classroom.jpgUnit 2 reviews and builds on the use of break-aparts of numbers as components of a math equation. Children are also introduced to standard math notation. They begin to translate what they have learned about the concept of equality and the relationship between part and whole from the concrete world into symbolic equations.

There are three types of addition/subtraction word problems. Within these types, three variations occur depending on which of the three quantities in the situation is unknown. The key to solving all these problems is understanding the situation and knowing which amount is unknown. Key words are important for understanding the situation, but they do not determine the solution method. The solution method depends on which quantity is unknown.
  • Change problems: change plus and change minus
  • Collection problems: put together, take apart, no action
  • Comparison problems
Extensive research shows that if children can count, they can begin to use their counting skills to solve simple word problems. Furthermore, they can advance those counting skills as they solve more problems. In fact, it is in solving word problems that young children have opportunities to display their most advanced levels of counting performance and to build a variety of procedures for computation.

In Unit 1, children were introduced to the terms partner and total. In Unit 2, they encounter situations in which either the total or one of the partners is unknown. The first step in solving one of these problems is recognizing which type of unknown must be found.

Representing Addition Situations Children begin by literally drawing the objects in the story problem. If they are adding 4 apples and 2 apples, they will draw 4 apples and then 2 more. Children progress rapidly to circle drawings, which simplifies the process by representing objects with circles rather than realistic drawings. At this point, children are encouraged to label the parts, the total, and the operation.
These simplified circle drawings resemble the break-apart drawings already familiar to children. Using this strategy gives children confidence and also facilitates communication.

Representing Subtraction Situations Subtraction problems begin in a way similar to addition. For subtraction, however, the objects being subtracted are crossed off after being separated with a break-apart line. If children are subtracting 4 apples from 6 apples, their pictures would look something like this: As with addition, children progress to circle drawings and label the various parts. In subtraction problems, the unknown will always be the part that remains.

Explaining Solution Methods Children use their drawings to explain their solution methods. At this stage, the explanation is usually a description of the drawings and does not reveal much about the thinking process. These explanations do give children valuable experience with early math communication. By asking questions, you can help children progress to explanations that show their thinking.
There are 6 baby pigs in the mud, so I drew 6 circles. Then 4 of them went into the barn, so I crossed out 4 circles, There are 2 circles left. That means their are 2 baby pigs left in the mud.
To keep their thinking grounded in the actual problem, children should be encouraged to give a labeled answer rather than just a number: 2 pigs rather than 2.

Writing Equations
Expressions
Children begin by writing expressions (number phrases) for their addition and subtraction drawings. 3 + 4
Equations Children progress as they see that the expressions equal the total or difference. This relationship is discussed as children learn to write numbers on each side of an equals sign to make and equation: 3 + 4 = 7 9 - 5 = 4

Children's Strategies
The following solution methods are ones that children almost universally create or understand. They may be different from the methods you may have learned as a child. However, children all over the world use these methods even if they are not taught in the classroom. Practicing these methods can help less-advanced children.

Counting On to Add Counting on differs from counting all in that the counting is abbreviated by counting on from the greater number. This is especially important when children start adding numbers greater than 10. Counting on to find a total and counting on to find a partner are the two variations. They may look the same to an observer, but the child is monitoring either the known partner or the known total to decide when to stop counting. For 9 + 3 = _, the child thinks 9 and counts on 3, 10, 11, 12. For 9 + __ = 12, the child thinks 9, counts until 12 is reached, keeping track of the count (may use fingers): 10, 11, 12, or 3 numbers. Children may also use this strategy to solve a subtraction problem.

Fuson, Karen, Math Expressions, Unit 2 Overview