The goal of Unit 1 is to explore numbers to 18 by breaking apart each total into two smaller numbers called "partners". Children discover the numbers "hiding" inside other numbers and come to understand the ten hiding inside teen numbers, for example, 14 = 10 + 4. Understanding the concept of two partners embedded in a number is a precursor to adding and subtracting multi-digit numbers and to understanding the inverse relationships of addition and subtraction.

For addition and subtraction, counting methods work well for children and help them to conceptualize adding and subtracting. Children will use counting on as a strategy to find the answers in a variety of addition and subtraction situations. They will count on from one addend to find the total. They will count on from a known addend to the known total to find the unknown addend, or partner. They will count on to subtract, finding the answer to exercises, such as 9 - 5 = and 15 - _ = 8. Children will also use the Make a Ten strategy when adding larger numbers. In this strategy, children will separate one number into partners so that they make a ten with the other number. For example, in the exercise 7 + 8 = _, 8 can be separated into the partners 3 and 5. The number 3 is added to 7 to make a ten. The exercise now becomes 10 + 5 = _.

Substantial research from all over the world now indicates that children move through a progression of different counting procedures to find the sum of single-digit numbers. First, children count out objects for the first addend, count out objects for the second addend, and count all of the objects (count all). This general counting-all procedure then becomes abbreviated, internalized, and abstracted as children become more experienced with it. Next, they notice that they do not have to count the objects for the first addend but can start with the first addend (or the larger addend) and count the objects in the other addend. With time, children recompose numbers into other numbers (4 is recomposed into 3 + 1) and use thinking strategies in which they turn an addition combination they do not know into one they do know (3 + 4 becomes 3 + 3 + 1).

The types of problems presented in this unit, in which the unknown can appear in any position, prepare children for writing algebraic equations with an unknown. They also help children develop the practice of reading a problem carefully in order to understand a given situation. This will aid children in mastering more difficult types of problems that often appear on tests. Some children may have difficulty with problems that start with an unknown, or those in which an unknown is added or subtracted. Mastery of these problems is not expected at this point; additional work with problems of this kind is provided in Unit 2.

For addition and subtraction, counting methods work well for children and help them to conceptualize adding and subtracting. Children will use counting on as a strategy to find the answers in a variety of addition and subtraction situations. They will count on from one addend to find the total. They will count on from a known addend to the known total to find the unknown addend, or partner. They will count on to subtract, finding the answer to exercises, such as 9 - 5 = and 15 - _ = 8. Children will also use the Make a Ten strategy when adding larger numbers. In this strategy, children will separate one number into partners so that they make a ten with the other number. For example, in the exercise 7 + 8 =

_, 8 can be separated into the partners 3 and 5. The number 3 is added to 7 to make a ten. The exercise now becomes 10 + 5 =_.Substantial research from all over the world now indicates that children move through a progression of different counting procedures to find the sum of single-digit numbers. First, children count out objects for the first addend, count out objects for the second addend, and count all of the objects (count all). This general counting-all procedure then becomes abbreviated, internalized, and abstracted as children become more experienced with it. Next, they notice that they do not have to count the objects for the first addend but can start with the first addend (or the larger addend) and count the objects in the other addend. With time, children recompose numbers into other numbers (4 is recomposed into 3 + 1) and use thinking strategies in which they turn an addition combination they do not know into one they do know (3 + 4 becomes 3 + 3 + 1).

The types of problems presented in this unit, in which the unknown can appear in any position, prepare children for writing algebraic equations with an unknown. They also help children develop the practice of reading a problem carefully in order to understand a given situation. This will aid children in mastering more difficult types of problems that often appear on tests. Some children may have difficulty with problems that start with an unknown, or those in which an unknown is added or subtracted. Mastery of these problems is not expected at this point; additional work with problems of this kind is provided in Unit 2.

Fuson, Karen,

Math Expressions, Unit 1 Overview