### 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 = □.)

 relationship smaller set A larger set B Hard Addition given given find Hard Subtraction 1* find given given Hard Subtraction 2* given find given

*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)