Rational Numbers on the Coordinate Plane6.NS.C.6c

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Lesson 14 – Ordered Pairs

• Objective:

– I can use ordered pairs to locate points on the coordinate plane.

• Guiding Question: (Write your answer on the lines below.)

– Why does order matter when using ordered pairs to locate points on a coordinate plane?

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Lesson 14 – Ordered Pairs

• New Vocabulary

– Write each term on a sticky note using the Frayer Model

– Ordered Pair – a set of numbers used to identify points EX: (2,3)

– First Coordinate – the first number in an ordered pair

– Second Coordinate – the second number in an ordered pair

– Coordinate Plane – a plane formed when a horizontal number line intersects with a vertical number line.

Lesson 14 – Ordered Pairs

The Coordinate Plane

Lesson 14 – Ordered Pairs – More New Vocabulary

Lesson 14 – Ordered Pair

• How to write an ordered pair:

– An ordered pair is written as (x, y)

– X represents the first number in the ordered pair – it is called the x – coordinate

– Y represents the second number in the ordered pair – it is called the y – coordinate

• How to use an ordered pair to find a point on a plane:

– Ordered pairs are like a set of directions;

– The first coordinate (x – coordinate) tells you where to go in one direction

– The second coordinate (y – coordinate) tells you where to go in the second direction.

• EX: To find point A (3,4):

– First move 3 units to the right on the x – axis (or horizontal number line)

– Then move 4 units up on the y – axis (or vertical number line)

Lesson 14 – Ordered Pair

2 3

Lesson 14 – Ordered Pair

When locating a point on a plane, always start at the origin (0, 0), then move left or right

on the x – axis, last move up or down on the y – axis.

Lesson 15 – Locating Ordered Pairs on a Coordinate Plane

• Objective:

– I can find a point on a coordinate plane using ordered pairs of rational numbers

• Guiding Question: (Write your answer on the lines below.)

– If a point lies on the x – axis or the y - axis, what must be true about its coordinates?

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Lesson 15 – Locating Ordered Pairs on a Coordinate Plane

• Remember from Lesson 14

Lesson 15 – Locating Ordered Pairs on a Coordinate Plane

Extending the Axes Beyond Zero

Lesson 15 – Locating Ordered Pairs on a Coordinate Plane

Points that lie on an axes –

• Points that lie on the x – axis have the following ordered pair:

– any number for the x – coordinate and 0 for the y – coordinate

– (any number, 0)

– EX: (2, 0)

• Points that lie on the y – axis have the following ordered pair:

– 0 for the x – coordinate and any number for the y – coordinate.

– (0, any number)

– EX: (0, -4)

Lesson 15 – Locating Ordered Pairs on a Coordinate PlaneNew Vocabulary – Quadrants

Quadrant I has all

positive numbers

EX:(5,4)

Quadrant II: x is

negative and y is

positive

EX: (-4, 3)

Quadrant III has all

negative numbers

EX: (-3, -2)

Quadrant IV: x is

positive and y is

negative

EX: (2, -4)

Lesson 16 – Symmetry in the Coordinate Plane

• Objective:

– I can use opposite numbers in ordered pairs to create reflections across axes.

• Guiding Question: (Write your answer on the lines below.)

– What is the relationship between (5, -1) and (5, 1)? How are they similar, how are they different?

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Lesson 16 – Symmetry in the Coordinate Plane

• New Vocabulary

• Symmetry and Reflection

Lesson 16 – Symmetry in the Coordinate Plane

• Extending Opposites in the Coordinate Plane

Lesson 16 – Symmetry in the Coordinate Plane

• Reflecting Points in the Coordinate Plane

How to reflect a point across an axis:

A point is reflected by creating another point that has an opposite

x – coordinate or y – coordinate or both.

To reflect the point S (5, 3) across the x – axis, create a new point

where the x – coordinate is the same and the y – coordinate is the

opposite (5, -3) and give the new point a new name – Point M.

