# 1.7 - Part-Whole Relationships and Addition/Subtraction Fluency up to 10

The student will

a) recognize and describe with fluency part-whole relationships for numbers up to 10; and

b) demonstrate fluency with addition and subtraction within 10.

### BIG IDEAS

So that I can understand the relationship between addition and subtraction

So that I can become more fluent in addition facts

So I will understand that numbers are made up of two or more smaller numbers

### UNDERSTANDING THE STANDARD

• Computational fluency is the ability to think flexibly in order to choose appropriate strategies to solve problems accurately and efficiently.
• Flexibility requires knowledge of more than one approach to solving a particular kind of problem.  Being flexible allows students to choose an appropriate strategy for the numbers involved.
• Mathematically fluent students are not only able to provide correct answers quickly but also to use facts and computation strategies they know to efficiently determine answers that they do not know.
• Composing and decomposing numbers flexibly forms a basis for understanding properties of the operations and later formal algebraic concepts and procedures.
• Parts of numbers to 10 should be represented in different ways, such as five frames, ten frames, strings of beads, arrangements of tiles or tooth picks, dot cards, or beaded number frames. • Dot patterns should be presented in both regular and irregular arrangements. This will help students to understand that numbers are made up of parts, and it will later assist them in combining parts as well as counting on. • Accuracy is the ability to determine a correct answer using knowledge of number facts and other important number relationships.
• Efficiency is the ability to carry out a strategy easily when solving a problem without getting bogged down in too many steps or losing track of the logic of the strategy being used.
• Addition and subtraction should be taught concurrently in order to develop understanding of the inverse relationship.
• Manipulatives should be used to develop an understanding of addition and subtraction facts.
• Automaticity of facts can be achieved through meaningful practice which may include games, hands-on activities, dot cards, and ten frames.
• Subtraction is the inverse of addition.  Subtraction can be viewed as a process of taking away or separating, or as a process of comparing two sets to determine the difference between them.
• Provide practice in the use and selection of strategies. Encourage students to develop efficient strategies. Examples of strategies for developing the addition and subtraction facts include:
• counting on;
• counting back;
• “one more than,” “two more than”;
• “one less than,” “two less than”;
• “doubles”  (e.g., 2 + 2 =__; 3 + 3 =__);
• “near doubles” (e.g., 3 + 4 = (3 + 3) + 1 = __);
• “make ten” (7 + 4 can be thought of as 7 + 3 + 1 in order to make a ten));
• “think addition for subtraction” (e.g., for 9 – 5 = __, think “5 and what number makes 9?”);
• use of the commutative property (e.g., 4 + 3 is the same as 3 + 4);
• use of related facts (e.g., 4 + 3 = 7 , 3 + 4 = 7, 7 – 4 = 3, and 7 – 3 = 4);
• use of the additive identity property (e.g., 4 + 0 = 4);  and
• use patterns to make sums (e.g., 0 + 5 = 5, 1 + 4 = 5, 2 + 3 = 5, etc.).
• Students at this level are not expected to name the properties.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Recognize and describe with fluency part-whole relationships for numbers up to 10 in a variety of configurations. (a)
• Identify + as a symbol for addition, - as a symbol for subtraction, and = as a symbol for equality. (b)
• Demonstrate fluency with addition and subtraction within 10. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018