Your child is likely to see two types of addition problems in school. I call one of those types Easy Addition and the other Hard Addition. The two types are distinguished from one another by the way in which each is modeled. The two types are discussed below; but first, here is an example of each. Easy Addition: You have 3 toy cars and I have 2 toy cars. How many toy cars do we have altogether? Hard Addition: You have 3 toy cars. I have 2 more toy cars than you have. How many toy cars do I have?

### 1. What Is The Model For Easy Addition?

Here is the simplest way to model the Easy Addition problem above:

• Count out 3 objects to represent the cars that "you" have,
• then count out 2 objects to represent the cars that "I" have,
• then join together the two sets of objects that represent the toy cars,
• and finally count those two collections altogether.

### 2. How Do You Teach Easy Addition?

You can help children with Easy Addition by posing simple problems for them to solve and then helping them make models and count.

• Here, at 2 years and 8 months, is an example of me helping Trixie to understand what she is supposed to do to solve an Easy Addition problem.
• By the time that she is 3 years and 4 months Trixie knows how to model Easy Addition word problems - she has stopped making the kind of mistakes illustrated above. Click here to see an example.

### 1. What Is The Model For Hard Addition?

Here is an example of a Hard Addition problem:

Suppose that you have 3 toy cars and that I have 2 more toy cars than you have. How many toy cars do I have?

The simplest way to model this problem is this:

• Count out 3 objects to represent the toy cars that you have,
• count out another 3 objects to represent the toy cars that I would have if I had the same number of toy cars that you have,
• count out an additional 2 toy cars for me,
• and finally count how many toy cars I have altogether.

### 2. How Do You Teach Hard Addition?

 Here is an example of me helping Trixie learn to model a Hard Addition problem. Although at 3 years and 4 months she had a pretty good understanding of Easy Addition (see the example above), she had little or no understanding of Hard Addition.

Easy Addition and Hard Addition are not the same thing. Easy Addition always involves two sets (for example, a set of 3 toy cars that you have and a set of 2 toy cars that I have) and the problem involves joining those two sets and finding the number of members that the join contains (in this case, the total number of toy cars).

Hard Addition always involves one set whose size is known (for example, 3 toy cars that you have) and a second set (the toy cars that I have) that is described only in terms of its relationship to the first set (for example, I have 2 more toy cars than you have). The problem is to find the number of members in that second set (the number of toy cars that I have).