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Guiding Question: In what ways can location be communicated?
The Cartesian plane: your mathematical map
The Cartesian plane: your mathematical map
The Origin Story: The Cartesian Plane is named after René Descartes, a French mathematician who supposedly watched a fly on his ceiling and realized he could describe its exact position using numbers.
The Grid: The Cartesian plane is made of two intersecting number lines:
x-axis: The horizontal number line (flat). All points here have a y-coordinate of zero.
y-axis: The vertical number line (up and down). All points here have an x-coordinate of zero.
The Origin (0,0): The exact center where the two axes cross.
Ordered Pairs (x, y):
Location is always written as (x, y).
The x-coordinate tells you how far to move horizontally from the y-axis.
The y-coordinate tells you how far to move vertically from the x-axis.
Mnemonic: "You have to walk to the elevator (x) before you can go up or down (y)."
Skills & Procedures:
Locating Points: To find (3, -2), start at the origin, move 3 units right, and 2 units down.
Modeling Polygons: A polygon (like a triangle or square) is created by plotting points (vertices) and connecting them with straight lines.
movement in space: transformations
movement in space: transformations
When we move a shape on a grid, it is called a Transformation. In Grade 6, we focus on 3 types:
translation
translation
Moving a shape up, down, left, or right without turning it or flipping it.
The Math: You add or subtract from the x and y coordinates.
Example: Moving "right 2, up 3" means adding 2 to x, and 3 to y.
reflection
reflection
Flipping a shape across a "mirror line."
Over the x-axis: The shape flips top-to-bottom. The x stays the same, but the y becomes its opposite
(e.g., (2, 3) becomes (2, -3)).
Over the y-axis: The shape flips left-to-right. The y stays the same, but the x becomes its opposite (e.g., (2, 3) becomes (-2, 3)).
rotation
rotation
Spinning a shape around a center of rotation (in Grade 6, this is usually one of the shape's own corners/vertices).
Angles: We use 90° (quarter turn), 180° (half turn), or 270° (three-quarter turn).
Direction: Clockwise (right) or Counter-clockwise (left).
Important Rule: During these movements, the shape’s location and orientation might change, but the shape itself stays congruent (same size and shape).
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