Unlocking Percents: Cracking the Code of 'What Percent Of' Problems

Mathematics Grades 7th Grade 4:37 Video
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Lesson Description

Learn how to solve tricky 'what percent of' word problems by translating them into algebraic equations and converting fractions to percentages. This lesson uses a real-world example to make understanding easy and fun!

Video Resource

Percent word problem example 4 | Decimals | Pre-Algebra | Khan Academy

Khan Academy

Duration: 4:37
Watch on YouTube

Key Concepts

  • Translating word problems into algebraic equations.
  • Solving for an unknown variable in a linear equation.
  • Converting between fractions, decimals, and percentages.

Learning Objectives

  • Students will be able to translate 'what percent of' word problems into algebraic equations.
  • Students will be able to solve for the unknown percentage by isolating the variable.
  • Students will be able to convert fractions to decimals and decimals to percentages.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the relationship between fractions, decimals, and percentages. Ask students to provide examples of where they encounter percentages in their daily lives (e.g., sales, grades, statistics).
  • Video Presentation (10 mins)
    Play the Khan Academy video 'Percent word problem example 4 | Decimals | Pre-Algebra'. Encourage students to take notes on the problem-solving process. Pause at key moments to clarify any confusion.
  • Guided Practice (15 mins)
    Work through similar 'what percent of' problems as a class, guiding students through each step: translating the word problem into an equation, solving for the variable, and converting the result to a percentage. Example problems: * '30 is what percent of 50?' * '75 is what percent of 60?'
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of 'what percent of' word problems to solve independently. Encourage them to use the strategies discussed in class and in the video. Circulate to provide support and answer questions.
  • Wrap-up and Discussion (5 mins)
    Review the key concepts of the lesson and address any remaining questions. Preview upcoming topics related to percentages, such as percent increase and decrease.

Interactive Exercises

  • Percent Problem Scavenger Hunt
    Hide index cards with 'what percent of' word problems around the classroom. Students work in pairs to find the cards, solve the problems, and check their answers with you. First team to correctly solve all the problems wins.

Discussion Questions

  • Why is it important to understand how to translate word problems into equations?
  • What are some real-world scenarios where solving 'what percent of' problems is useful?
  • What strategies can you use to check your answer and make sure it is reasonable?

Skills Developed

  • Problem-solving
  • Algebraic reasoning
  • Mathematical communication
  • Critical Thinking

Multiple Choice Questions

Question 1:

15 is what percent of 50?

Correct Answer: 30%

Question 2:

In the equation 80x = 100, what does 'x' represent?

Correct Answer: The unknown percentage

Question 3:

To convert a decimal to a percentage, you multiply by:

Correct Answer: 100

Question 4:

What is 5/4 expressed as a decimal?

Correct Answer: 1.25

Question 5:

If a shirt costs $20 and is 25% off, what is the discount amount?

Correct Answer: $5

Question 6:

What is the first step in solving the problem '25 is what percent of 200'?

Correct Answer: Divide 200 by 25.

Question 7:

120 is what percent of 80?

Correct Answer: 150%

Question 8:

Which of the following is equivalent to 175%?

Correct Answer: 1.75

Question 9:

If you get 18 out of 20 questions correct on a quiz, what is your percentage score?

Correct Answer: 90%

Question 10:

The easiest way to convert a fraction into a percentage is to first:

Correct Answer: Convert it to a decimal

Fill in the Blank Questions

Question 1:

To find what percent a number is of another, you first need to write an __________.

Correct Answer: equation

Question 2:

When converting a decimal to a percent, you move the decimal point two places to the _________.

Correct Answer: right

Question 3:

5/4 as a percentage is _________%

Correct Answer: 125

Question 4:

If 'x' is equal to 1.5, then as a percentage, 'x' is equal to __________%.

Correct Answer: 150

Question 5:

To solve for x in the equation 5x = 25, you must ___________ both sides by 5.

Correct Answer: divide

Question 6:

When you have an equation that includes a variable, your goal is to _______ the variable to find it's value

Correct Answer: isolate

Question 7:

20 is what _________ of 80?

Correct Answer: percent

Question 8:

If 100% of something equals 1, then 50% of something equals _________.

Correct Answer: 0.5

Question 9:

In mathematics, a variable is a symbol that represents an ____________ quantity.

Correct Answer: unknown

Question 10:

Writing word problems into equations is a helpful skill in order to solve for the __________.

Correct Answer: answer

Educational Standards

7.A.3.1:Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. 7.N.1.1:Compare and order rational numbers expressed in various forms using the symbols '<', '>', and '='. 7.A.2.2:Solve multi-step problems with proportional relationships (e.g., distance-time, percent increase or decrease, discounts, tips, unit pricing, mixtures and concentrations, similar figures, other mathematical situations).

Teaching Materials

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