Fractions to Mixed Numbers

Objective

Students will be able to divide improper fractions by mixed numbers and express the quotients as improper fractions or mixed numbers. This lesson aligns with Common Core State Standard:
CCSS.MATH.CONTENT.6.NS.A.1 – Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

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Standards Addressed

• CCSS.MATH.CONTENT.6.NS.A.1
• CCSS.MATH.CONTENT.6.NS.B.3 – Fluently divide multi-digit numbers using the standard algorithm.
• CCSS.MATH.PRACTICE.MP1 (Make sense of problems and persevere in solving them)
• CCSS.MATH.PRACTICE.MP4 (Model with mathematics)

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Materials Needed

• Whiteboard and markers
• Fraction strips and number lines
• Graphic organizers for step-by-step fraction division
• Dyslexia-friendly fraction task cards (using larger, clear fonts with spacing, and color-coded examples)
• Calculators (optional, for checking answers)
• Student notebooks or math journals

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Time Breakdown (20 minutes total)

1. Introduction & Warm-Up (4 minutes)

• Engage the students by revisiting the concept of improper fractions and mixed numbers (e.g., 7/4 and 1 3/4). Use fraction strips or visuals.
• Quick oral questions to recall how to convert between improper fractions and mixed numbers.
• Ask: "How do we think about division when fractions are involved?"

Differentiation

• Use color-coded visuals to support learners with dyslexia and visual processing challenges.
• Provide verbal repetition alongside visuals to reinforce concepts.

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2. Direct Instruction (7 minutes)

• Explain the process of dividing an improper fraction by a mixed number. Steps:

  1. Convert the mixed number into an improper fraction.
  2. Rewrite the division problem as multiplication by the reciprocal.
  3. Multiply the numerators and denominators.
  4. Simplify the resulting fraction or convert to a mixed number.

• Write example on the board:
  Divide ( \frac{9}{4} \div 2 \frac{1}{3} )

  • Convert (2 \frac{1}{3} = \frac{7}{3} )
  • Rewrite: ( \frac{9}{4} \times \frac{3}{7} )
  • Multiply: ( \frac{27}{28} )
  • Result: ( \frac{27}{28} ) (improper fraction, simplify if possible)

• Use a graphic organizer to visually break down each part of the process.

Differentiation

• Use a step-by-step poster or handout with bullet points and icons representing each step (helps with working memory).
• Provide dyslexia-friendly reading materials by using high-contrast colors and clear typefaces such as OpenDyslexic font for printed steps.

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3. Guided Practice (6 minutes)

• Provide 3-4 practice problems of dividing improper fractions by mixed numbers on dyslexia-friendly task cards. Examples:
  • ( \frac{11}{6} \div 1 \frac{2}{5} )
  • ( \frac{7}{3} \div 2 \frac{1}{4} )
• Students work in pairs or small groups. Walk around to support students one-on-one.
• Encourage them to use graphic organizers and fraction strips to visualize.

Differentiation

• Pair students strategically so peers can support each other.
• Allow some students to use manipulatives or calculators to verify their steps if necessary.
• Simplify problems or present fewer steps for students who need additional support.

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4. Exit Ticket / Formative Assessment (3 minutes)

• Distribute a quick problem as an exit ticket:
  Divide ( \frac{13}{5} \div 1 \frac{1}{2} ). Show all your work.
• Collect these for review and to identify who needs further scaffolding.

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Additional Notes for Special Education Resource Class

• Use multi-sensory teaching approaches (visual, auditory, and kinesthetic). For example, use fraction strips to physically manipulate fractions.
• Break instructions into small, timed chunks with frequent checks for understanding.
• Allow extended time or one-on-one support if needed.
• Use positive reinforcement for effort as well as accuracy to encourage persistence.

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Reflection and Feedback

• After class, reflect on which students needed more support and adjust upcoming lessons accordingly.
• Consider using student feedback to adapt visual and written materials for better dyslexia accessibility.

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This lesson maximizes engagement and clarity within a 20-minute timeframe while offering differentiated supports for diverse learners in a 6th grade special education classroom setting.