Blog Recap: Day 4 of Mathematics as a Second Language

Get better acquainted with others in the group.  Showing the NCTM and what it offers, such as the publication “Teaching Children Mathematics.”  We did a “Gallery-walk” for the iceberg posters, adding sticky notes with comments.

After the morning break we dug into the rules of sign for multiplication of integers in several ways.  Hopefully we shed light on a few ways of why two negatives should multiply to make a positive.

We then spent some time exploring some of the peculiarities of division, and considered how the many faces of division lead to confusion.  After lunch we explored division in light of its being “un-multiplication” and how fact families with multiplication can make sense of rules like “you can’t divide by zero” and how the signs work for integer division.

At the end of the day we also consider how the repeated addition and area models for multiplication can provide models of division, together with the number line model of splitting a length into smaller (equally-long) segments.  We also classified division problems according to whether they were “partitive” (i.e., we are given the number of groups and want to know how big the groups will be) and “quotitive” (i.e., we were given the size of the groups and want to know how groups can be made).  [Not discussed in class, but relevant: the terms “partitive” and “quotitive” can be seen to refer to the divisor.  In partitive division the divisor describes the number of parts, while in quotitive division the divisor describes “how many per group” (like a quota).


  • Unit 5: The Many Faces of Division (28 pages)


  • “Practice Problems for Division” (pp. 5.17-19)
    • Problem 3.  Try to explain your method of solution in at least two different ways.  (Note: “way” is not the same as “showing different work.”  Two different mindsets can still produce the same work.)
    • Problem 5ab: Evaluating the division to a numerical value or a simplified form itself is not the point.  It’s the process of conversion.
    • Problem 10.
  • Solve: “Fran has a 5-foot ribbon and wants to cut it into 10-inch segments.  How many segments will she get?”

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