# Homework: Goals and Structure

Recent Homework assignments:  (mostly available as Word documents)

Solution Keys:  HW_keys#1to#8

## What are our main goals in assigning homework?

1. Provide thoughtful practice, not drill. Hopefully in an independent setting, without help, so we can see how the learning is going.
2. To allow for long periods of time (weeks) to repeat the visual representation of important topics. We only do one problem or two per topic. Fractions, multiplication, division, decimals. Here we withhold the algorithm for weeks, until the concept is internalized.

A few notes on our HW problems:

Problem #1 (all HW’s):    Fractions.  We’re still having them draw. We’ve had them draw addition, subtraction (with borrowing) and multiplication. We’re still withholding algorithms.  If we teach the algorithms too early, students discard their visual understanding and use the (more easily acquired) algorithm. The danger here, of course is that learning is superficial and temporary.  Fractions are a make or break concept in algebra and beyond, and the time spent drawing is worth it.

Problem #2:   2-digit Multiplication.  Again, we are keeping this visual, withholding the traditional algorithm.

Problem #3:  One-digit multiplication.  This is an optional problem composed of dot arrays to help students finish mastering their times tables. Students who do not yet know their times tables completely in 5th grade are probably not going to learn them with the traditional methods of flash cards and drill.

Problem #4:  Multiplication/Division by powers of 10.  This is a valuable way to build place value concepts while encouraging mental math skill development.

Challenge Problem:  Calculation in different bases. The logic behind this work is that it is good for the fastest students (those who have time to get to these challenge problems). They are forced to ignore traditional algorithms and focus on visualization of the concepts of multiplication and division.

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