Ordering Rational Numbers
Online practice
|
|
Rational Numbers |
Number Line |
Standard
Use rational numbers (fractions, decimals, and integers) to represent real-world contexts and understand the meaning of 0 in each situation. Example: a. Use an integer to represent 30 feet below sea level. -25 b. Use an integer to represent 30 feet above sea level. +25 c. What would 0 (zero) represent in the scenario above? 0 sea level Vocabulary
Resources Explanation of rational numbers - videos Graphing IntegersStandards
What axis are the ordered pairs (-2, 4) and (-2, -4) reflected over? Solution The y-coordinates differ only by signs, which represents a reflection across the x-axis. Vocabulary
Origin - The point where the x-axis and the y-axis intersect on the coordinate plane. The coordinates of the origin are (0,0). Ordered Pair - A pair of numbers used to locate a point on a coordinate grid, such as (5,-2). The x-axis coordinate is always first because “x” comes before “y” alphabetically. Coordinates - One of the numbers in an ordered pair. The x value is the first coordinate of the pair and the y value is the second coordinate. Resources How to plot integers on a graph - video Identify quadrant ordered pairs below in -practice IXL: M4 Distance Between PointsStandards
Find the distance between points when ordered pairs have the same x-coordinate (vertical) or same y-coordinate (horizontal). Example: What is the distance between (–5, 2) and (–9, 2)? Solution: The distance would be 4 units. This would be a horizontal line since the y-coordinates are the same. Absolute ValueStandard
ExaExample: Which numbers have an absolute value of 7 Solution: 7 and –7 since both numbers have a distance of 7 units from 0 on the number line. Greatest Absolute ValueStandard
Understand that for negative numbers, as the absolute value increases, the value of the negative number decreases. Example: The absolute value of –24 is greater than the absolute value of –14. Vocabulary Absolute value - a numbers distance from zero Resources Absolute value - video IXL: M2 |
Standards
Example
What is the opposite of 2 1 /2 ? Solution: - 2 1/2 because it is the same distance from 0 on the opposite side Example:
Place the following numbers would be on a number line: Solution
Vocabulary
Negative integer - numbers less than zero. Positive integer - numbers greater than zero. Opposite - numbers that are equal distance from zero. Zero - an integer that is neither positive or negative Resources What is an integer - video Graphing numbers on a number line - video IXL: M1, M3, M5 InequalitiesStandards
Example: Which is greater 3 or -3? Solution Example:
Which is greater -3 or -5 Solution Vocabulary
Inequality - An inequality says that two values are not equal. a ≠ b says that a is not equal to b. Signs such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’ are used to compare two numbers. Resources Plotting inequalities on a number line - video Comparing Rational NumbersStandard
Understand that as the negative number increases (moves to the left on a number line), the value of the number decreases. Example: –24 is less than –14 because –24 is located to the left of –14 on the number line.. Standard
Write statements using < or > to compare rational number in a real-world context. Example: The balance in Sue’s checkbook was –$12.55. The balance in John’s checkbook was –$10.45. Write an inequality to show the relationship between these amounts. Who owes more? Solution: –12.55 < –10.45, Sue owes more than John. The interpretation could also be “John owes less than Sue”. Example a. Which is the colder temperature?
b. How much colder? c. Write an inequality to show the relationship between the temperatures and explain how the model shows this relationship. Solution
a. & b. The left thermometer is colder by 4 degrees c. Either -7 < -3 or -3 > -7 Resources |