Number Talk What is a Number Talk? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.

Commonalities

Commonalities

Chapter 2 –Sets, Whole Number and Numeration Much of elementary school mathematics is devoted to the study of numbers. Children first learn to count using the natural numbers or counting numbers (the ellipsis, or three periods, means “and so on”). This chapter develops the ideas that lead to the concepts central to the system of whole numbers (the counting numbers together with zero) and the symbols that are used to represent them. First, the notion of a one-to-one correspondence between two sets is shown to be the idea central to the formation of the concept of number. Then operations on sets are discussed. These operations form the foundation of addition, subtraction, multiplication, and division of whole numbers. Finally, the Hindu-Arabic numeration system, our system of symbols that represent numbers, is presented after its various attributes are introduced by considering other ancient numeration systems

Draw a Diagram

Solve-It A survey was taken of 150 college freshmen. Forty of them were majoring in mathematics, 30 of them were majoring in English, 20 were majoring in science, 7 had a double major of mathematics and English, and none had a double (or triple) major with science. How many students had majors other than mathematics, English, or science?

2.1 SETS AS A BASIS FOR WHOLE NUMBERS

Sets A collection of objects is called a set and the objects are called elements or members of the set. Sets can be defined in three common ways: (1) a verbal description, (2) a listing of the elements separated by commas, with braces (“{” and “}”) used to enclose the list of elements, and (3) set-builder notation. For example, the verbal description “the set of all states in the United States that border the Pacific Ocean” can be represented in the other two ways as follows: Sets are usually denoted by capital letters such as A,B,C , and so on. The symbols “ ” and “ ” are used to indicate that an object is or is not an element of a set, respectively. For example, if S represents the set of all U.S. states bordering the Pacific, then Alaska and Michigan . The set without elements is called the empty set (or null set) and is denoted by “{ }” or the symbol . The set of all U.S. states bordering Antarctica is the empty set.

1-1 Correspondence A 1-1 correspondence between two sets A and B is a pairing of the elements of A with the elements of B so that each element of corresponds to exactly one element of B , and vice versa. If there is a 1-1 correspondence between sets A and B , we write A~B and say that A and B are equivalent or matching sets. n Two sets A and B are equal, written A=B, if and only if they have precisely the same elements.

Kinder Common Core State Standards Class Connections Kinder Common Core State Standards

Subsets Set A is said to be a subset of B , written , if and only if every element of A is also an element of B. DO NOW: Think of a Set of numbers that is a subset of another Set of numbers, then Share it with others.

Infinite or Finite? There are two broad categories of sets: finite and infinite. Informally, a set is finite if it is empty or can have its elements listed (where the list eventually ends), and a set is infinite if it goes on without end. A little more formally, a set is finite if (1) it is empty or (2) it can be put into a 1-1 correspondence with a set of the form { 1, 2, 3, … n}, where n is a counting number. On the other hand, a set is infinite if it is not finite.

Union of Sets The union of two sets A and B, written , is the set that consists of all elements belonging either to A or to B (or to both). = {m, n, p, q} Note: Two sets A and B that have no elements in common are called disjoint sets.

Intersection of Sets The intersection of sets A and B, written , is the set of all elements common to sets A and B . Note: Two sets A and B that have no elements in common are called disjoint sets.

Solve It Thirty elementary teachers were asked which high school courses they appreciated: algebra or geometry. Seventeen appreciated algebra and 15 appreciated geometry; of these, 5 said that they appreciated both. How many appreciated neither?