2-1 Integers and the Number Line

Objective: To state the coordinate of a point on a number line, to graph integers on a number line, and to add integers by

using a number line.

Drill #16*Simplify

1. 6s + 2r + 3r + s

2. 9(a + 2b) – 2a

Evaluate if a = 5, b = 4, and c = 3

3. 3ac – bc

4. b – c + 2ab

Drills and Classwork

Put your drills and classwork on a separate sheet of paper each day.

The drills and classwork from one day will be collected each unit.

Create Groups!Group the following numbers together

• at least 3 different groups

• Name each group according to characteristics

3 -15 15.3 17 280

-5 -12 10 11.0 -280

½ 0 ¾ - ¼ 6.253

The Number Line **(1.)

Definition: A line with equal distances marked off to represent numbers.

Example:

• Number lines should have arrows on each end to indicate that they go on forever.

• We use a number line to add and subtract numbers.

• Number lines are a one dimensional graph.

-2 -1 0 1 2-3

Use the Number Line to add and Subtract Numbers

Show the similarity:5 + -3

5 – 3

Show the difference:-6 – 3

-6 + 3

Venn Diagram for Real Numbers**(2.)

Reals, R

I = irrationals

Q = rationals

Z = integers

W = wholes

N = naturals

I QZ

WN

SetsProperties of sets:

Defined by braces { }

Contain numbers or objects (such as ordered pairs) separated by commas

They help us group things together (they are like a container).

Natural Numbers (N)**(3.)

Definition: The set of counting numbers, starting at 1, and including all the positive whole numbers. {1, 2, 3, 4, 5, 6, 7, 8, 9, … }

‘…’ means that it continues on to infinity.

The natural numbers are a set of numbers.

Whole Numbers (W)**(4.)

Definition: The set of numbers that includes all the Natural numbers, and 0.

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, … }

What is the difference between Natural numbers and Whole numbers?

Is 0 a natural number? Is 0 positive or negative?

Integers (Z) **(5.)

Definition: The set of numbers that includes all the Whole numbers and all the negative Natural numbers.

{ …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …}

The set of integers starts at negative infinity, and counts by ones all the way to positive infinity.

Venn Diagram for Real Numbers

Reals, R

I = irrationals

Q = rationals

Z = integers

W = wholes

N = naturals

I QZ

WN

Examples:

Sets Examples

Natural Numbers (N) 1, 2, 3, 4, 5, 6, 7, 8, 9, …

Whole Numbers (W) 0, 1, 2, 3, 4, 5, 6, 7, 8, …

Integers (Z) -4, -3, -2, -1, 0, 1, 2, 3, ...

Classwork *(#16)

Name the set of numbers graphed. Name the set of numbers that each number belongs to:

5.

6.

-2 -1 0 1 2-3

-2 -1 0 1 2-3

Graph and Coordinate ** (6., 7.)

6. Graph: To plot a point on number line.

7. Coordinate: The number that corresponds to a point on a number line.

Name the coordinate of the point that is graphed on the number line below.

-2 -1 0 1 2-3

Graph each set on number line* (# 16)

7. { -1, 0, 1, 2 }

8. Integers less than zero

9. Integers less than zero but greater than -6

Write an addition sentence

Start at -1, add 3, subtract 5 (add negative 5)

-1 + 3 – 5 or -1 + 3 + -5

-2 -1 0 1 2-3

+3-5

Rewind…

A number line is …

Natural Numbers are ?

Whole Numbers are ?

Integers are ?

All Natural Numbers are in the set of _______ and _______