module 3 lessons 14 & 15
TRANSCRIPT
Module 3 Lessons 14 & 15.notebook
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February 25, 2014
MODULE 3 Raonal NumbersTopic C: Raonal Numbers & the Coordinate Plane
Lesson 14: Ordered PairsLesson 15: Locang Ordered Pairs on the
Coordinate Plane
Module 3 Lessons 14 & 15.notebook
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Classwork
Example 1: The Order in Ordered Pairs
The first number of an ordered pair is called the _____________________________________.
The second number of an ordered pair is called the __________________________________.
Ordered pairs are like a set of direcons; they indicate where to go in one direcon , and then indicate where to go in the second direcon .
Module 3 Lessons 14 & 15.notebook
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For Exercises 1 and 2, the first coordinates of the ordered pairs represent the numbers on the line labeled x and the second coordinates represent the numbers on the line labeled y.
Module 3 Lessons 14 & 15.notebook
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2. List the ordered pair of numbers that corresponds with each leer from the grid below.
Module 3 Lessons 14 & 15.notebook
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Lesson Summary
§ The order of numbers in an ordered pair is important because the ordered pair should describe one locaon in the coordinate plane.
§ The first number (called the first coordinate) describes a locaon using the horizontal direcon.
§ The second number (called the second coordinate) describes a locaon using the vercal direcon.
Module 3 Lessons 14 & 15.notebook
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Example 2: Components of the Coordinate PlaneAll points on the coordinate plane are described with reference to the origin. What is the origin, and what are its coordinates?
To describe locaons of points in the coordinate plane we use
of numbers. Order is important, so on the coordinate plane we use the form
( ). The first coordinate represents the point’s locaon from zero
on the ‐axis, and the second coordinate represents the point’s locaon
from zero on the ‐axis.
Lesson 15
Module 3 Lessons 14 & 15.notebook
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Example 3: Quadrants of the Coordinate Plane
§ The x‐ and y‐axes divide the coordinate plane into regions called Quadrants. Why are the regions called quadrants?
ú The axes cut the plane into four regions. The prefix “quad” means four.
§ Which of the four regions did you work with most in Grade 5, and why was it the only region you used?
ú The region on the top right of the coordinate plane. We only used this region because we had not learned about negave numbers yet.
§ The four quadrants are numbered one through four using Roman Numerals. The upper right quadrant is Quadrant I and the remaining quadrants are numbered moving counter‐clockwise from Quadrant I; Quadrant II, Quadrant III, and Quadrant IV. What was the first axis that we extended in Example 1 and what did it reveal?
ú We extended the x‐axis to the le beyond zero and it revealed another region of the coordinate plane.
Module 3 Lessons 14 & 15.notebook
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§ This top le region is called Quadrant II. Label Quadrant II in your student materials. These regions only make up half of the coordinate plane. Where does the remaining half of the coordinate plane come from? Explain.
ú We need to extend the y‐axis down below zero to show its negave values. This reveals two other regions on the plane; one to the le of the x‐axis and one to the right of the y‐axis.
§ The quadrants of the coordinate plane are in a counter‐clockwise direcon starng with Quadrant I. Label the remaining quadrants in your student materials.
Module 3 Lessons 14 & 15.notebook
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Module 3 Lessons 14 & 15.notebook
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February 25, 2014
Exercises
Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.
yaxis
xaxis
Module 3 Lessons 14 & 15.notebook
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6. Do you see any similaries in the points within each quadrant? Explain your reasoning.
The ordered pairs in.....Quadrant I contain both posive values. (+x, +y)
Quadrant II the first value is negave but second coordinate is a posive value. (‐x, +y)
Quadrant III contain both negave values. (‐x, ‐y)
Quadrant IV the first value is a posive, but the second coordinate is a negave value. (+x, ‐y)
If a point lies on the x‐axis, the second coordinate (y‐coordinate) will be zero.
If a point lies on the y‐axis, the first coordinate (x‐coordinate) will be zero.
Module 3 Lessons 14 & 15.notebook
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Module 3 Lessons 14 & 15.notebook
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February 25, 2014
Lesson Summary§ The x ‐axis and y‐axis of the coordinate plane are number lines that intersect at zero on each number line.
§ The axes create four quadrants in the coordinate plane.
§ Points in the coordinate plane lie either on an axis or in one of the four quadrants.
Please take out your exit tickets for Lesson 14 & 15 close your binder, and complete the exit ticket. These will be
collected.