To reflect Point S ( 5, 3)across the y – axis, create a new point where

the x – coordinate is the opposite and the y – coordinate is the

same (-5, 3) and give the new point a new name – Point L.

Lesson 16 – Symmetry in the Coordinate Plane

• Reflecting Points in the Coordinate Plane

How to reflect a point across an axis:

A point is reflected by creating another point that

has an opposite x – coordinate or y – coordinate

or both.

To reflect the point S (5, 3) across both axes,

create a new point where the x – coordinate is

the opposite and the y – coordinate is the

opposite (-5, -3) and give the new point a new

name – Point A.

Lesson 17 – Drawing the Coordinate Plane and Points on the Coordinate Plane

• Objective:

– I can draw the coordinate plane including all parts and graph points on the coordinate plane.

• Guiding Question: (Write your answer on the lines below.)

– Why is it important to label the axes when setting up a coordinate plane?

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Lesson 17 – Drawing the Coordinate Plane and Points on the Coordinate Plane

The Coordinate Plane

Ordered Pair

Point

Quadrant I has

all positive

numbers EX:(5,4)

Quadrant II: x is

negative and y

is positive

EX: (-4, 3)

Quadrant III has

all negative

numbers

EX: (-3, -2)

Quadrant IV: x

is positive and y

is negative

EX: (2, -4)

Lesson 17 – The Coordinate Plane

When locating a point on a plane, always start at the origin (0, 0), then move left or right

on the x – axis, last move up or down on the y – axis.

Lesson 18 – Distance the Coordinate Plane

• Objective:

– I can compute the length of line segments with integer coordinates for end points in the coordinate plane by counting the number of units between end points and using absolute value.

• Guiding Question: (Write your answer on the lines below.)

– How do you find the length of a line segment using two ordered pairs?

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Lesson 18 – Distance the Coordinate PlaneFinding the distance

between two points by counting units.

Point J (-5, 4)

Point Z (-5, -6)

Point J and Z will createstraight vertical line when connected since both x –coordinates are the same.

Since the x – coordinates arethe same, count the units

between the y – coordinates.

How many units are between 4 and -6?

The are 10 units between 4and -6.

Therefore the distance between points J and Z is 10

units.

Lesson 18 – Distance the Coordinate PlaneFinding the distance

between two points by using absolute value.

Point J (-5, 4)

Point Z (-5, -6)

Point J and Z will createstraight vertical line when connected since both x –coordinates are the same.

Since the x – coordinates arethe same, you can add the absolute values of the y –

coordinates.

The absolute value of 4 is 4.

The absolute value of -6 is 6

Add: 4 + 6 = 10

Therefore the distance between points J and Z is 10

units.

Lesson 18 – Distance the Coordinate PlaneFinding the distance between two points by using absolute value.

If two points have the same x – coordinate or y – coordinate you can use absolute value to find the distance between them.

How to use absolute value:

For integers that have opposite signs (one positive, one negative), add their absolute values.

EX: (5, 4) and (5, -6) – 4 is positive and 6 is negative

The absolute value of 4 is 4.

The absolute value of -6 is 6

Add: 4 + 6 = 10, therefore, the distance between (5, 4) and (5, -6) is 10 units.

For integers that have the same signs (both positive or both negative), subtract their absolute values.

EX: (-8, 2) and (-5, 2): 8 is negative and 5 is negative

The absolute value of -8 is 8.

The absolute value of -5 is 5

Add: 8 – 5 = 3, therefore, the distance between (-8, 2) and (-5, 2) is 3 units.

Completing the exercises using absolute value…

a. (-3, 4) and (-3, 9)

1. Cross out the coordinates that are the same.

2. Circle the coordinates that are different.

1. Are the signs the same?

1. If yes - subtract.

2. If no – add

4 and 9 are both positive so we subtract their absolute values.9 – 4 = 5, Therefore, the distance between (-3, 4) and (-3, 9) is 5.

Lesson 18 – Distance the Coordinate Plane