Inequality Explorers: Describing Real-World Math!

Mathematics Grades 7th Grade 2:53 Video
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Lesson Description

Learn how to translate real-world situations into mathematical inequalities. This lesson will help you write and interpret inequalities using variables and numbers.

Video Resource

How to describe real-world situations with inequalities | 6th grade | Khan Academy

Khan Academy

Duration: 2:53
Watch on YouTube

Key Concepts

  • Inequalities
  • Variables
  • Real-world applications of inequalities

Learning Objectives

  • Students will be able to translate real-world scenarios into mathematical inequalities.
  • Students will be able to identify the appropriate inequality symbol (<, >, ≤, ≥) based on the given context.
  • Students will be able to express inequalities with the variable on either side of the inequality symbol.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students if they've ever encountered situations where things aren't just 'equal'. For example, a minimum age requirement for a ride or a maximum weight limit on an elevator. Introduce the concept of inequalities as a way to represent these situations mathematically.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'How to describe real-world situations with inequalities | 6th grade | Khan Academy'. Encourage students to take notes on the examples provided.
  • Guided Practice (10 mins)
    Work through similar examples as in the video, but with different scenarios. For instance: 'A student needs to score at least 80 points to get a B in the class. Write an inequality to represent the possible scores, s, the student can achieve to get a B.' Guide students through identifying the variable, the relevant numbers, and the correct inequality symbol.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing various real-world scenarios. Have them independently write inequalities to represent each situation. Examples: 'You must be taller than 48 inches to ride the roller coaster.', 'The temperature needs to be below 32 degrees Fahrenheit for it to snow.', 'You must be at least 16 years old to get your driver's license.'
  • Review and Discussion (8 mins)
    Review the answers to the independent practice problems. Discuss any challenges students faced and clarify any misconceptions. Emphasize the importance of carefully reading the problem to determine the correct inequality symbol.

Interactive Exercises

  • Inequality Charades
    Divide the class into teams. Each team creates scenarios that can be represented by inequalities. Teams then act out the scenarios, and the other teams must write the corresponding inequality.

Discussion Questions

  • What are some everyday situations where we use inequalities?
  • How does the wording of a problem help you determine the correct inequality symbol to use?

Skills Developed

  • Translating word problems into mathematical expressions
  • Critical thinking
  • Problem-solving

Multiple Choice Questions

Question 1:

Which inequality represents 'x is greater than 5'?

Correct Answer: x > 5

Question 2:

Which inequality represents 'y is less than or equal to 10'?

Correct Answer: y ≤ 10

Question 3:

The speed limit is no more than 55 mph. Which inequality represents the possible speeds, s?

Correct Answer: s ≤ 55

Question 4:

You must be at least 48 inches tall to ride the ride. Which inequality represents the height requirement, h?

Correct Answer: h ≥ 48

Question 5:

The temperature must be below 32°F for it to snow. Which inequality represents the temperature, t?

Correct Answer: t < 32

Question 6:

What does the symbol '≤' mean?

Correct Answer: Less than or equal to

Question 7:

What does the symbol '>' mean?

Correct Answer: Greater than

Question 8:

Which of the following means the same as x > 3?

Correct Answer: 3 is less than x

Question 9:

The sign says 'Maximum weight: 100 lbs'. If 'w' represents the weight, which inequality is correct?

Correct Answer: w ≤ 100

Question 10:

A store offers a discount if you spend more than $50. Which inequality represents the spending amount, s, to get the discount?

Correct Answer: s > 50

Fill in the Blank Questions

Question 1:

The inequality 'x < 7' means 'x is _______ than 7'.

Correct Answer: less

Question 2:

The inequality 'y ≥ 3' means 'y is greater than or ________ to 3'.

Correct Answer: equal

Question 3:

To represent 'at least', you would use the symbol ______.

Correct Answer: ≥

Question 4:

To represent 'no more than', you would use the symbol ______.

Correct Answer: ≤

Question 5:

If a problem says 'exceeds', you would use the symbol ______.

Correct Answer: >

Question 6:

The phrase 'is under' translates to the inequality symbol ______.

Correct Answer: <

Question 7:

An internal temperature less than 135 means the steak is ________.

Correct Answer: undercooked

Question 8:

768 < s can also be written as s _____ 768

Correct Answer: >

Question 9:

Simone will go snowboarding if the temperature is less than or ________ to 5 degrees Celsius.

Correct Answer: equal

Question 10:

A speed ______ than the speed of sound will create a sonic boom.

Correct Answer: greater

Educational Standards

7.A.3:Represent mathematical situations using equations and inequalities involving variables and rational numbers. 7.A.3.2:Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p and q are nonnegative rational numbers.

Teaching Materials

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