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Inequalities (Grade 6)

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Lesson Plans and Worksheets for Grade 6
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Common Core For Grade 6

Examples, solutions, videos, and lessons to help Grade 6 students learn how to write an inequality of the for x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c orx < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Common Core: 6.EE.8

Suggested Learning Targets

  • I can write inequalities and recognize that inequalities can have infinite solutions.
  • I can represent inequalities on a number line.
  • I can identify the constraint or condition in a real-world or mathematical problem in
    order to set up an inequality.
  • I can recognize that inequalities of the form x>c or x<c have infinitely many solutions.
  • I can write an inequality of the form x>c or x<c to represent a constraint or condition in a real-world or mathematical problem.
  • I can represent solutions to inequalities or the form x>c or x<c, with infinitely many
    solutions, on the number line diagrams

Writing, using, and understanding inequalities (Common Core Standard 6.EE.8)

Writing and Graphing Inequalities (6.EE.8)
Writing Inequalities for the Real World
1. You are hiking on a mountain which has a summit of 9,382 feet. Write an inequality for the altitude, a, you must be at.
2. For an experiment in your Chemistry class, you need to keep the temperature of a solution above -6 degrees Celsius. Write an inequality for the temperature, T.

Graphing Inequalities
Rule: Use an open circle for > and < inequalities, and a closed circle (dot) for ≥ and ≤ inequalities.

Equations vs. Inequalities
When you solve an inequality, you're finding infinite solutions.
When you solve an equation, you're finding one solution.

Writing Inequalities
How can you use inequalities to represent real-world situations?
Write an inequality for each statement below. Use x as your variable.
a) A Boeing 747 airplane can hold up to 524 passengers.
b) There are at least 34,000 species of spiders.
c) A presidential candidate must gain at least 270 electoral college votes to win the presidency.
d) The distance from Earth to the Moon is more than 238,000 miles.
e) The SMART car weighs at most 2,000 pounds.
f) The average person sees at least 100 movies in a year. Inequalities Writing Basic Inequalities
1. Total number of boys and girls on a field trip is less than or equal to 150.
2. The perimeter of a rectangle is greater than 250 cm.
3. At a summer camp, counselors are paid $9.50 and hour and sports instructors are paid $15 an hour. The budget for these employee's salary is less than $900.
4. In a group of tourists, there are at most three times as many Francophones as there are Anglophones Writing An Inequality From A Word Problem
The elevator of a local school has a maximum weight capacity of 2,000 pounds. If there are already 3 people on the elevator that have a combined weight of 460 pounds, write an inequality expressing the possible weights that may be added to the elevator. Use "w" to represent the weight.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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