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The Division Process: Division with Remainders: Representational Level

More Teaching Plans on this topic: Concrete, 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 for drawing solutions to division equations.

2) Choose an appropriate criteria to indicate mastery (8 out of 8 up to 10 out of 10 correct is appropriate for drawing solutions). Provide an appropriate amount of time for students to complete problems. However, this time frame should be no more than 5 minutes since this evaluation technique should not require a lot of class time.

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 a division equation while showing it visually), 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 representational level skills, this should be 100% – e.g. 8 out of 8 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:

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

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



Flexible Math Interview

Purpose: to evaluate specific conceptual or procedural misunderstandings selected students who are demonstrating difficulty have as a means to re-teach the concept/skill.


Teacher -

  • Selected examples of division story problems or division equations

Students -

  • Paper for responding to selected division story problems or division equations
  • Pencil for writing/drawing
  • Appropriate concrete materials to help describe their understanding as needed


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

*Providing students opportunities to describe their drawings with concrete materials can sometimes help you and the student better understand their misconceptions.


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