Chapter 7 Cartesian Coordinate System Part 1 Parts

Part…. . 1. Parts Of the Coordinate Plane 2. Plotting Points 3. Identifying Ordered

Vocabulary • Coordinate Plane- A coordinate system formed by the intersection of a horizontal

Today’s Standard 6. NS. C. 6. c. Find and position integers and other rational

Parts of a Coordinate Plane Please clear your desk of everything except for a

Word Bank for Notes • • • • Intersection Horizontal Vertical X-axis Y-axis Capitol

Wrap it Up • Review • Questions • Exit Tickets

Instructions: Bell Work Label the four quadrants in red. Number both the x and

Vocabulary • A coordinate system formed by the intersection of a horizontal and a

Graphing Ordered Pairs Essential Understanding: • This is an example of an ordered pair

Identifying Points Essential Understanding: • To identify a plotted point when given an ordered

Today’s Standard 6. NS. C. 8 Solve real-world and mathematical problems by graphing points

Distance on the Coordinate Plane Essential Understanding: • The distance between two points is

Today’s Standard 6. NS. C. 6. b. Understand signs of numbers in ordered pairs

Reflections (Don’t Copy) Essential Understanding: • A reflection can be thought of as folding

Reflections Essential Understanding: Reflecting points across the x and y axis is easy. •

Today’s Standard 6. G. A. 3 Draw polygons in the coordinate plane given coordinates

Essential Understanding: Plotting Figures In order to graph a figure in the coordinate plane,

Today’s Standard 6. G. A. 1 Find the area of right triangles, other triangles,

Finding Area and Perimeter Essential Understanding: • Perimeter is found by adding all side

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Chapter 7 Cartesian Coordinate System

Part…. . 1. Parts Of the Coordinate Plane 2. Plotting Points 3. Identifying Ordered Pairs 4. Distance Between Points 5. Reflections and Opposites 6. Plotting Figures 7. Reflecting Figures 8. Area of Figures

Part 1

Vocabulary • Coordinate Plane- A coordinate system formed by the intersection of a horizontal and a vertical number line • X-axis - The horizontal number line • Y-axis - The vertical number line • Ordered Pair- A pair of numbers that can be used to represent a point in the coordinate plane. • X-coordinate - The first number given in an ordered pair ( 3, 7 ) • Y-coordinate - The second number given in an ordered pair ( 5, 9 ) • Point - An ordered pair graphed and labeled with a capital letter • Origin - The point where the x-axis intersects with the y-axis. This point is ( 0, 0) • Quadrant- The four regions that the coordinate plane is divided into.

Today’s Standard 6. NS. C. 6. c. 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.

Parts of a Coordinate Plane Please clear your desk of everything except for a pencil and the provided note taking page. ***Please refer to the in class notes for review***

Word Bank for Notes • • • • Intersection Horizontal Vertical X-axis Y-axis Capitol Letters X-coordinate Y-coordinate (x, y) Point How far left or right to move from the origin How far up or down to move from the origin The 4 regions the coordinate plane is divided into. Corresponds Point

Wrap it Up • Review • Questions • Exit Tickets

Part 2

Instructions: Bell Work Label the four quadrants in red. Number both the x and y axis from -20 to 20. Color the X-axis yellow. Color the Y-axis orange. Place a blue dot at the origin. Find and plot the following points using green dots: (-2, 6) (-5, -8) (1, 9) (15, -14) • Label your plotted points M, A, T, H • • •

Vocabulary • A coordinate system formed by the intersection of a horizontal and a vertical number line • X-axis - The horizontal number line • Y-axis - The vertical number line • Ordered Pair- A pair of numbers that can be used to represent a point in the coordinate plane. • X-coordinate - The first number given in an ordered pair ( 3, 7 ) • Y-coordinate - The second number given in an ordered pair ( 5, 9 ) • Point - An ordered pair graphed and labeled with a capital letter • Origin - The point where the x-axis intersects with the y-axis. This point is ( 0, 0) • Quadrant- The four regions that the coordinate plane is divided into.

