Teacher Script: Proportional Percents

Warm-Up & Introduction (5 minutes)

(Display Proportional Percent Problems Slide Deck - Slide 1)

"Good morning, class! Let's start with a quick warm-up. If you scored 4 out of 5 on a mini-quiz, what fraction of the questions did you answer correctly? And how could we express that as a percentage? Take a moment to think about it and jot down your answer."

"(Pause for student responses) Great! 4 out of 5 is indeed 4/5, and to get a percentage, we know that 4/5 is equivalent to 80/100, which is 80%. Many of you probably already know how to convert fractions to percentages, and that's fantastic because today we're going to build on that idea."

"Look around you, or think about your daily lives. Where do you see percentages being used? Can anyone give me an example?"

"(Listen for student examples like sales, tips, grades, weather forecasts.) Exactly! Percentages are everywhere – from shopping discounts to calculating how much of your phone battery is left. They help us understand parts of a whole in a standardized way. Today, we're going to learn a super powerful method for solving all kinds of percent problems using something called proportions. By the end of this lesson, you'll be able to set up and solve these problems like pros!"

Understanding the Proportion (10 minutes)

(Display Proportional Percent Problems Slide Deck - Slide 2)

"Our secret weapon for today is this simple, yet incredibly powerful, proportion: Part over Whole equals Percent over 100."

"Let's break down what each of these terms means. The Part is the amount we're interested in – it's often 'is' something 'of' something else. The Whole is the total amount, or the entire quantity. The Percent is the number with the percent sign (%). And the 100? That number always stays the same, because percentages are always out of 100!"

"Think of it like this: if you have 25% of a pizza, the 'part' is the amount you have, and the 'whole' is the entire pizza. And the '25' is your percent, out of a total of '100' percent for the whole pizza."

(Display Proportional Percent Problems Slide Deck - Slide 3)

"Let's try an example together. 'What is 25% of 80?'"

"First, let's identify what we know and what we need to find. Who can tell me what the percent is in this problem?"

"(Wait for '25') "That's right, 25 is our percent. What about the whole amount? What is the total we're taking a percent of?"

"(Wait for '80') "Exactly, 80 is our whole. And what are we trying to find? We want to know 'what is' that 25% part of 80. So, our part is unknown. We'll use a variable, like 'x', for the part."

"Now, how would we set this up using our proportion: part/whole = percent/100? Talk with a partner for a moment and write it down."

"(Allow students to discuss and write.) "Okay, let's see. We have 'x' as the part, '80' as the whole, and '25' as the percent. So, we set it up as x/80 = 25/100."

(Display Proportional Percent Problems Slide Deck - Slide 4)

"Now, how do we solve a proportion? We use cross-multiplication! We multiply the numerator of one fraction by the denominator of the other, and set them equal. So, 100 times x equals 80 times 25."

"100x equals 2000. To get x by itself, what do we do?"

"(Wait for 'divide by 100') "Yes! We divide both sides by 100. And what do we get? x equals 20. So, 25% of 80 is 20."

(Display Proportional Percent Problems Slide Deck - Slide 5)

"Let's try another type. '30 is what percent of 120?'"

"Who can identify the part, the whole, and the percent this time? What do we know, and what are we looking for?"

"(Guide students to identify 30 as the part, 120 as the whole, and the percent as unknown (x).)"

"Excellent! 30 is the part, 120 is the whole, and 'x' is our unknown percent. How would we set up this proportion?"

"(Allow students to set it up) "We set it up as 30/120 = x/100."

(Display Proportional Percent Problems Slide Deck - Slide 6)

"Now, everyone, solve this one on your own using cross-multiplication. What do you get for x?"

"(Give students time to solve. Then reveal the answer.) "If you cross-multiplied, you got 30 times 100, which is 3000, and 120 times x, which is 120x. So, 3000 = 120x. Dividing both sides by 120, x equals 25. So, 30 is 25% of 120. Great job!"

(Display Proportional Percent Problems Slide Deck - Slide 7)

"One last type. '15 is 50% of what number?'"

"Again, let's break it down: part, whole, percent. What are they?"

"(Guide students: 15 is the part, 50 is the percent, and the whole is unknown (x).)"

"That's right! 15 is the part, 50 is the percent, and 'x' is the whole. Go ahead and set up the proportion."

"(Allow students to set it up.) "So, we have 15/x = 50/100."

(Display Proportional Percent Problems Slide Deck - Slide 8)

"Now solve it!"

"(Give students time to solve.) "Cross-multiply and you get 15 times 100, which is 1500, and 50 times x, which is 50x. So, 1500 = 50x. Divide by 50, and x equals 30. So, 15 is 50% of 30!"

Guided Practice (8 minutes)

"Alright, you've seen me do it, and you've tried a few with my help. Now let's do some more together. I'm handing out the Proportional Percent Practice Worksheet. We're going to work on the first few problems as a class."

(Distribute Proportional Percent Practice Worksheet)

"Let's look at problem #1. 'A store is having a sale, and everything is 20% off. If an item originally cost $60, what is the discount amount?'"

"Who can identify the part, whole, and percent here? What are we trying to find?"

"(Guide students: 20 is the percent, 60 is the whole, and the part (discount amount) is unknown. Have a student or volunteer come to the board to set up the proportion and solve.)"

"Fantastic! It's x/60 = 20/100. And solving that gives us x = 12. So, the discount is $12."

"Let's try problem #2. 'You got 18 questions correct on a test with 25 total questions. What percent did you get correct?'"

"Part, whole, percent? What are they?"

"(Guide students: 18 is the part, 25 is the whole, and the percent is unknown. Work through this example with student input, or have another student solve on the board.)"

"Excellent! 18/25 = x/100. And solving that gives us x = 72. So, you got 72% correct."

