2-1 Integers and the Number Line

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. -3 -2 -1 0 1 2

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 Q I Z W N

Sets Properties 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 Q I Z W N

Examples:

Classwork *(#16) Name the set of numbers graphed. Name the set of numbers that each number belongs to: 5. 6. -3 -2 -1 0 1 2 -3 -2 -1 0 1 2

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. -3 -2 -1 0 1 2

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 -5 +3 -3 -2 -1 0 1 2

Rewind… A number line is … Natural Numbers are ? Whole Numbers are ? Integers are ? All Natural Numbers are in the set of _______ and _______

2-1 Integers and the Number Line