K.4 - Part-Whole Relationships

The student will

a) recognize and describe with fluency part-whole relationships for numbers up to 5;

b)  investigate and describe part-whole relationships for numbers up to 10.

BIG IDEAS

• So that I can become better at adding and subtracting numbers
• So that I can solve addition and subtraction facts more quickly
• So that I can become better at adding and subtracting numbers
• So that I can solve addition and subtraction facts more quickly
• So that I can use strategies by understanding 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.
• Composing and decomposing numbers flexibly forms a basis for understanding properties of the operations and later formal algebraic concepts and procedures.
• Parts of 5 and 10 should be represented in a variety of 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 will later assist them in combining parts as well as counting on.
• Numbers can be composed and decomposed using part-part-whole relationships (e.g., 4 can be decomposed as 3 and 1, 2 and 2, 4 and 0).
• Quickly recognizing and naming the number of objects in a small group without counting is called subitizing.  The size of the group a student can subitize is dependent upon the arrangement of the dots or objects. At this age, students should subitize regular arrangements up to 5.
• When students are able to combine or separate groups to create a number, they are building a foundation for addition and subtraction.
• Benchmarks of 5 and 10 are essential in building place value knowledge through the understanding of decomposition of the numbers of 5 and 10.
• 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.
• 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 they do not know.

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 5 in a variety of configurations. (a)
• Investigate and describe part-whole relationships for numbers up to 10 using a variety of configurations. (b)

KEY VOCABULARY

Updated: Aug 22, 2018