Exploring Unit Rate

Grade Level

7th Grade

Duration

60 minutes

Class Size

25 students

---

Common Core State Standards (CCSS) Alignment

CCSS.MATH.CONTENT.7.RP.A.2
Recognize and represent proportional relationships between quantities.

• Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
• Identify the unit rate (e.g., miles per hour, price per pound) associated with a ratio, including ratios of fractions, and use rate language in the context of a ratio relationship.
• Solve real-world and mathematical problems involving unit rates, including those involving unit pricing and constant speed.

---

Learning Objectives

By the end of this lesson, students will be able to:

1. Define and explain the concept of a unit rate.
2. Calculate unit rates from various real-life scenarios including whole numbers and fractional values.
3. Represent unit rates as ratios and decimals, using rate language effectively.
4. Solve problems involving unit rates, including word problems involving proportional relationships.
5. Demonstrate understanding through collaborative and individual activities.

---

Materials

• Whiteboard and markers
• Student notebooks or math journals
• Calculators (optional)
• Large chart paper or posters for group work
• Pre-prepared real-world problem task cards
• Exit tickets

---

Lesson Structure

1. Warm-Up & Introduction (10 minutes)

Activity: Ratio Quick Review and Naming

• Write on the board two ratios, e.g., 6 miles in 2 hours and 8 lbs for $24.
• Ask students to express each ratio in simplest form and discuss what these ratios tell us.
• Briefly recap what a ratio is and transition into unit rate by introducing the term “per one” (per 1 unit).
• Explain that a unit rate compares two quantities where the second quantity is one unit (e.g., miles per hour, dollars per pound).

Teacher Talking Points:

• "We use unit rates to compare quantities where one part of the ratio is exactly one. It helps us understand how much one thing corresponds to another."
• Emphasize rate language: “miles per hour” not “miles for hours.”

---

2. Direct Instruction (15 minutes)

Concept Exploration and Modeling

• Model calculating unit rates from example scenarios on the board:
  • Example 1: 90 miles in 3 hours → miles per 1 hour
    Calculation: 90 ÷ 3 = 30 miles per hour
  • Example 2: 15 cans for $5 → cost per 1 can
    Calculation: 5 ÷ 15 = $0.33 per can
• Show how to represent unit rates as fractions and decimals.
• Use a visual table or double number line to visualize the concept.

Strategies:

• Use think-alouds to explain steps and thought processes clearly.
• Highlight the importance of label units in answers.

---

3. Guided Practice (15 minutes)

Collaborative Problem Solving - Real World Task Cards

• Divide class into 5 groups of 5 students. Give each group a set of 3-4 task cards with real-world unit rate problems. Example problems:
  1. A car travels 150 miles in 5 hours. Find the speed in miles per hour.
  2. A recipe calls for 3 cups of sugar for every 4 cups of flour. What is the sugar per 1 cup of flour?
  3. A store sells 12 apples for $9. What is the cost per apple?
• Each group solves problems collaboratively on chart paper and writes complete sentences including units.
• Circulate among groups to prompt critical thinking and correct misconceptions.

---

4. Independent Practice (10 minutes)

Student Notebook or Math Journal

• Provide 3 individual problems with increasing difficulty:
  1. Calculate the unit rate of 24 miles in 4 hours.
  2. If 5 pounds of candy cost $7.50, find the price per pound.
  3. A cyclist covers 2/3 of a mile in 1/6 of an hour. What is the speed in miles per hour?
• Students write their calculations and explain answers using appropriate rate language.

---

5. Assessment & Closure (10 minutes)

Exit Ticket

• Distribute a short exit ticket with 2 questions:
  1. Define unit rate in your own words.
  2. A printer uses 18 sheets of paper for 3 minutes. What is the number of sheets used per minute? Show your work.

Wrap-Up Discussion

• Quickly review answers and clarify any mistakes or misunderstandings.
• Reinforce usefulness of unit rates in everyday decision-making.

---

Differentiation Strategies

• For students needing extra support:
  Use visual aids like number lines, manipulatives, and additional modeling with step-by-step guidance.
• For advanced learners:
  Introduce unit rates involving fractions and decimals in more complex real-world scenarios, including comparisons of multiple unit rates to determine best buy or fastest speed.

---

Reflection for Teachers

• Assess engagement during group work and ability to articulate unit rates.
• Use exit tickets to identify students needing further individualized reinforcement.
• Consider incorporating technology next time (graphing calculators or apps) for visualizing proportional relationships.

---

Extensions / Home Connection

• Encourage students to find at least two examples of unit rates at home (e.g., price per item, speed from a family trip), and bring this data for next class to discuss and analyze.

---

End of plan. This approach encourages conceptual understanding, collaboration, and practical application—all aligned with CCSS and appropriate for 7th graders mastering unit rates.