Math: Geometry
5.G.A. (1 - 4)
5.G.A. (1 - 4)
All 5th graders need to know how to graph points on a coordinate plane to solve real-world and mathematical problems.
Let's start with the basics... A point = an exact position or location on a plane surface. Important note: a point is not a thing, but a place. We show a point by drawing a dot with a pencil, but a point actually has no size! Points often have names! The name is usually a capital letter, like X. coordinate plane: plane: a flat surface that extends infinitely on all sides. A plane is like a huge sheet of paper that extends from one side of the universe to the other. Though it is infinite, we draw it with boundaries. It has 2 dimensions (2D): length and width, just like the paper on a table. The picture above is how we usually represent a plane, like a table top.
Notice it's drawn with boundaries, though a real plane has no boundaries. On this plane are 3 points, or 3 exact places: A, B, & C. A coordinate plane:
If we draw a 2-dimensional grid on the plane, it might look like the one above. It all starts from the origin! There is an origin, which is a starting point. If you walked from your home to our school, your home would be the origin, or starting point. A good explanation of "origin" (study.com) On a coordinate grid, two perpendicular lines intersect at the origin. The horizontal line extends sideways, left and right.
We call that line the X-axis. The vertical line extends up and down. We call that line the Y-axis. If we write numbers to measure distance from the origin, we create a number line. On the X-axis: Numbers going to the right of the origin are positive. Numbers going to the left of the origin are negative. On the Y--axis:
Numbers going up from the origin are positive. Numbers going down from the origin are negative. If you look at the coordinate plane above, you'll notice there are 4 sections. Each section is called a "quadrant." "quad" = 4 In 5th grade, we focus on positive numbers. Therefore, we focus on Quadrant 1. That gives us a grid like the one below... Coordinate Geometry
This term might sound complex, but it's just a system of geometry where we draw a grid plane and then position points on it, and each point's location is described by using an "ordered pair" of numbers. A system of geometry where the position of points on the plane is described using an ordered pair of numbers. Thanks to MathOpenRef.com for some of the illustrations! |
How do you graph points on a coordinate plane?
Every point has an ordered pair. Example: (2,3) Pair = two (there are two numbers) Ordered = the order is important! (X,Y) The coordinate plane is like a map, and the ordered pair tells you how to find the point (location). Remember: Start at the origin [center: (0,0)]! ~ The 1st number is the X-coordinate. A positive number moves you to the right. ~ The 2nd number is the Y-coordinate. A positive number moves you up. Example: (3,6) X = 3 and Y = 6 So you move 3 units to the right and 6 units up. Student-Friendly Standards (I can):
I can graph points on the coordinate plane to solve real-world and mathematical problems. Video: Introduction to the Coordinate Plane 5.G.A.1 I can understand a coordinate plane and ordered pairs of number coordinates on that plane. Practice: Identify Coordinates 5.G.A.1 I can graph ordered pairs of numbers on a coordinate plane using what I have learned about the x-axis and coordinate and the y-axis and coordinate. Video: Coordinate Plane: Graphing Points Practice: Graph Points Review how to graph Points! 5.G.A.2 I can represent real-world and mathematical problems by graphing points in the first quadrant of a coordinate plane.
Video: Plotting corners of a rectangle Practice: Shapes on the Coordinate Plane 5.G.A.2 I can understand coordinate values in the context of a real-world or mathematical problem. Video: Coordinate Plane: Graph Real-World Problems Practice: Coordinate Plane Real-World Problems I can classify 2-dimensional shapes into categories based on their properties.
5.G.B.3 I can understand how attributes of 2-dimensional shapes in a category also belong to all subcategories of those shapes. Example: Destinee has a puzzle piece that is shaped like a quadrilateral. The puzzle piece has two right angles, and one pair of parallel sides. What type of quadrilateral is the puzzle piece? Draw a diagram to support your answer. Solution: 1) a "quadrilateral" has 4 sides. 2) "one pair of parallel sides"... since squares, rectangles and rhombuses have 2 pairs of parallel sides, the answer cannot be any of those shapes. 3) A trapezoid can have "2 right angles," and it has one pair of parallel sides. Answer: The puzzle piece is a "right trapezoid." 5.G.B.4 I can classify 2-dimensional shapes based on their properties.
Video: Introduction to Quadrilateral (4-sided shapes) Mini-Practice: Count the Right Angles! The Common Core Standards:
Graph points on the coordinate plane to solve real-world and mathematical problems. 1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 2. Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Classify two-dimensional figures into categories based on their properties. 3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 4. Classify two-dimensional figures in a hierarchy based on properties. |