Mastering Fractions

Curriculum Area and Level

US Common Core State Standards, Grade 7

• CCSS.MATH.CONTENT.7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
• CCSS.MATH.CONTENT.7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

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Lesson Objectives

By the end of this 45-minute session, students will:

1. Review the concept of fractions, including numerators and denominators.
2. Perform addition, subtraction, multiplication, and division of fractions.
3. Solve real-world problems involving fractions.
4. Build confidence manipulating fractions by working in collaborative teams.

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Materials Needed

1. Whiteboard and markers.
2. Printed activity sheets with fraction problems.
3. Fraction strips or manipulatives for conceptual demonstrations.
4. Timer or stopwatch.
5. A container with pre-written real-life fraction scenarios (for group activity).

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Lesson Timeline

1. Warm-Up (5 minutes)

Objective: Activate prior knowledge of fractions.

1. Project the following question on the whiteboard:
   "What do fractions represent? Explain in 1-2 sentences."
2. Give students 1 minute to jot down answers in their math journals.
3. Call on 2-3 students randomly to share their answers.
4. Briefly recap key points: Fractions represent parts of a whole, numerators (top) are the number of parts, and denominators (bottom) represent total parts of the whole.

Challenge Hook:
Write the following problem on the board and leave it unanswered:
"If you eat 2/5 of a pizza and your friend eats 1/2 of the same pizza, how much of the pizza is left?"

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2. Concept Exploration (10 minutes)

Objective: Teach how to perform operations with fractions.

Addition and Subtraction of Fractions

1. Begin by reminding students that a common denominator is needed for addition and subtraction.
2. Solve a problem on the whiteboard:
   • 1/4 + 2/3 = ?
   • Demonstrate finding the common denominator (12).
   • Convert fractions: 3/12 + 8/12 = 11/12.

Multiplication of Fractions
3. Introduce multiplying fractions: Multiply numerators and denominators directly.

• Solve: 2/5 × 3/4 = 6/20 = 3/10.

Division of Fractions
4. Introduce the concept of keep-change-flip for division.

• Solve: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Throughout these examples, ask guiding questions to keep students engaged:

• "Why do we need common denominators for addition but not for multiplication?"
• "What happens if the numerator is larger than the denominator?"

Quick Check
Have students solve independently:

• 1/6 + 1/4
• 3/5 × 7/8
• 2/3 ÷ 5/6

Call on 2 students to explain their solutions.

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3. Collaborative Activity: Real-Life Fractions (15 minutes)

Objective: Apply learned fraction skills to solve real-world problems.

1. Divide students into 8 groups of 4 (adjust as necessary).

2. Give each group one “real-life fraction scenario” card from the prepared container. Examples:

   • "You’re baking cookies. The recipe needs 3/4 cup of sugar, but you accidentally poured 1/2 cup. How much more do you need?"
   • "You run 2/5 of a mile in the morning and 3/10 in the evening. How far did you run in total?"
   • "You share 3/8 of a pizza with 2 friends equally. How much does each friend get?"

3. Encourage groups to work together to solve their assigned problem using fraction operations.

4. Each team writes their solution on a mini whiteboard.

5. Groups present their solutions briefly, explaining their reasoning.

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4. Independent Practice (8 minutes)

Objective: Solidify understanding with individual work.

1. Hand out a quick worksheet with 5 fraction problems (1 addition, 1 subtraction, 1 multiplication, 1 division, and 1 mixed). Example:

   • 5/8 − 1/4
   • 7/12 ÷ 2/3
   • 3/4 × 4/5
   • 2/3 + 5/6
   • Your sibling eats 1/3 of a cake, and you eat 1/4. How much did you eat together?

2. Students work individually. Walk around to assist as needed.

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5. Closing Reflection and Challenge Question (7 minutes)

Objective: Reinforce learning and ensure conceptual clarity.

1. Revisit the hook problem from the warm-up:
   "If you eat 2/5 of a pizza and your friend eats 1/2, how much of the pizza is left?"

   • Solve as a class with student input.

2. Ask reflection questions:

   • "What was the most challenging part of working with fractions today?"
   • "Where do we use fractions in everyday life?"

3. Share a quick “Fraction Fun Fact” to end on a light note:

   • Did you know? The word 'fraction' comes from the Latin word 'fractio,' meaning to break!

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Assessment and Homework

1. In-Class: Evaluate group presentations and independent worksheet performance.
2. Homework: Create 3 real-life word problems involving fractions and solve them.

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Differentiation Strategies

• For advanced learners: Assign more complex, multi-step fraction problems or introduce improper fractions and mixed numbers.
• For struggling learners: Pair them with peers for support, provide fraction strips/manipulatives, or reduce problem complexity (e.g., simplified denominators).

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Teacher Reflection

Ensure to note:

• Which part students found most engaging?
• Were collaborative activities effective in promoting understanding?
• Were any misconceptions about fractions revealed that need revisiting?