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Class & Multiplication problem & Division (by multiplier) 
   & Division (by multiplicand) \\
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Equal groups
& 3 children each have 4 oranges.  How many oranges do they have altogether?
& 12 oranges are shared equally among 3 children.  How many does each get?
& If you have 12 oranges, how many children can you give 4 oranges?  \\
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Equal measures
& 3 children each have $4.2$ liters of orange juice.  
   How much orange juice do they have together?
& $12.6$ liters of orange jice is shared qqually among 3 children.
   How much does each get? 
& If you have $12.6$ liters of oranged juice, to how many children
   can you give $4.2$ liters?  \\
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Rate
& A boat moves at a steady speed of $4.3$ meters per second.  
   How far does it move in $3.3$ seconds?
& A boat moves $13.9$ meters in $3.3$ seconds.  
   What is its average speed in meters per second?
& How long does it take a boat to move $13.9$ meters at a speed of
   $4.2$ meters per second?  \\ 
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Measure conversion
& An inch is about $2.54$ centimeters.  About how long in $3.1$ inches 
   in centimeters?
& $3.1$ inches is about $7.81$ centimeters.  About how many centimeters
   are there in an inch?
& An inch is about $2.54$ centimeters.  About how long in inches is 
   $7.84$ centimeters?  \\ 
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Multiplicative comparison
& Iron is $0.88$ times as heavy as copper.  If a piece of copper weighs 
   $4.2$ kg, how much does a piece of iron of the same size weigh?
& Iron is $0.88$ times as heavy as copper.  If a piece of iron weighs 
   $3.7$ kg, how much does a piece of copper of the same size weigh?
& If equally sized pieces of iron and copper weigh $3.7$ kg and $4.2$ kg 
   respectively, how heavy is iron relative to copper? \\
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Part/whole
& A college passed the top $3/5$ of its students in an exam.
   If 80 students took the exam, how many passed?
& A college passed the top $3/5$ of its students in an exam.
   If 48 passed, how many students took the exam?
& A college passed the top 48 out of 80 students who took an exam.
   What fraction passed? \\ 
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Multiplicative change
& A piece of elastic can be stretched to $3.3$ times its original length.
   What is the length of a piece $4.2$ meters long, when fully stretched?
& A piece of elastic can be stretched to $3.3$ times its original length.
   When fully stretched it is $13.9$ meters long.  What was its 
   original length?
& A piece of elastic $4.2$ meters long can be stretched to a maximum of 
   $13.9$ meters.  By what factor is it lengthened? \\ 
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Cartesian product
& If there are 3 routes from A to B, and 4 routes from B to C, 
   how many different ways are there of going from A to C via B?
& \multicolumn{2}{c} {If there are 12 different routes from A to C via B, 
   and 3 routes from A to B, how many routes are there from B to C?} \\ 
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Rectangular area
& What is the area of a rectangle $3.3$ meters long by $4.2$ meters wide?
& \multicolumn{2}{c} {If the area of a rectangle is $13.9 \, {\rm m}^2$,
   and the length is $3.3$ m., what is the width?} \\
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Product of measures
& If a heater uses $3.3$ kilowatts of electricity for $4.2$ hours,
  how many kilowatt-hours is that?
& \multicolumn{2}{c} {A heater uses energy at the rate of $3.3$ kilowatts.  
   For how long can it run before it uses $13.9$ kilowatt-hours?} \\
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