Independent Practice & Wrap-up (7 minutes)

(Display Proportional Percent Problems Slide Deck - Slide 9)

"You've done a great job with our guided practice! Now it's your turn to work independently on the remaining problems on the Proportional Percent Practice Worksheet. Remember our key formula: Part over Whole equals Percent over 100. Take your time, read each problem carefully, and set up your proportions before solving."

"I'll be walking around to answer any questions you might have and provide support. If you finish early, double-check your work."

(Circulate and provide individual assistance.)

"We have just a couple of minutes left. Let's quickly review problem #3. Can anyone share how they set it up and their answer?"

"(Call on a student to share. Provide the correct setup and answer, referring to the Proportional Percent Practice Answer Key if needed.)"

"Great work today, everyone! You now have a powerful tool for solving percent problems. Remember this proportion, it will help you in many situations. If you didn't finish the worksheet, please complete it for homework. We'll continue to build on this next time!"

Proportional Percent Practice Worksheet

Directions: For each problem, set up a proportion using the formula $\frac{\text{Part}}{\text{Whole}} = \frac{\text{Percent}}{100}$. Then, solve for the unknown value. Show all your work.

1. Finding the Part

A store is having a sale, and everything is 20% off. If an item originally cost $60, what is the discount amount?

Identify the Part, Whole, and Percent:
Part =

Whole =

Percent =

Set up the proportion:

Solve:

Answer:

2. Finding the Percent

You got 18 questions correct on a test with 25 total questions. What percent did you get correct?

Identify the Part, Whole, and Percent:
Part =

Whole =

Percent =

Set up the proportion:

Solve:

Answer:

3. Finding the Whole

Sarah found a jacket on sale for $45, which was 75% of its original price. What was the original price of the jacket?

Identify the Part, Whole, and Percent:
Part =

Whole =

Percent =

Set up the proportion:

Solve:

Answer:

4. Real-World Application

Mr. Henderson wants to leave a 15% tip on a meal that cost $32. How much should he leave for the tip?

Identify the Part, Whole, and Percent:
Part =

Whole =

Percent =

Set up the proportion:

Solve:

Answer:

5. Challenge Problem

A survey found that 240 students, which represents 60% of the school, prefer pizza for lunch. How many students are in the entire school?

Identify the Part, Whole, and Percent:
Part =

Whole =

Percent =

Set up the proportion:

Solve:

Answer:

Proportional Percent Practice Answer Key

Formula: $\frac{\text{Part}}{\text{Whole}} = \frac{\text{Percent}}{100}$

1. Finding the Part

A store is having a sale, and everything is 20% off. If an item originally cost $60, what is the discount amount?

Identify the Part, Whole, and Percent:
Part = x (unknown discount amount)

Whole = $60 (original price)

Percent = 20

Set up the proportion:
$$\frac{\text{x}}{60} = \frac{20}{100}$$

Solve:
Cross-multiply:

$$100 \times \text{x} = 60 \times 20$$

$$100\text{x} = 1200$$

Divide both sides by 100:

$$\frac{100\text{x}}{100} = \frac{1200}{100}$$

$$\text{x} = 12$$

Answer: The discount amount is $12.

2. Finding the Percent

You got 18 questions correct on a test with 25 total questions. What percent did you get correct?

Identify the Part, Whole, and Percent:
Part = 18 (correct questions)

Whole = 25 (total questions)

Percent = x (unknown percent)

Set up the proportion:
$$\frac{18}{25} = \frac{\text{x}}{100}$$

Solve:
Cross-multiply:

$$18 \times 100 = 25 \times \text{x}$$

$$1800 = 25\text{x}$$

Divide both sides by 25:

$$\frac{1800}{25} = \frac{25\text{x}}{25}$$

$$\text{x} = 72$$

Answer: You got 72% correct.

3. Finding the Whole

Sarah found a jacket on sale for $45, which was 75% of its original price. What was the original price of the jacket?

Identify the Part, Whole, and Percent:
Part = $45 (sale price)

Whole = x (unknown original price)

Percent = 75

Set up the proportion:
$$\frac{45}{\text{x}} = \frac{75}{100}$$

Solve:
Cross-multiply:

$$45 \times 100 = 75 \times \text{x}$$

$$4500 = 75\text{x}$$

Divide both sides by 75:

$$\frac{4500}{75} = \frac{75\text{x}}{75}$$

$$\text{x} = 60$$

Answer: The original price of the jacket was $60.

4. Real-World Application

Mr. Henderson wants to leave a 15% tip on a meal that cost $32. How much should he leave for the tip?

Identify the Part, Whole, and Percent:
Part = x (unknown tip amount)

Whole = $32 (cost of the meal)

Percent = 15

Set up the proportion:
$$\frac{\text{x}}{32} = \frac{15}{100}$$

Solve:
Cross-multiply:

$$100 \times \text{x} = 32 \times 15$$

$$100\text{x} = 480$$

Divide both sides by 100:

$$\frac{100\text{x}}{100} = \frac{480}{100}$$

$$\text{x} = 4.80$$

Answer: Mr. Henderson should leave a tip of $4.80.

5. Challenge Problem

A survey found that 240 students, which represents 60% of the school, prefer pizza for lunch. How many students are in the entire school?

Identify the Part, Whole, and Percent:
Part = 240 (students who prefer pizza)

Whole = x (unknown total number of students)

Percent = 60

Set up the proportion:
$$\frac{240}{\text{x}} = \frac{60}{100}$$

Solve:
Cross-multiply:

$$240 \times 100 = 60 \times \text{x}$$

$$24000 = 60\text{x}$$

Divide both sides by 60:

$$\frac{24000}{60} = \frac{60\text{x}}{60}$$

$$\text{x} = 400$$

Answer: There are 400 students in the entire school.