Ratio Rally! Worksheet

Instructions: Read each question carefully and show your work where necessary. Good luck!

Part 1: Writing Ratios

1. In a classroom, there are 12 boys and 15 girls. Write the ratio of boys to girls in three different ways.
   
   
   
   
2. A fruit basket contains 5 apples, 3 oranges, and 4 bananas. Write the ratio of oranges to total fruit.
   
   
   
   

Part 2: Identifying Proportions

Determine if each pair of ratios forms a proportion. Write "Yes" or "No".

3. 1/2 and 4/8
   
   
   
   
4. 3:5 and 9:10
   
   
   
   

Part 3: Solving Proportions

Solve each proportion for the missing value.

5. 2/3 = x/9
   
   
   
   
6. If 5 pencils cost $2.50, how much do 10 pencils cost?
   
   
   
   
7. A car travels 150 miles on 5 gallons of gas. How many miles can it travel on 8 gallons of gas?
   
   
   
   

Ratio Rally! Worksheet Answer Key

Part 1: Writing Ratios

1. In a classroom, there are 12 boys and 15 girls. Write the ratio of boys to girls in three different ways.
   • Thought Process: The question asks for the ratio of boys to girls. There are 12 boys and 15 girls. We can write this directly.
   • Answer: 12:15, 12 to 15, 12/15 (or simplified: 4:5, 4 to 5, 4/5)
     
     
     
     
2. A fruit basket contains 5 apples, 3 oranges, and 4 bananas. Write the ratio of oranges to total fruit.
   • Thought Process: First, find the total number of fruits: 5 + 3 + 4 = 12. Then, identify the number of oranges, which is 3. The ratio of oranges to total fruit is 3 to 12.
   • Answer: 3:12, 3 to 12, 3/12 (or simplified: 1:4, 1 to 4, 1/4)
     
     
     
     

Part 2: Identifying Proportions

Determine if each pair of ratios forms a proportion. Write "Yes" or "No".

3. 1/2 and 4/8
   • Thought Process: To check if two ratios form a proportion, we can cross-multiply or simplify both ratios. If 1/2 = 4/8, then 18 = 24, which is 8 = 8. Alternatively, 4/8 simplifies to 1/2.
   • Answer: Yes
     
     
     
     
4. 3:5 and 9:10
   • Thought Process: To check if 3/5 = 9/10, we can cross-multiply: 310 = 59. This means 30 = 45, which is false. Therefore, they do not form a proportion.
   • Answer: No
     
     
     
     

Part 3: Solving Proportions

Solve each proportion for the missing value.

5. 2/3 = x/9
   • Thought Process: We can see that 3 multiplied by 3 gives 9. So, we multiply 2 by 3 to find x. 2 * 3 = 6. Alternatively, cross-multiply: 29 = 3x -> 18 = 3x -> x = 6.
   • Answer: x = 6
     
     
     
     
6. If 5 pencils cost $2.50, how much do 10 pencils cost?
   • Thought Process: Set up a proportion: 5 pencils / $2.50 = 10 pencils / x. We can see that 5 multiplied by 2 gives 10. So, we multiply $2.50 by 2 to find x. $2.50 * 2 = $5.00.
   • Answer: $5.00
     
     
     
     
7. A car travels 150 miles on 5 gallons of gas. How many miles can it travel on 8 gallons of gas?
   • Thought Process: Set up a proportion: 150 miles / 5 gallons = x miles / 8 gallons. First, find the miles per gallon: 150/5 = 30 miles per gallon. Then, multiply by 8 gallons: 30 * 8 = 240 miles. Alternatively, cross-multiply: 1508 = 5x -> 1200 = 5x -> x = 240.
   • Answer: 240 miles
     
     
     
     

Ratio Rally! Script

Warm-Up: What's the Connection? (5 minutes)

(Teacher says): "Good morning, mathematicians! Today, we're going to talk about how things relate to each other. Has anyone ever noticed how we compare things in our everyday lives? Maybe you've seen something like 'for every 1 teacher, there are 25 students' or 'my recipe uses 2 cups of flour for every 1 cup of sugar.' What are some other comparisons you've heard or made?"

(Teacher says): "Great examples! Those comparisons are actually a big part of what we'll be exploring today. We're going to dive into the world of ratios and proportions! Please take a look at our first slide in the Ratio Rally! Slide Deck titled 'Ratio Rally!'"

Introducing Ratios and Proportions (10 minutes)

(Teacher says): "Alright, let's start with ratios. Look at the slide titled 'What is a Ratio?'. A ratio is simply a way to compare two quantities. For example, if I have 2 blue pens and 3 red pens, the ratio of blue pens to red pens is 2 to 3. There are a few ways we can write ratios. Can you see them on the slide?"

(Teacher says): "That's right! We can use a colon, the word 'to', or write it as a fraction. Now, where do we see ratios in real life? Turn to the slide 'Ratios in Real Life'. Who can tell me one place they see ratios mentioned or used?"

(Teacher says): "Excellent! Ratios are everywhere! From baking a cake to understanding a map. Now, let's move on to something related: proportions. Look at the slide titled 'What is a Proportion?'. A proportion happens when two ratios are equal. Think about it like this: if one apple costs 50 cents, and two apples cost one dollar, those two situations form a proportion because the ratio of apples to cost is the same. The slide shows an example."

(Teacher says): "Sometimes we need to find a missing part of a proportion. Let's look at the slide 'Solving Proportions'. If 3 pencils cost $1, how much do 9 pencils cost? How would you set up that comparison?"

(Teacher says): "That's a great start! We can set it up as 3 pencils / $1 = 9 pencils / x dollars. We can see that 3 multiplied by 3 gives 9, so what do you think we should do with the $1?"

(Teacher says): "Exactly! If we multiply $1 by 3, we get $3. So 9 pencils would cost $3. Good job!"

Practice Makes Perfect (10 minutes)

(Teacher says): "Now it's your turn to put what we've learned into practice! I'm going to hand out the Ratio Rally! Worksheet. We'll do the first problem or two together as a class, and then you'll work independently or with a partner on the rest. Don't worry, I'll be walking around to help!"

(Distribute Ratio Rally! Worksheet. Guide students through the first two problems, then allow them to work. Circulate and assist as needed. Refer to the Ratio Rally! Worksheet Answer Key for guidance.)

Wrap-Up: Ratio Review (5 minutes)

(Teacher says): "Alright everyone, let's bring it back together. We're going to quickly review a couple of problems from the worksheet. Can someone share their answer and thought process for problem #5, 'Solve 2/3 = x/9'?"

(Teacher says): "Fantastic! Before we finish, I want everyone to think about one new thing they learned today about ratios or proportions. No need to share out loud, just think about it for a moment."

(Teacher says): "To recap, today we learned what ratios are and how to write them, how they appear in our daily lives, and what proportions are and how to solve them. You've done a wonderful job understanding these important math concepts! Let's remember that ratios and proportions help us understand how quantities relate, and that's a super useful skill!"