Hard Addition and Hard Subtraction Word Problems
All Hard Addition and Hard Subtraction word problems involve two sets and the relationship between those two sets.
Suppose that set A (the smaller set) consists of 2 lollipops
that Eva has. (The number 2 is an addend.)
Suppose that the relationship is that Rose has 3 more lollipops
than Eva has.
(The number 3 is also an addend.)
Then Rose has 5 lollipops. (The number 5 is the sum.)
We can make up word problems involving the set A, the set B, and the relationship between the two sets in three different ways.
1. Eva has 2
lollipops. Rose has 3 more lollipops than Eva has. How many lollipops
does Rose have? (This is an example of Hard Addition. The
number of elements in A (the smaller set) is given. The relationship
between the smaller set A and the larger set B is given. The problem is
to find the number of elements in B, the larger set. The corresponding
equation is 3 + 2 = 5.)
2. Rose has 5 lollipops and Eva has 2 lollipops. How many more
lollipops does Rose have than Eva? (This is an example of Hard
Subtraction 1. The number of elements in both A and B is given. The
problem is to find the relationship between the two sets. The
corresponding equation is 5 – 2 = □.)
3. Rose has 5 lollipops. Rose has 3 more lollipops than Eva has. How
many lollipops does Eva have? (This is an example of Hard
Subtraction 2. The number of elements in B (the larger set) is
given. The relationship between the larger set B and the smaller set A
is given. The problem is to find the number of elements in A, the
smaller set. The corresponding equation is 5 – 3 = □.)




Hard Addition 



Hard Subtraction 1^{*} 



Hard Subtraction 2^{*} 



^{*}It is
important to notice that the not only are the two subtraction
problems different from one another, they are not even the same type of
problem.
(back to Subtraction)