Teacher Script: Ratio Royale: Win With Rates!

Warm-Up: Ratio Race! (5 minutes)

Teacher: "Good morning, future math champions! Let's kick off our lesson with a quick 'Ratio Race!' I've handed out a warm-up sheet. Please take about 3 minutes to complete it individually. Don't worry if you don't know all the answers yet; it's just to get our brains thinking about comparing quantities!"

(Allow 3 minutes for students to work.)

Teacher: "Alright, pencils down! Let's quickly review. For question 1, 'In a basket of fruit, there are 4 apples and 6 bananas. What is the ratio of apples to bananas?' What did you get?"

Student: "4 to 6!"

Teacher: "Excellent! And can anyone tell me another way to write that ratio?"

Student: "4:6 or 4/6."

Teacher: "Perfect! We'll explore more about simplifying these soon. Let's move on to our main event!"

Introduction to Ratios & Rates (10 minutes)

(Display Ratio Royale Slide Deck - Slide 1: "Ratio Royale: Win With Rates!")

Teacher: "Welcome, adventurers, to 'Ratio Royale: Win With Rates!' Today, we're embarking on a quest to master the art of comparing quantities, which are super useful skills in the real world. By the end of this lesson, you'll be able to define ratios and rates, calculate unit rates, and solve awesome real-world problems. Who's ready?"

(Display Ratio Royale Slide Deck - Slide 2: "What's a Ratio?")

Teacher: "So, what exactly is a ratio? A ratio is simply a comparison of two quantities. Think of it like comparing how many apples to how many bananas you have. There are three main ways we can write ratios. Can someone read them for us?"

Student: (Reads from slide) "Using a colon: 2:3, Using the word 'to': 2 to 3, As a fraction: 2/3."

Teacher: "Fantastic! Let's look at an example. If we have 15 girls and 10 boys in a class, the ratio of girls to boys is 15 to 10. Does anyone see how this connects to our warm-up?"

(Allow a moment for responses.)

(Display Ratio Royale Slide Deck - Slide 3: "Simplifying Ratios")

Teacher: "Just like fractions, ratios can often be simplified. We do this by finding the greatest common factor of both numbers and dividing them. In our example of 15 girls to 10 boys, what's the greatest common factor of 15 and 10?"

Student: "5!"

Teacher: "Exactly! So, if we divide both by 5, what's our simplified ratio?"

Student: "3:2."

Teacher: "That means for every 3 girls, there are 2 boys. This simplified ratio helps us understand the comparison more clearly. Any questions so far about ratios?"

(Address questions.)

(Display Ratio Royale Slide Deck - Slide 4: "From Ratios to Rates!")

Teacher: "Now, let's level up! What if the quantities we're comparing have different units? That's when we're talking about a rate! Can someone give me an example of a rate they've heard before? Think about driving, or even grocery shopping!"

Student: "Miles per hour!"

Student: "Dollars per pound!"

Teacher: "Awesome examples! You hear rates all the time. Speed is miles per hour, prices are dollars per pound, typing speed is words per minute. The key is those different units. How is that different from the ratios we just discussed?"

(Allow a moment for responses, guiding them to note that ratios can have the same or no units, while rates always have different units.)

(Display Ratio Royale Slide Deck - Slide 5: "Unit Rates: The 'Per 1' Power!")

Teacher: "Now, for the superhero of rates: the unit rate! A unit rate tells you 'how much per one' of something. It's incredibly useful for comparing things fairly. To find a unit rate, you simply divide the first quantity by the second quantity. Let's look at an example: if you drive 120 miles in 2 hours, what's your speed per hour? We'll solve this together in our guided practice!"

Guided Practice: Rate Reality (10 minutes)

(Display Ratio Royale Slide Deck - Slide 6: "Guided Practice: Pizza Price Patrol!")

Teacher: "Time to be smart shoppers! Imagine you're at the store, and you see two pizza deals. Pizza A is $15 for 3 slices, and Pizza B is $20 for 4 slices. Which one is the better deal? To figure this out, we need to find the unit price – that's the price per one slice. Who wants to try calculating the unit price for Pizza A?"

Student: "$15 divided by 3 slices is $5 per slice!"

Teacher: "Fantastic! So Pizza A is $5 per slice. Now, how about Pizza B?"

Student: "$20 divided by 4 slices is $5 per slice!"

Teacher: "Excellent! In this case, both pizzas are the same unit price. What if Pizza B was $24 for 4 slices? Which would be the better deal then?"

Student: "Pizza A, because $24 divided by 4 is $6 per slice."

Teacher: "Great thinking! You can see how unit rates help us make smart choices."

(Display Ratio Royale Slide Deck - Slide 7: "Guided Practice: Typing Test Triumph!")

Teacher: "Let's try another one. Sarah typed 300 words in 5 minutes. We want to know her typing speed in words per minute. How would we set up this rate?"

Student: "300 words / 5 minutes."

Teacher: "Perfect! Now, to find the unit rate, what calculation do we need to do?"

Student: "Divide 300 by 5!"

Teacher: "And what do we get?"

Student: "60 words per minute!"

Teacher: "That's right! Sarah types 60 words per minute. That's pretty fast!"

Independent Practice: Worksheet Workout (5 minutes)

(Display Ratio Royale Slide Deck - Slide 8: "Quick Check!")

Teacher: "Alright, for a quick check, can someone tell me: what's the main difference between a ratio and a rate?"

Student: "A ratio compares two quantities, and a rate compares two quantities with different units."

Teacher: "Exactly! And why are unit rates so helpful in real life?"

Student: "They help us compare things, like prices, to find the best deal!"

