Big to Small & Small to Big Task

Goal: The goal is to develop your student’s conceptual understanding of linear conversions.

Role: You are a 3rd grade teacher.

Audience: The target audience is a group of typical 3rd grade students.

Situation: You have just taught a lesson dealing with the conversion of linear measurements.  Within the lesson you said, “When you go from a big unit to a small unit you multiply and form a small unit to a big unit you divide.”  By this you meant that if you are converting from a big unit (for example, feet) to a smaller unit (for example, inches) you multiply and when converting from a small unit (for example, inches) to a bigger unit (for example, feet) you divide.  Several of your students have asked why this works.

Product: You are to prepare a dialogue with anticipated student responses aimed at enabling your students to understand why this “saying” works.  The dialogue should include pictures or diagrams that will aid in your explanation.

Standards: Do not use phrases like, “it just makes sense” or “you would expect to get a bigger number so you multiply” or “multiplication means make bigger.”  Instead, focus on the meaning of multiplication and division and how this relates to the conversion problems.  You may assume that your students have some understanding of the meaning of multiplication and division.  Your task should be typed; however, pictures may be drawn by hand.  You should include a copy of the attached rubric with your task.

Scoring Rubric:

 Category 4-5 points 2-3 points 0-1 points Dialogue: Mathematical Concepts Explanation shows complete understanding of the mathematical concepts involved. Explanation shows some understanding of the mathematical concepts involved. Explanation shows limited understanding of the underlying concepts involved OR is not written. Dialogue: Mathematical Explanation Explanation is detailed and clear. Explanation is a little difficult to understand, but includes critical components. Explanation is difficult to understand and is missing several components OR is not included. Dialogue: Pictures and/or Diagrams Pictures and/or diagrams that effectively support the explanation are included within the dialogue. Pictures and/or diagrams are included within the dialogue but do not effectively support the explanation. No pictures and/or diagrams are included within the dialogue. Standards for Dialogue Dialogue clearly focuses on developing conceptual understanding of linear conversion. Dialogue somewhat develops students’ conceptual understanding of linear conversion but there is some confusion. Dialogue does not develop the students’ conceptual understanding of linear conversion. Neatness, Grammar, Spelling, Etc. The work is presented in a neat, clear, organized fashion that is easy to read.  Writer makes no errors in grammar or spelling. The work is presented in an organized fashion but may be hard to read at times.  Writer makes up to 4 errors in grammar and/or spelling. The work appears sloppy and unorganized.  It is hard to know what information goes together.  Writer makes more than 4 errors in grammar and/or spelling.