Teacher Script: Ratios: Your Life's Recipe?

Warm Up: What's Your Ratio? (5 minutes)

"Good morning, everyone! Today, we're diving into a really cool math topic that helps us understand the world around us. To get us started, I want you to think about some comparisons in your daily life. Take a look at these prompts:"

• Slide 1: Ratios: Your Life's Recipe?

"What does comparing ingredients, sports scores, or even your favorite snack have in common? Think about it for a moment. Then, turn to a partner and discuss: Can you think of a time you compared two things today? Maybe the number of siblings you have versus your partner, or the number of pencils to pens in your bag?"

"Alright, let's hear some of your comparisons! Who wants to share an example of how they compared two things?" (Listen to student responses and affirm their ideas, gently steering towards numerical comparisons if needed.)

Introduction to Ratios (10 minutes)

"Excellent! We actually just dipped our toes into the concept of ratios. So, what exactly is a ratio?"

• Slide 2: What's a Ratio?

"A ratio is simply a way to compare two quantities. It tells us how much of one thing there is compared to another. Think of it like a recipe for comparison!"

"There are a few ways we can write ratios. We can say 'a to b', like '3 to 5'. We can use a colon, 'a:b', so '3:5'. Or, we can write it as a fraction, 'a/b', like '3/5'. All three mean the exact same thing!"

"Let's try an example together. Imagine in our class, there are 15 girls and 10 boys. What is the ratio of girls to boys? How would we write that using the three different ways?" (Call on students to provide answers and write them on the board: 15 to 10, 15:10, 15/10. Emphasize simplification to 3 to 2, 3:2, 3/2.)

• Slide 3: Ratio Example: Fruit Salad Fun

"Here's another one. You're making a delicious fruit salad. You use 2 apples and 6 oranges. What is the ratio of apples to oranges? Turn to your partner and work it out in all three ways." (Give students a moment to discuss.) "Okay, what did you get? (2 to 6, 2:6, 2/6, which simplifies to 1 to 3, 1:3, 1/3). Great!"

"Now, what if I asked for the ratio of oranges to apples? Is it the same? (No, it's 6 to 2, or 3 to 1). Exactly! The order matters in ratios!"

"And finally, what is the ratio of apples to total fruit? First, how many total fruits are there? (8). So the ratio of apples to total fruit is? (2 to 8, or 1 to 4). Fantastic!"

Exploring Proportions (8 minutes)

"Sometimes, we have two ratios that are equal to each other. When that happens, we call it a proportion."

• Slide 4: Proportions: Keeping it Balanced

"A proportion is an equation that says two ratios are equivalent. Think of it like balancing two scales. If one side is equal, the other side must be too."

"Why are proportions so useful? They help us in so many ways: scaling recipes up or down, converting measurements, and finding unknown values when we know a relationship. For example, if 2 apples cost $1, how much would 6 apples cost? We can use a proportion to solve this!"

"We'd set it up like this: 2 apples / $1 = 6 apples / x. To solve this, we can use something called cross-multiplication. Who remembers how to cross-multiply?" (Guide students to multiply 2 by x and 6 by 1, then solve for x. Answer: $3.)

• Slide 5: Proportion Example: Baking Cookies

"Let's try another one. A recipe calls for 3 cups of flour for every 2 eggs. If you want to use 6 eggs, how many cups of flour do you need? How would you set up this proportion?" (Write on board: 3 cups / 2 eggs = x cups / 6 eggs. Guide students to cross-multiply and solve. Answer: 9 cups of flour.)

Independent Practice: Ratio Real-World Worksheet (5 minutes)

"You've done a great job with our examples. Now it's time to put your new skills to the test! I'm handing out a Ratio Real-World Worksheet. You can work independently or with a partner. I'll be walking around to help if you have any questions."

(Distribute the worksheets and circulate, providing support. Briefly review a few answers if time allows.)

Cool Down: Ratio Reflection (2 minutes)

"Alright everyone, bring your attention back up here. To wrap up our lesson today, I want each of you to complete this quick Ratio Reflection Cool Down. Just a sentence or two to summarize what you learned or what you found most interesting about ratios and proportions today."

"Think about: What's the main idea you're taking away from today's lesson? Why are ratios and proportions helpful in real life? Please write your response on the sheet and turn it in as you leave."

• Slide 6: Quick Check!

"Thank you, everyone! Great work today. See you next time!"

What's Your Ratio? Warm Up

Instructions: Think about the questions below and be ready to share your ideas with a partner or the class.

1. Can you think of a time you compared two things today? Describe what you compared.
   
   
   

2. If you have 8 pens and 4 pencils, how would you describe the relationship between your pens and pencils?
   
   
   

3. Why do you think it might be useful to compare quantities in everyday life?
   
   
   

Ratio Real-World Worksheet

Instructions: Read each problem carefully and answer the questions. Show your work when solving proportions.

