Unlocking Percent Problems with Algebra

Mathematics Grades 7th Grade 6:17 Video
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Lesson Description

Learn how to solve percent problems using algebraic equations. Discover the relationship between percent, amount, and base, and practice setting up and solving equations.

Video Resource

Solving percent problems | Decimals | Pre-Algebra | Khan Academy

Khan Academy

Duration: 6:17
Watch on YouTube

Key Concepts

  • Percent as a ratio or rate per 100
  • Translating word problems into algebraic equations
  • Identifying the percent, amount, and base in a percent problem

Learning Objectives

  • Students will be able to translate percent problems into algebraic equations.
  • Students will be able to identify the percent, amount, and base in a given percent problem.
  • Students will be able to solve for the unknown variable in a percent problem using algebraic methods.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what percentages represent and their relationship to decimals and fractions. Briefly discuss the concept of 'percent of' and its relationship to multiplication.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Solving percent problems' (https://www.youtube.com/watch?v=TvSKeTFsaj4). Encourage students to take notes on the key steps the instructor takes to set up and solve the problem.
  • Guided Practice (15 mins)
    Work through a couple of example problems as a class. Model how to identify the percent, amount, and base. Demonstrate how to translate the word problem into an algebraic equation. Solve for the unknown variable, explaining each step clearly.
  • Independent Practice (15 mins)
    Provide students with a set of percent problems to solve independently. Encourage them to use the techniques demonstrated in the video and during guided practice. 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. Briefly introduce the concept of using proportions to solve percent problems as an alternative method.

Interactive Exercises

  • Percent Problem Match
    Create a worksheet where students match percent problems with their corresponding algebraic equations.
  • Interactive Whiteboard Practice
    Use an interactive whiteboard to display percent problems and allow students to come up and solve them in real-time, explaining their reasoning to the class.

Discussion Questions

  • What are some real-world situations where you might need to solve percent problems?
  • Why is it important to be able to translate word problems into algebraic equations?
  • How does understanding the relationship between percent, amount, and base help you solve percent problems?

Skills Developed

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

Multiple Choice Questions

Question 1:

In the equation 'Amount = Percent x Base', what does 'Base' represent?

Correct Answer: The number you're taking the percent of.

Question 2:

What is 25% expressed as a decimal?

Correct Answer: 0.25

Question 3:

Which equation represents '30 is 10% of what number?'

Correct Answer: 30 = 0.10x

Question 4:

If 50 is 20% of a number, what is that number?

Correct Answer: 250

Question 5:

What is the first step in solving a percent problem using algebra?

Correct Answer: Identify the percent, amount, and base.

Question 6:

If you know the amount and the base, how do you find the percent?

Correct Answer: Divide the amount by the base.

Question 7:

What is the value of x in the equation 0.5x = 100?

Correct Answer: 200

Question 8:

Which of the following is equivalent to 1/4?

Correct Answer: 25%

Question 9:

If a store offers a 15% discount on a $80 item, how much is the discount?

Correct Answer: $12

Question 10:

What does 'x' represent in the problem '10 is x% of 50'?

Correct Answer: The percent

Fill in the Blank Questions

Question 1:

In the percent equation, the __________ is the number you are taking the percentage of.

Correct Answer: base

Question 2:

To convert a percentage to a decimal, you divide by __________.

Correct Answer: 100

Question 3:

The equation to solve 'What is 20% of 80?' is x = 0.20 * __________.

Correct Answer: 80

Question 4:

If 10% of a number is 5, the number is __________.

Correct Answer: 50

Question 5:

The formula Amount = Percent x Base can be used to find the __________ if you know the percent and the base.

Correct Answer: amount

Question 6:

25% is equivalent to the fraction __________.

Correct Answer: 1/4

Question 7:

When solving for x in the equation 0.75x = 150, you must __________ both sides by 0.75.

Correct Answer: divide

Question 8:

If a store offers a 30% discount, you pay __________% of the original price.

Correct Answer: 70

Question 9:

In the problem, 40 is 50% of what number, 40 represents the _______.

Correct Answer: amount

Question 10:

The decimal form of 120% is _________.

Correct Answer: 1.2

Educational Standards

7.RP.A.3:Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.EE.B.4:Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Teaching Materials

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