Plot at least 3 points in your assigned quadrant, and label them with their coordinates.
13.2
Activity
Signs of Numbers in Coordinates
Standards Alignment
Building On
Addressing
6.NS.6.b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Coordinate plane, origin O, horizontal axis negative 7 through 7 by ones, vertical axis negative 5 through 5 by ones. Point A is 4 units to the right of the origin and 3 units up. Point B is 6 units down from point A. Point C is 1 unit to the left and 2 units down from point B. Point D is 7 units to the left and 2 units up from point C. Point E is 2 units to the left and 6 units up from point D.
Answer these questions for each pair of points.
How are the coordinates the same? How are they different?
How far away are they from the -axis? To the left or to the right of it?
How far away are they from the -axis? Above or below it?
and
and
and
Point has the same coordinates as point , except its -coordinate has the opposite sign.
Plot point in the coordinate plane, and label it with its coordinates.
How far away are and from the -axis?
Point has the same coordinates as point , except its -coordinate has the opposite sign.
Plot point in the coordinate plane, and label it with its coordinates.
How far away are and from the -axis?
Point has the same coordinates as point , except both coordinates have opposite signs. In which quadrant is point ?
13.3
Activity
Differences and Distances
Standards Alignment
Building On
Addressing
7.NS.1.c
Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
Plot and label these points in the coordinate plane: , , , .
Connect the dots in order. What shape is made?
What are the side lengths of figure ?
What is the difference between the -coordinates of and ?
What is the difference between the -coordinates of and ?
How do the differences of the coordinates relate to the distances between the points?
13.4
Activity
Plotting Polygons
Standards Alignment
Building On
6.G.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Here are the coordinates for four polygons. Plot them on the coordinate plane, connect the points in the order that they are listed, and label each polygon with its letter name.
Polygon A:
Polygon B:
Polygon C:
Polygon D:
Student Lesson Summary
The points , and are shown in the coordinate plane. Notice that they all have almost the same coordinates, except the signs are different. They are all the same distance from each axis but are in different quadrants.
Notice that the vertical distance between points and is 4 units because point is 2 units above the horizontal axis and point is 2 units below the horizontal axis. The horizontal distance between points and is 10 units because point is 5 units to the left of the vertical axis and point is 5 units to the right of the vertical axis.
We can always tell which quadrant a point is located in by the signs of its coordinates.
quadrant
positive
positive
I
negative
positive
II
negative
negative
III
positive
negative
IV
Glossary
None
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Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.