Teacher: "You've got it! Now, it's your turn to practice. I'm handing out the Ratio Practice Worksheet. You'll have about 5 minutes to get started on it in class, and anything you don't finish will be homework. I'll be walking around to help if you have any questions."

(Distribute worksheets and circulate, providing support.)

Teacher: "Excellent work today, everyone! Keep practicing those ratios and rates, and you'll be math royalty in no time!"

Ratio Warm-Up: Comparing Quantities!

Instructions: Read each question carefully and write your answer in the space provided. Try your best!

1. In a fruit bowl, there are 3 apples and 5 oranges.
   What is the ratio of apples to oranges?
   
   
   

2. A class has 12 girls and 8 boys.
   What is the ratio of boys to girls?
   
   
   

3. You read 60 pages in 2 hours.
   How many pages did you read per hour?
   
   
   

4. A car travels 150 miles on 5 gallons of gas.
   How many miles does the car travel per gallon?
   
   
   

Ratio Practice Worksheet

Instructions: Read each problem carefully and show your work. Write your answers in the space provided.

Part 1: Ratios

1. In a classroom, there are 18 students and 3 computers. What is the ratio of students to computers? Write your answer in three different ways and simplify if possible.
   
   
   
   
   
   
   

2. A recipe calls for 2 cups of flour and 3 eggs. What is the ratio of flour to eggs?
   
   
   
   

3. Simplify the following ratios:
   a) 20:5
   
   
   
   b) 9 to 27
   
   
   
   c) 14/7
   
   
   

Part 2: Rates and Unit Rates

4. A cyclist travels 100 miles in 4 hours. What is the cyclist's average speed in miles per hour?
   
   
   
   
   
   
   

5. You bought 6 bags of chips for $12. What is the unit price of one bag of chips?
   
   
   
   
   
   
   

6. A printer can print 45 pages in 3 minutes. How many pages can it print per minute?
   
   
   
   
   
   
   

7. Store A sells 10 apples for $5.00. Store B sells 12 apples for $7.20. Which store offers a better deal per apple?
   
   
   
   
   
   
   
   
   
   
   
   
   

8. A factory produces 500 toys in 10 hours. How many toys does it produce per hour?
   
   
   
   
   
   
   

Ratio Practice Answer Key

Ratio Warm-Up: Comparing Quantities!

1. In a fruit bowl, there are 3 apples and 5 oranges. What is the ratio of apples to oranges?

• Thought Process: A ratio compares two quantities. We are comparing apples to oranges, so we put the number of apples first and oranges second.
• Answer: 3:5 or 3 to 5 or 3/5

2. A class has 12 girls and 8 boys. What is the ratio of boys to girls?

• Thought Process: We need to be careful with the order here! The question asks for the ratio of boys to girls.
• Answer: 8:12 or 8 to 12 or 8/12 (can be simplified to 2:3)

3. You read 60 pages in 2 hours. How many pages did you read per hour?

• Thought Process: This is asking for a unit rate (pages per one hour). To find it, divide the total pages by the total hours.
• Answer: 60 pages / 2 hours = 30 pages per hour

4. A car travels 150 miles on 5 gallons of gas. How many miles does the car travel per gallon?

• Thought Process: This is also a unit rate (miles per one gallon). Divide the total miles by the total gallons.
• Answer: 150 miles / 5 gallons = 30 miles per gallon

Ratio Practice Worksheet

Part 1: Ratios

1. In a classroom, there are 18 students and 3 computers. What is the ratio of students to computers? Write your answer in three different ways and simplify if possible.

• Thought Process: Compare students to computers (18 to 3). Then, find the greatest common factor (GCF) to simplify the ratio. The GCF of 18 and 3 is 3.
• Answer:
  • 18:3 (simplified to 6:1)
  • 18 to 3 (simplified to 6 to 1)
  • 18/3 (simplified to 6/1 or 6)

2. A recipe calls for 2 cups of flour and 3 eggs. What is the ratio of flour to eggs?

• Thought Process: The order is flour to eggs.
• Answer: 2:3 or 2 to 3 or 2/3

3. Simplify the following ratios:

• a) 20:5
  • Thought Process: Divide both numbers by their GCF, which is 5.
  • Answer: 4:1
• b) 9 to 27
  • Thought Process: Divide both numbers by their GCF, which is 9.
  • Answer: 1 to 3
• c) 14/7
  • Thought Process: Divide both numbers by their GCF, which is 7.
  • Answer: 2/1 or 2

Part 2: Rates and Unit Rates

4. A cyclist travels 100 miles in 4 hours. What is the cyclist's average speed in miles per hour?

• Thought Process: This is a unit rate problem. Divide miles by hours.
• Answer: 100 miles / 4 hours = 25 miles per hour

5. You bought 6 bags of chips for $12. What is the unit price of one bag of chips?

• Thought Process: Find the price per single bag. Divide total cost by number of bags.
• Answer: $12 / 6 bags = $2 per bag

6. A printer can print 45 pages in 3 minutes. How many pages can it print per minute?

• Thought Process: Find the pages printed per single minute. Divide total pages by total minutes.
• Answer: 45 pages / 3 minutes = 15 pages per minute

7. Store A sells 10 apples for $5.00. Store B sells 12 apples for $7.20. Which store offers a better deal per apple?

• Thought Process: Calculate the unit price (price per apple) for each store and compare.
  • Store A: $5.00 / 10 apples = $0.50 per apple
  • Store B: $7.20 / 12 apples = $0.60 per apple
• Answer: Store A ($0.50 per apple) offers a better deal than Store B ($0.60 per apple).

8. A factory produces 500 toys in 10 hours. How many toys does it produce per hour?

• Thought Process: Find the number of toys produced per single hour. Divide total toys by total hours.
• Answer: 500 toys / 10 hours = 50 toys per hour