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 _______