Homework Check

Graphing Ordered Pairs Essential Understanding: • This is an example of an ordered pair ( 5, -7) • The first number given in an ordered pair is the x-coordinate. It tells you how far left (negative #) or how far right (positive #) you must move along the x-axis. • The second number given in an ordered pair is the y- coordinate. It tells you how far up (positive #) or how far down (negative #) you must move along the y-axis. • To plot a point move along the x-axis to the given coordinate. Then move up or down the y-axis from your current position on the x-axis. • The point given will be plotted where the x-coordinate and y-coordinate intersect. • Remember you must run before you jump or dive. • Think “alphabetical order” (x before y) Examples:

Part 3

Bell Work

Homework Check-up

Identifying Points Essential Understanding: • To identify a plotted point when given an ordered pair, you follow the same procedure as when you are plotting the point yourself. (You must find the point where the x and y coordinates intersect). • To do this, you first determine how far left or right you move, based on your xcoordinate. • Then determine how far up or down your point is located from there, based on your ycoordinate. Examples:

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Part 4

Bell Work

Homework Check-up

Today’s Standard 6. NS. C. 8 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.

Distance on the Coordinate Plane Essential Understanding: • The distance between two points is calculated by determining how many units there are between them. In 6 th grade we only focus on points that fall in a straight line. • This can be done two ways: 1. Counting the units when the points are plotted. – Ex: A (5, 4) B (5, -3) C (-6, 4) Glue your grid here!!!! 1. Determining the absolute value for the coordinates. – We can determine the distance between point A and point B because they have the same x-coordinate. This means they are in a vertical line. » Ex: – We can determine the distance between point A and point c because they have the same y-coordinate. This means they are in a horizontal line. » Ex:

Wrap it Up • Review • Questions • Exit Tickets

Part 5

Bell Work

Homework Check-up

Today’s Standard 6. NS. C. 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.

Reflections (Don’t Copy) Essential Understanding: • A reflection can be thought of as folding or "flipping" an object over the line of reflection. • An object and its reflection have the same shape and size, but the figures face in opposite directions. The objects appear as if they are mirror reflections, with right and left reversed. Example: • A reflection can be seen, for example, in water, a mirror, or in a shiny surface. Take a look at the following reflections. Example:

Reflections Essential Understanding: Reflecting points across the x and y axis is easy. • Begin by identifying the points current coordinates. Example: • Next, determine what axis you will be reflecting across • If you are reflecting across the x-axis, the x-coordinate will remain the same. The y-coordinate will become the opposite of the original ycoordinate. Example: • If you are reflecting across the y-axis, the y-coordinate will remain the same. The x-coordinate will become the opposite of the original xcoordinate. Example: More Examples:

Wrap it Up • Review • Questions • Exit Tickets

Part 6

Bell Work

Homework Check-up

Today’s Standard 6. G. A. 3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or horizontal segments only). Know and apply these techniques in the context of solving real-world and mathematical problems.

Essential Understanding: Plotting Figures In order to graph a figure in the coordinate plane, you just graph each of the vertices and then connect them with straight lines so that none of the lines cross. The number of sides you have is the same as the number of vertices. So a triangle, for example, is defined with three vertices. Example: Graph a figure with the coordinates A(− 4, 3) B(2, 3) C(2, − 1) D(− 4, − 1). First, plot each point on the coordinate grid and then connect the lines. Then, in order to determine what kind of shape it is, count the number of sides.

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Part 7

Bell Work

Homework Check-up

Today’s Standard 6. G. A. 1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; know and apply these techniques in the context of solving real-world and mathematical problems.

Finding Area and Perimeter Essential Understanding: • Perimeter is found by adding all side lengths for any given figure. Example: • Area is found by substituting the side lengths into the appropriate formula. Example: • You are expected to know/memorize the following formulas: – – Square/Rectangle A=lw Triangle A= ½bh Parallelogram A=bh Trapezoid A= ½(b 1 +b 2)h

Wrap it Up • Review • Questions • Exit Tickets