Ratio Rescue Warm-Up

Instructions: Answer the following questions to get your brain ready for our Ratio Rescue Mission!

1. In a basket, there are 3 red apples and 5 green apples. What is the ratio of red apples to green apples?
   
   
   
   

2. If a car travels 100 miles in 2 hours, how many miles does it travel in 1 hour? (This is a rate!)
   
   
   
   

3. Circle the statement that represents a ratio:
   a) Eating 2 slices of pizza.
   b) Comparing 4 cats to 2 dogs.
   c) Running for 30 minutes.
   d) Having 10 friends.

Ratio Rescue Worksheet

Instructions: Help our Ratio Rescuers by solving the problems below. Show your work!

Part 1: Ratios and Rates

1. A class has 15 boys and 10 girls. What is the ratio of boys to girls?
   
   
   
   

2. You read 60 pages in 30 minutes. What is the rate of pages per minute?
   
   
   
   

3. Write two different ways to express the ratio of triangles to squares:

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Part 2: Unit Rates

4. A grocery store sells 4 oranges for $2.00. What is the unit price per orange?
   
   
   
   
   
   
   

5. If a cyclist travels 90 miles in 3 hours, what is their average speed in miles per hour (unit rate)?
   
   
   
   
   
   
   

6. Which is the better deal: 6 pens for $3.00 or 10 pens for $4.00? Show your work to prove it!
   
   
   
   
   
   
   
   
   
   
   
   
   

Part 3: Apply Your Knowledge!

7. You are baking cookies. The recipe calls for 2 cups of flour for every 1 cup of sugar. If you want to use 3 cups of sugar, how much flour do you need?
   
   
   
   
   
   
   

8. A car uses 5 gallons of gas to travel 150 miles. How many miles can the car travel on 1 gallon of gas?
   
   
   
   
   
   
   

Ratio Rescue Answer Key

Ratio Rescue Warm-Up Answers

1. In a basket, there are 3 red apples and 5 green apples. What is the ratio of red apples to green apples?

   • Thought Process: A ratio compares two quantities. We are comparing red apples to green apples.
   • Answer: 3 to 5 or 3:5 or 3/5

2. If a car travels 100 miles in 2 hours, how many miles does it travel in 1 hour?

   • Thought Process: To find out how many miles in 1 hour (unit rate), divide the total miles by the total hours.
   • Calculation: 100 miles / 2 hours = 50 miles/hour
   • Answer: 50 miles per hour

3. Circle the statement that represents a ratio:

   • Thought Process: A ratio compares two quantities. Option (b) explicitly compares two different items.
   • Answer: b) Comparing 4 cats to 2 dogs.

Ratio Rescue Worksheet Answers

Part 1: Ratios and Rates

1. A class has 15 boys and 10 girls. What is the ratio of boys to girls?

   • Thought Process: Compare the number of boys to the number of girls.
   • Answer: 15 to 10, or 15:10. This can be simplified to 3 to 2, or 3:2.

2. You read 60 pages in 30 minutes. What is the rate of pages per minute?

   • Thought Process: A rate compares two quantities with different units. To find the rate, divide pages by minutes.
   • Calculation: 60 pages / 30 minutes = 2 pages/minute
   • Answer: 2 pages per minute

3. Write two different ways to express the ratio of triangles to squares:

   △ △ △ □ □

   • Thought Process: Count the triangles and squares, then express the comparison.
   • Answer: 3 to 2, 3:2

Part 2: Unit Rates

4. A grocery store sells 4 oranges for $2.00. What is the unit price per orange?

   • Thought Process: To find the unit price, divide the total cost by the number of oranges.
   • Calculation: $2.00 / 4 oranges = $0.50/orange
   • Answer: $0.50 per orange

5. If a cyclist travels 90 miles in 3 hours, what is their average speed in miles per hour (unit rate)?

   • Thought Process: To find the unit rate (miles per hour), divide the total miles by the total hours.
   • Calculation: 90 miles / 3 hours = 30 miles/hour
   • Answer: 30 miles per hour

6. Which is the better deal: 6 pens for $3.00 or 10 pens for $4.00? Show your work to prove it!

   • Thought Process: Calculate the unit price for each option and compare.
   • Calculation for 6 pens: $3.00 / 6 pens = $0.50 per pen
   • Calculation for 10 pens: $4.00 / 10 pens = $0.40 per pen
   • Answer: 10 pens for $4.00 is the better deal because each pen costs $0.40, which is less than $0.50.

