Exploring Ratios

Grade: 7th

Duration: 45 minutes

Curriculum Alignment:

This lesson is aligned with CCSS.MATH.CONTENT.7.RP.A.1: "Analyze proportional relationships and use them to solve real-world and mathematical problems." Students will compute unit rates associated with ratios of fractions and interpret ratios in real-life contexts.

---

Learning Objectives

By the end of the lesson, students will:

1. Understand the meaning of ratios and their representations (e.g., 3:2, 3/2, and "3 to 2").
2. Identify and calculate equivalent ratios.
3. Apply ratios to solve real-world problems, such as recipes and scaling.

---

Materials Needed

1. Whiteboard, markers
2. Chart paper
3. A set of measuring cups and cooking ingredients (e.g., rice, flour, colored water)
4. Bag of colored candies (e.g., Skittles or M&Ms)
5. Pre-printed worksheets with ratio problems
6. Calculators (optional but available)

---

Lesson Outline

1. Warm-Up Activity (5 minutes)

Objective: Activate prior knowledge and engage students

1. Write the following on the whiteboard:
   • "In a group of students, 3 are wearing glasses and 6 are not. What is the ratio of students with glasses to students without glasses? How else can this ratio be written?"
2. Prompt students to discuss in pairs and share their answers.
3. Review the concept of ratios, ensuring students understand that it’s a way to compare two quantities.

Quick Question:
Change the numbers: What would the ratio be if 4 students wear glasses and 8 don't?

---

2. Direct Instruction (10 minutes)

Objective: Teach the fundamentals of ratios

1. Definition and Representation

   • Explain that ratios can compare part to part (e.g., 3 boys: 5 girls) or part to whole (e.g., 3 boys out of 8 students).
   • Highlight how ratios can be written in three ways: "a to b," "a:b," and as a fraction (a/b).

2. Equivalent Ratios

   • Write this example on the board: "If the ratio of apples to oranges is 2:3, then doubling would give 4:6. Halving would give 1:1.5."
   • Demonstrate with visual aids (e.g., pictures of apples and oranges).

3. Unit Rate

   • Explain unit rates as ratios with a denominator of 1, relevant to real-world problems (e.g., cost per mile or price per ounce).

---

3. Interactive Activity (15 minutes)

Objective: Explore ratios through hands-on learning

Activity #1: Candy Color Ratios (8 minutes)

1. Give each group of 4-5 students a small pack of colored candies.

2. Ask students to:

   • Count the number of each candy color and record their results.
   • Write ratios for different color combinations (e.g., red to green, blue to total candies).
   • Simplify ratios to their simplest forms.

3. Groups will take turns sharing a color ratio they discovered.

Activity #2: Cooking Ratios (7 minutes)

1. Using measuring cups and mock ingredients (e.g., colored water, rice, flour), students will recreate a simple recipe:
   • Example: Lemonade ratio is 1 part lemon juice: 3 parts water.
   • Ask: “If you have 4 cups of lemon juice, how much water would you need?”
2. Students can physically measure out ingredients to see the scaling concept in action.
3. Discuss: What happens if we change the ratio? (e.g., stronger lemonade if more lemon juice is added).

---

4. Guided Practice Discussion (8 minutes)

Objective: Connect ratios to real-world scenarios and build critical thinking.

1. Write 3 real-life ratio problems on the board:

   • A car travels 300 miles in 5 hours. What is the ratio of miles to hours?
   • A fruit basket has 6 apples, 10 bananas, and 4 oranges. What is the ratio of bananas to total fruits?
   • If 2 out of every 5 students prefer pizza, how many would prefer pizza out of 25 students?

2. Students will work on these problems individually for 5 minutes, then discuss answers as a class.

---

5. Cool Down (5 minutes)

Objective: Reflect and summarize learning

1. Pose the closing question:
   • “Can you think of another example of ratios in your daily life? How would you write it?”
2. Students will write their examples on sticky notes and place them on the board.
3. Quickly read out a few examples, encouraging creative or unique answers (e.g., sibling comparisons, sports wins, etc.).

---

Homework

Assigned Worksheet:

• Problems involving reading and interpreting ratios (e.g., word problems, finding missing values in equivalent ratios).
• Bonus challenge: Write a short paragraph about when you’ve used ratios in real life.

---

Assessment Methods

1. Informal Observation: Check for active participation during activities and class discussions.
2. Worksheets: Review students' answers and check their understanding of ratios and applications in different formats (written ratios, simplified forms, etc.).
3. Exit Slip (Optional):
   • At the end of the class, collect student examples of real-life ratios to gauge their grasp of conceptual applications.

---

Differentiation Strategies

1. For Advanced Learners:

   • Provide challenging ratio problems involving fractions or decimals.
   • Ask them to design their own ratio-based word problems.

2. For Struggling Learners:

   • Offer visual aids and manipulatives (e.g., drawings, physical counters).
   • Pair with a peer mentor for group activities.

3. For ELL Students:

   • Use visuals and clear, simplified language when defining concepts.
   • Check for understanding by asking them to explain a concept using their own words.

---

Teacher’s Notes

• Ensure every student handles the physical materials during hands-on activities to maintain engagement.
• Use positive reinforcement to encourage participation and highlight creative real-world applications.
• Keep transitions between activities quick and organized; designate materials managers to save time.