#### Math - 2018-19

# 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.

*Adopted: 2016*

### 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*