2 (2.1) intro number sense

2.1 Number SenseNatural, Whole, and Integer Number Systems

Objective: to develop some of the basic properties of numbers and number systems

Warm-up: are phone numbers considered mathematical objects?

Number System: A set of objects used together with

operations that satisfy some predetermined properties.

Objects: 0, 1, 2, -4, 0.6, ⅔, IV

Operations: +, - , • , ÷

Properties: = , > , < , ≠

How did the earliest cultures use math?

Number Symbols

Natural NumbersAre also called the counting numbers because

they are the numbers we use to count with.

N: 1, 2, 3, 4, 5,…

These numbers were originally used the keep track of the number of animals, as rankings (1st place, 2nd place, 3rd place, etc.), or creating calendars.

What kinds of numbers are missing from this set?

Whole Numbers

This set of numbers is the same as the set of natural (counting) numbers except for the symbol to represent nothing (0).

W: 0, 1, 2, 3, 4, 5…

Besides representing nothing, what other important role does the symbol 0 have in our current number system?

Limitations on Natural & Whole Numbers

1) If we add together any two whole numbers, is the result always a whole number?

2) If we subtract any two whole numbers, is the result always a whole number?

3) If we multiply any two whole numbers, is the result always a whole number?

4) If we divide any two whole numbers, is the result always a whole number?

Integers

This set of numbers includes the set of whole numbers and the negative integers, which are values below zero.

… -3, -2, -1, 0, 1, 2, 3,…

Why do you think we need negative numbers?

Where do we see them in our daily lives?

Limitations on Integers

1) If we add together any two integers, is the result always a integer?

2) If we subtract any two integers, is the result always a integer?

3) If we multiply any two integers, is the result always a integer?

4) If we divide any two integers, is the result always a integers?

… - 3, - 2, - 1…

Integers

0 1, 2, 3…

Natural Numbers

Whole Numbers