Part 1: Ratios

1. In a basket, there are 12 red apples and 18 green apples.
   a. What is the ratio of red apples to green apples? (Write in three ways and simplify)
   
   
   
   
   
   
   b. What is the ratio of green apples to total apples? (Write in three ways and simplify)
   
   
   
   
   
   

2. A class has 20 students. 12 of them are girls.
   a. What is the ratio of girls to boys in the class? (Simplify)
   
   
   
   
   
   
   b. What is the ratio of boys to total students? (Simplify)
   
   
   
   
   
   

Part 2: Proportions

3. A baker uses 3 cups of flour to make 2 dozen cookies. If she wants to make 8 dozen cookies, how many cups of flour will she need? Show your proportion and solve.
   
   
   
   
   
   
   
   
   
   
   
   

4. On a map, 1 inch represents 20 miles. If two cities are 4.5 inches apart on the map, what is the actual distance between them? Show your proportion and solve.
   
   
   
   
   
   
   
   
   
   
   
   

5. You are painting a room. You mix 2 parts blue paint with 3 parts white paint. If you use 10 quarts of blue paint, how many quarts of white paint do you need? Show your proportion and solve.
   
   
   
   
   
   
   
   
   
   
   
   

Ratio Real-World Worksheet Answer Key

Part 1: Ratios

1. In a basket, there are 12 red apples and 18 green apples.
   a. What is the ratio of red apples to green apples? (Write in three ways and simplify)
   * Thought Process: Identify the two quantities (12 red apples, 18 green apples). Write the ratio as 12 to 18, 12:18, or 12/18. Find the greatest common factor (GCF) of 12 and 18, which is 6. Divide both parts of the ratio by 6 to simplify.
   * Answer: 12 to 18, 12:18, 12/18. Simplified: 2 to 3, 2:3, 2/3.

   b. What is the ratio of green apples to total apples? (Write in three ways and simplify)
   * Thought Process: First, find the total number of apples: 12 red + 18 green = 30 total apples. The two quantities are 18 green apples and 30 total apples. Write the ratio as 18 to 30, 18:30, or 18/30. The GCF of 18 and 30 is 6. Divide both parts by 6 to simplify.
   * Answer: 18 to 30, 18:30, 18/30. Simplified: 3 to 5, 3:5, 3/5.

2. A class has 20 students. 12 of them are girls.
   a. What is the ratio of girls to boys in the class? (Simplify)
   * Thought Process: Identify the number of girls (12). Find the number of boys: 20 total students - 12 girls = 8 boys. The two quantities are 12 girls and 8 boys. Write the ratio as 12 to 8 or 12/8. The GCF of 12 and 8 is 4. Divide both by 4 to simplify.
   * Answer: 12 to 8. Simplified: 3 to 2.

   b. What is the ratio of boys to total students? (Simplify)
   * Thought Process: The two quantities are 8 boys and 20 total students. Write the ratio as 8 to 20 or 8/20. The GCF of 8 and 20 is 4. Divide both by 4 to simplify.
   * Answer: 8 to 20. Simplified: 2 to 5.

Part 2: Proportions

3. A baker uses 3 cups of flour to make 2 dozen cookies. If she wants to make 8 dozen cookies, how many cups of flour will she need? Show your proportion and solve.

   • Thought Process: Set up a proportion comparing cups of flour to dozens of cookies. Let 'x' be the unknown number of cups of flour.
     3 cups / 2 dozen = x cups / 8 dozen
     Cross-multiply: 2 * x = 3 * 8
     2x = 24
     Divide by 2: x = 12
   • Answer: She will need 12 cups of flour.

4. On a map, 1 inch represents 20 miles. If two cities are 4.5 inches apart on the map, what is the actual distance between them? Show your proportion and solve.

   • Thought Process: Set up a proportion comparing inches on the map to actual miles. Let 'x' be the unknown actual distance.
     1 inch / 20 miles = 4.5 inches / x miles
     Cross-multiply: 1 * x = 20 * 4.5
     x = 90
   • Answer: The actual distance between the cities is 90 miles.

5. You are painting a room. You mix 2 parts blue paint with 3 parts white paint. If you use 10 quarts of blue paint, how many quarts of white paint do you need? Show your proportion and solve.

   • Thought Process: Set up a proportion comparing blue paint parts to white paint parts. Let 'x' be the unknown quarts of white paint.
     2 parts blue / 3 parts white = 10 quarts blue / x quarts white
     Cross-multiply: 2 * x = 3 * 10
     2x = 30
     Divide by 2: x = 15
   • Answer: You will need 15 quarts of white paint.

Ratio Reflection Cool Down

Instructions: In 1-2 sentences, answer the questions below.

1. What is one new thing you learned or understood better about ratios or proportions today?
   
   
   

2. Can you think of one real-life situation where understanding ratios or proportions would be important?