Fractions and Mixed Numbers

Grade: 6

Duration: 30 minutes

Class Size: 13 students

Unit: Mastering Numbers & Ratios

Lesson: 7 of 30

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Learning Objectives

Students will be able to:

• I can define what a fraction is and understand its components (numerator and denominator).
• I can identify and represent mixed numbers and explain how they differ from improper fractions.
• I can visualize fractions and mixed numbers using models and diagrams.

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Common Core State Standards Alignment

• CCSS.MATH.CONTENT.6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. (Introductory understanding level—prepares for future operations).
• CCSS.MATH.CONTENT.4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n×a)/(n×b) by using visual fraction models (review to build foundation in 6th grade).
• CCSS.MATH.CONTENT.4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Foundational for understanding mixed numbers.)
• CCSS.MATH.PRACTICE.MP4: Model with mathematics - Use visual models to represent and solve problems related to fractions and mixed numbers.

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Success Criteria

• I can explain the parts of a fraction using the correct vocabulary.
• I can identify whether a number is a proper fraction, improper fraction, or a mixed number.
• I can draw and label visual fraction models for fractions and mixed numbers that show the whole and parts clearly.

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Materials Needed

• Whiteboard and markers
• Fraction strips or fraction circles (physical manipulatives)
• Printed mixed number visual cards (with images of pizzas, bars, or other relatable models)
• Student math notebooks
• Dyslexia-friendly printed handout summarizing definitions and visuals (with clear fonts and spacing)
• Colored pencils or markers for visual work

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Lesson Breakdown

1. Introduction and Engagement (5 minutes)

• Start with a question: "Have you ever shared a pizza or a candy bar? How do you describe the pieces you shared?"
• Write students' responses emphasizing the language of parts (pieces), whole, and sharing.
• Introduce the fraction as parts of a whole using a visual pizza model on the board.
• I can introduce fractions by defining numerator and denominator clearly.

2. Direct Instruction: Fractions and Mixed Numbers (8 minutes)

• Define a fraction: numerator (top number) shows how many parts we have, denominator (bottom number) shows how many equal parts the whole is divided into.
• Use visual fraction strips or circles to illustrate examples of proper fractions (like 3/4) and improper fractions (like 7/4).
• Introduce mixed numbers: explain that mixed numbers combine a whole number and a fraction (e.g., 1 3/4). Show visual comparisons between improper fractions and mixed numbers (e.g., 7/4 = 1 3/4).
• Display labeled diagrams for further clarity, pointing to numerators, denominators, whole parts in mixed numbers.
• Use clear, dyslexia-friendly fonts and spacing on all visuals.

3. Guided Practice: Visual Representation (10 minutes)

• Distribute fraction strips or circles and printed visual cards to each student.
• Ask students to model and color:
  • Proper fractions (e.g., 2/5)
  • Improper fractions (e.g., 9/5)
  • Mixed numbers (e.g., 1 4/5)
• Partner students to explain to each other what their visual models represent using “I can” sentences, e.g., “I can show 1 4/5 as one whole and four-fifths.”
• Circulate and provide scaffolding or challenge questions.

4. Assessment and Reflection (5 minutes)

• Quick exit ticket with three questions:
  1. What is the numerator in the fraction 5/8?
  2. Is 7/3 a proper fraction, improper fraction, or mixed number?
  3. Draw a diagram for 1 1/2 and label the parts.
• Collect and quickly review to gauge understanding.

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Differentiation Strategies

• For struggling learners and students with dyslexia:

  • Use dyslexia-friendly fonts (like OpenDyslexic or Arial), high-contrast printed handouts.
  • Provide fraction strips/circles manipulative for tactile learning.
  • Provide sentence stems (“I can show…,” “The numerator is…”) to guide expression.
  • Allow extra time and one-on-one assistance during guided practice.

• For advanced learners:

  • Challenge students to convert improper fractions to mixed numbers and vice versa with multiple examples.
  • Introduce adding and subtracting simple mixed numbers visually (preview for future lessons).
  • Have advanced students create their own word problems involving mixed numbers and fractions to share with the class.

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Extension Activity (For Early Finishers or Advanced Students)

• Have students use fraction strips or draw diagrams to compare fractions and mixed numbers using inequality symbols (>, <, =).
• Example prompt: "Which is greater: 1 1/3 or 4/3? Explain with visuals."

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Notes for the Teacher

• Maintain steady, age-appropriate pacing to cover all activities within 30 minutes.
• Emphasize using visual models consistently as a foundation for understanding in upcoming lessons.
• Use positive reinforcement when students accurately use vocabulary and create models.
• Encourage clear oral explanation using “I can” statements, building mathematical communication skills.

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Thank you for using this lesson plan to engage your 6th graders in the exciting world of fractions and mixed numbers!