Blog Recap: Day 5 of Math as a Second Language

Whew!  What a week!

In a large horseshoe we discussed norms in these workshops and norms in the classroom.  We watched two videos about establishing norms for your classroom, then soon after discussed ways to establishing a “productive struggle” norm.

As for mathematical content, it was “Fractions Friday,” and we saw a lot.  We began with models of fractions, and how to motivate and underscore equivalent fractions. By lunchtime we used the adjective-noun theme to motivate the need for a common denominator when adding or subtracting fractions.  During the working lunch we wrote problems requiring addition, subtraction, multiplication, and division of fractions.  We saw that some problems that may appear to be subtraction may actually involve multiplication depending on the “nouns” involved (e..g, “I ate a quarter a pizza, then a third of the remaining portion.  How much is left?”  actually calls for multiplication because the “third” is of the remaining 3/4 of a pizza).  Fractions as lengths or distances (as opposed to part-of-a-whole) often provide a more natural context for addition and subtraction problems.

We closed the day with a discussion of multiplication and division of fractions.  We saw two ways to justify the “invert-and-multiply” (or “keep it, switch it, flip it”) rule.  The first involved fact-families and some algebra.  The second involving finding common denominators and observing the results.  We also used the ribbon problem from last night’s homework as a context where dividing by fractions is natural (again, length-based problems make for a more natural context than part-of-a-whole).


  • Solutions for Unit 3
  • Solutions for Unit 4
  • Solutions for Unit 5
  • Unit 6
  • (There will be no solutions for Unit 6)


  • Look at the 17 horses problem.  What’s going on?
  • Relax and enjoy your weekend.

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