Unlocking Ratios: Comparing Apples and Oranges (and More!)

Algebra 1 Grades High School 3:58 Video
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Lesson Description

Explore the fundamentals of ratios and proportions, learning how to represent relationships between quantities and simplify them for easier comparison.

Video Resource

Introduction to ratios | Ratios, rates, and percentages | 6th grade | Khan Academy

Khan Academy

Duration: 3:58
Watch on YouTube

Key Concepts

  • Ratio as a comparison of two quantities
  • Different notations for representing ratios (e.g., 'a to b', 'a:b')
  • Simplifying ratios by dividing by a common factor
  • Understanding the importance of order in ratios (apples to oranges vs. oranges to apples)

Learning Objectives

  • Students will be able to define ratio and explain its purpose.
  • Students will be able to represent ratios using different notations.
  • Students will be able to simplify ratios by finding common factors.
  • Students will be able to correctly interpret the order of quantities in a ratio.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students if they've heard the term 'ratio' before. Discuss real-world examples where ratios are used (e.g., mixing paint, cooking recipes, sports statistics). Briefly introduce the Khan Academy video and its purpose.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Introduction to ratios' (https://www.youtube.com/watch?v=bIKmw0aTmYc). Instruct students to take notes on the different ways to represent ratios and how to simplify them.
  • Guided Practice (10 mins)
    Work through examples similar to the video on the board. Start with simple examples and gradually increase the complexity. Emphasize the importance of identifying common factors when simplifying ratios. Example: What is the ratio of girls to boys in the class if there are 15 girls and 10 boys? Simplify the ratio. Then reverse it, boys to girls.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing ratio problems to solve independently. Include problems that require simplification and problems where the order of the quantities is reversed. Examples: 1. A bag contains 12 red marbles and 8 blue marbles. What is the ratio of red marbles to blue marbles? What is the simplified ratio? 2. In a garden, there are 7 roses and 14 tulips. What is the ratio of tulips to roses? What is the simplified ratio?
  • Wrap-up and Discussion (3 mins)
    Review the key concepts of ratios and proportions. Address any remaining questions or misconceptions. Preview the next lesson on more complex ratio problems.

Interactive Exercises

  • Ratio Scavenger Hunt
    Have students find and record ratios of different objects in the classroom (e.g., number of pencils to number of erasers, number of chairs to number of desks). Then they will simplify the ratios.

Discussion Questions

  • Can you think of any real-life situations where ratios are used?
  • Why is it important to simplify ratios?
  • How does the order of the quantities affect the ratio?

Skills Developed

  • Ratio simplification
  • Proportional reasoning
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

What is a ratio?

Correct Answer: A comparison of two quantities

Question 2:

Which of the following is NOT a way to represent a ratio?

Correct Answer: a + b

Question 3:

What is the simplified form of the ratio 12:18?

Correct Answer: 2:3

Question 4:

If the ratio of apples to bananas is 3:5, what does this mean?

Correct Answer: There are 3 apples for every 5 bananas

Question 5:

What is the ratio of vowels to consonants in the word 'ALGEBRA'?

Correct Answer: 3:4

Question 6:

A recipe calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar?

Correct Answer: 2:1

Question 7:

Simplify the ratio 25:10

Correct Answer: 5:2

Question 8:

If there are 8 dogs and 12 cats, what is the ratio of dogs to the total number of pets?

Correct Answer: 2:5

Question 9:

What is the ratio of prime numbers to composite numbers in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

Correct Answer: 4:5

Question 10:

Which ratio is equivalent to 4:6?

Correct Answer: 2:3

Fill in the Blank Questions

Question 1:

A ______ is a comparison of two quantities.

Correct Answer: ratio

Question 2:

The ratio of apples to oranges can be written as 'apples ______ oranges'.

Correct Answer: to

Question 3:

To simplify a ratio, you divide both quantities by a common ______.

Correct Answer: factor

Question 4:

In the ratio 5:7, the first quantity is ______.

Correct Answer: 5

Question 5:

If a team wins 8 games and loses 2, the ratio of wins to losses is ______.

Correct Answer: 4:1

Question 6:

A class has 10 boys and 15 girls. The ratio of boys to girls in simplest form is ______.

Correct Answer: 2:3

Question 7:

The ratio of the number of sides in a square to the number of angles in a square is ______.

Correct Answer: 1:1

Question 8:

If the ratio of x to y is 3:4, then for every 3 units of x, there are ______ units of y.

Correct Answer: 4

Question 9:

The simplified ratio of 100 cm to 1 meter is ______.

Correct Answer: 1:1

Question 10:

If a store sells 5 red shirts for every 3 blue shirts, the ratio of red shirts to total shirts is ______.

Correct Answer: 5:8

Educational Standards

A1.A.3.4:Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y. A1.N.1:[Standard] Extend the understanding of exponents to include square roots and cube roots.

Teaching Materials

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