Part 3: Apply Your Knowledge!

7. You are baking cookies. The recipe calls for 2 cups of flour for every 1 cup of sugar. If you want to use 3 cups of sugar, how much flour do you need?

   • Thought Process: The ratio of flour to sugar is 2:1. If you multiply the sugar by 3, you must multiply the flour by 3 to maintain the ratio.
   • Calculation: 2 cups flour / 1 cup sugar = X cups flour / 3 cups sugar. X = 2 * 3 = 6 cups flour.
   • Answer: You need 6 cups of flour.

8. A car uses 5 gallons of gas to travel 150 miles. How many miles can the car travel on 1 gallon of gas?

   • Thought Process: This is a unit rate problem. Divide total miles by total gallons to find miles per gallon.
   • Calculation: 150 miles / 5 gallons = 30 miles/gallon
   • Answer: The car can travel 30 miles on 1 gallon of gas.

Ratio Rescue Cool-Down

Instructions: Please answer the following questions to help me understand how well you understood today's mission!

1. In your own words, what is a ratio?
   
   
   
   
   
   
   

2. Give one example of a unit rate you encounter in your daily life.
   
   
   
   

3. On a scale of 1 to 5, with 5 being

Ratio Rescue Script

Warm-Up: Ratio Rapid-Fire (5 minutes)

Teacher: "Good morning, future mathematicians! Today we're embarking on a very important 'Ratio Rescue Mission'! To get our brains warmed up, I've handed out a quick 'Ratio Rescue Warm-Up'. Please work independently on these three questions for about three minutes. This will help us activate what we already know about comparing things."

(Allow students 3 minutes to work. Circulate and observe.)

Teacher: "Alright, let's go over these quickly. For question 1, 'In a basket, there are 3 red apples and 5 green apples. What is the ratio of red apples to green apples?' Who can tell me their answer? Yes, [Student Name]?"

(Listen to student response, guide if necessary. Confirm 3:5, 3 to 5, or 3/5.)

Teacher: "Excellent! For question 2, 'If a car travels 100 miles in 2 hours, how many miles does it travel in 1 hour?' This is a rate! What did you get, [Student Name]?"

(Listen to student response. Confirm 50 miles per hour.)

Teacher: "Perfect! And finally, for question 3, 'Circle the statement that represents a ratio.' What did you choose, [Student Name]?"

(Listen to student response. Confirm option b: Comparing 4 cats to 2 dogs.)

Teacher: "Fantastic! You're already proving to be great Ratio Rescuers! Let's dive deeper into our mission."

Introduction to Ratios & Rates (8 minutes)

(Display Ratio Rescue Mission Slide Deck - Slide 1 - Title Slide)

Teacher: "As you can see, our mission today is to crack the code of comparison. We're going to understand ratios, rates, and unit rates. Why is this important? Because ratios and rates are everywhere! They help us cook, shop smart, understand sports statistics, and so much more. This is a fundamental skill that will help you in all your future math and even in everyday life."

(Display Ratio Rescue Mission Slide Deck - Slide 2 - What's a Ratio Anyway?)

Teacher: "So, what exactly is a ratio? A ratio is simply a way to compare two or more quantities. Think of it like a recipe. If a recipe says 'for every 1 cup of rice, you need 2 cups of water,' that's a ratio! We can write it as 1 to 2, 1:2, or even as a fraction, 1/2."

