • Pencil for writing

Students -

  • Appropriate concrete objects


As students are working independently or in pairs, ask them to describe their solutions and how they arrived at them. Encourage students to both use concrete materials to do this as well as “talk about” what they are doing with their concrete materials.


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