Hard Multiplication,
Hard Measurement and Hard Partition Word Problems
Just as Hard Addition and Hard Subtraction problems involves 2 sets and
the relationship between those 2 sets, so also with Hard
Multiplication, Hard Measurement
and Hard Division.
Suppose that Trixie has 2 fish and that Rose has 3 times as many fish.
Then
Rose has 6 fish altogether. Here
is a representation of that situation.
The number 2 (of fish that Trixie has) is called the multiplicand
and the number 3 is called the multiplier. (The multiplier
tells the
relationship between the number of fish that Trixie has and the
number of fish
that Rose has.) The number 6 is called the product.
All Hard Multiplication, all Hard Measurement, and all Hard Partition
word problems involve 3 numbers  a multiplier, a multiplicand and a
product. We can make up word problems involving these numbers in 3
different ways.
1. Hard Multiplication: Trixie has 2 fish. Rose has 3 times as
many
fish as Trixie has. How many fish does Rose have? (We are given the
number 2, the multiplicand, and the number 3 the multiplier. We need to
find the product.
2 x 3 = □)
2. Hard Measurement: Rose has 6 fish. Trixie has 2 fish. Rose
has how many times as many fish as Trixie has? (We are given the number
6, the product, and the number 2, the multiplicand. We need to find the
multiplier. 6 ÷ 2 = □)
3. Hard Partition: Rose has 6 fish. She has 3 times as many fish
as Trixie has. How many fish does Trixie have? (We are given the number
6, the product, and the number 3, the multiplier. We need to find the
multiplicand. 6 ÷ 3 = □)
This chart summarizes the relationship between Easy Multiplication,
Easy Partition and Easy Measurement.

multiplier (relationship)

multiplicand

product

Hard Multiplication 
given

given

find

Hard Measurement 
find

given

given

Hard Partition 
given

find

given

It is worthwhile comparing this chart with the charts for
Together, these 4 charts describe 11 of the 12 different types of word
problems that
are part of the typical elementary school arithmetic curriculum.
(back)