Teacher: "Can anyone think of a ratio they see or hear about in their everyday life? Maybe in sports, or even right here in our classroom? Don't be shy, there are no wrong answers!"

(Allow 1-2 minutes for student responses. Guide with examples if needed, e.g., 'What about the ratio of boys to girls in our class?')

(Display Ratio Rescue Mission Slide Deck - Slide 3 - Ratios Get Real: Welcome to Rates!)

Teacher: "Now, sometimes ratios get a little more specific. A rate is a special kind of ratio that compares two quantities with different units. For example, 'miles per hour' compares distance (miles) with time (hours). Or 'dollars per pound' compares money with weight. What's another common rate you might have heard of? Think about typing or driving!"

(Encourage responses like 'words per minute' or 'price per gallon'. Discuss how the units are different.)

Teacher: "So, how is a rate different from the simple '1 to 2' ratio of rice to water? The key is those different units! In our rice example, both 'cups' are units of volume. But with 'miles per hour,' miles are distance and hours are time. Does that distinction make sense? Give me a thumbs up if you're with me, thumbs down if you're a bit confused, or thumbs sideways if you're not sure yet."

(Gauge understanding and address any thumbs-down/sideways with further explanation or rephrasing.)

Unit Rate Exploration (7 minutes)

(Display Ratio Rescue Mission Slide Deck - Slide 4 - The Power of One: Unit Rates!)

Teacher: "Alright, let's talk about the 'Power of One' – unit rates! A unit rate tells us how much of something there is per one unit of another quantity. This is super useful for comparing things and finding the 'best deal.'"

Teacher: "To find a unit rate, it's actually quite simple: You set up your ratio as a fraction, and then you divide the first quantity by the second quantity."

Teacher: "Let's look at an example on the slide: 'If you drive 120 miles in 2 hours, what's your unit rate?' How would we set this up as a fraction? [Student Name]?"

(Guide student to 120 miles / 2 hours.)

Teacher: "And if we divide 120 by 2, what do we get? [Student Name]?"

(Guide student to 60.)

Teacher: "So, our unit rate is 60 miles per hour! This means for every 1 hour, you travel 60 miles."

Teacher: "Now, for some guided practice: 'If a store sells 3 apples for $1.50, what's the unit price per apple?' I want you to try this on your own or with a partner for about a minute. Think about what goes on top and what goes on the bottom of your fraction, and then divide."

(Allow 1 minute for students to work.)

Teacher: "Okay, who can share their unit price per apple? [Student Name]? How did you figure it out?"

(Listen to student explanation. Guide them to divide $1.50 by 3 apples to get $0.50 per apple. Reinforce the 'per one' concept.)

Teacher: "Fantastic! You're getting the hang of finding those powerful unit rates!

Worksheet Practice: Ratio Rescue (7 minutes)

(Display Ratio Rescue Mission Slide Deck - Slide 5 - Time to Practice: Ratio Rescue Worksheet!)

Teacher: "Now it's time for you to truly become Ratio Rescuers! I'm handing out the Ratio Rescue Worksheet. Your mission, should you choose to accept it, is to work through these problems independently. Remember to show your work clearly. If you get stuck, don't panic! Look back at our slides, use your notes, or quietly raise your hand and I'll come over to help. You have about 7 minutes for this."

(Distribute worksheets. Circulate around the room, providing individual support, answering questions, and checking on progress. Remind students to show their work.)

Cool-Down: Rate Your Understanding (3 minutes)

(Display Ratio Rescue Mission Slide Deck - Slide 6 - Mission Accomplished? Cool-Down Time!)

Teacher: "Alright, Ratio Rescuers, let's bring it back together. For the last few minutes of class, I'm handing out a Ratio Rescue Cool-Down. This is a quick exit ticket to help you reflect on what you've learned and to help me understand what we might need to review or practice more next time."

Teacher: "Please complete this cool-down independently and turn it in as you leave. Thank you for being such attentive and engaged Ratio Rescuers today! You did a great job!"

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