UNIT 7 - RATIONAL EXPLORATIONS
PARENT LETTERS
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OVERVIEW
In this unit students will:
- Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.
- Understand a rational number as a point on thenuber 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.
- Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.
- recognize that the opposite of the opposite of a number is the number itself.
- 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.
- 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.
- Understand ordering and absolute value of rational numbers.
- Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
- Write, interpret, and explain statements of order for rational numbers in real-world contexts.
- Understand the absolute value of a rational number as its distance from 0 on the number line
- Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
- Distinguish comparisons of absolute value from statements about order.
- Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
VOCABULARY
- Absolute value: The distance between a number and zero on the number line. The symbol for absolute value is shown in the equation .
- Integers: The set of whole numbers and their opposites
- Magnitude: Greatness in size or amount
- Negative numbers: The set of numbers with a value less than zero
- Opposite number: Two different numbers that have the same absolute value. Example: 4 and are opposite numbers because both have an absolute value of 4. They are the same distance from zero, in opposite directions.
- Rational number: The set of numbers that can be written in the form where a and b are integers and .
- Sign: a symbol that indicates whether a number is positive or negative. Example: in , the sign hows this number is read “negative four”.
- Cartesian Coordinate Plane: A plane containing two perpendicular axes (x and y) intersecting at a point called origin (0, 0).
- Coordinates: An ordered pair, , that locates a point in a plane.
- Distance: amount of separation between 2 points.
- Inequality: Any mathematical sentence that contains the symbols > (greater than), < (less than), < (less than or equal to), or > (greater than or equal to).
- Ordered Pair: A pair of numbers, , that indicate the position of a point on the Cartesian coordinate Plane.
- Origin: The point of intersection of the vertical and horizontal axes of a Cartesian coordinate plane. The coordinates of the origin are (0, 0).
- Polygon: A closed figure formed by three or more line segments.
- Quadrant: One of the four regions on a Coordinate plane formed by the intersection of the x-axis and the y-axis.
- x-axis: The horizontal number line on the Cartesian coordinate plane.
- x-coordinate: The first number of in ordered pair; the position of a point relative to the vertical axis
- y-axis: The vertical number line on the Cartesian coordinate plane
- y-coordinate: The second number in an ordered pair; the position of a point relative to the horizontal axis