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Grade Level

6th Grade Accelerated Mathematics

Duration

90 minutes

Standards Alignment

Common Core State Standards (CCSS):

• CCSS.MATH.CONTENT.6.NS.A.1 – Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
• CCSS.MATH.CONTENT.6.NS.A.2 – Fluently divide multi-digit numbers using the standard algorithm.
• CCSS.MATH.CONTENT.6.NS.B.3 – Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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Learning Objectives ("I Can" Statements)

• I can explain what division of rational numbers means.
• I can divide fractions and decimals fluently.
• I can solve real-world problems involving division of rational numbers.
• I can explain why dividing by a rational number works the way it does using visual models.

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Success Criteria

• I can accurately divide rational numbers, including fractions and decimals.
• I can represent division problems with visual models or equations.
• I can explain my reasoning clearly in writing or verbally.
• I can solve word problems that require dividing rational numbers.

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Materials Needed

• Fraction strips or fraction circles (physical manipulatives)
• Whiteboards and markers
• Student math journals or notebooks
• Graph paper
• Calculators (for decimal operations)
• Pre-prepared story problems and exit tickets
• Digital projector/smartboard

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Lesson Breakdown

1. Invitation / Engagement (10 minutes)

Activity:

• Begin with a simple problem on the board: "If you have 3/4 of a cake and want to share it equally among 1/2 a group, how much cake does each person get?"
• Ask students to discuss their initial thoughts with a partner and share out.
• Highlight how this is a division problem with fractions.

Purpose:

• Hooks student interest with a real-world scenario.
• Activates prior knowledge about fractions and division.

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2. Direct Instruction and Modeling (20 minutes)

Focus: Dividing Fractions and Decimals using visual models and algorithmic methods.

• Use fraction strips/circles to model dividing fractions visually. For example, show 3/4 ÷ 1/2 by physically comparing how many 1/2 segments fit into 3/4.
• Connect the visual to the division rule: "To divide fractions, multiply by the reciprocal."
• Model division of decimals (e.g., 1.2 ÷ 0.3) on the whiteboard using place value understanding and long division.
• Write the algorithm and model it step-by-step.

Success Checks:

• Ask students to represent a division expression on their whiteboards and explain steps briefly.

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3. Guided Practice (25 minutes)

Hands-on Activity: "Fraction Division Stations"

• Divide the class into groups of 4 and rotate through 3 stations, spending about 7-8 minutes each.

Station 1: Visual Model Station

• Using fraction strips, students solve problems like 2/3 ÷ 1/4 and explain their reasoning.
  Station 2: Algorithm Application Station
• Solve fraction division problems with paper and pencil, checking answers with reciprocal multiplication method.
  Station 3: Decimal Division Station
• Use calculators and long division methods to divide decimal rational numbers (e.g., 4.8 ÷ 0.6), discussing why decimal division works.

Teacher Role:

• Circulate to provide support, prompt mathematical discourse, and offer scaffolds.

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4. Independent Practice (15 minutes)

• Individual problem set combining fraction and decimal division problems.
• Include word problems to apply skills in real-world contexts.
• Example problem: "A recipe calls for 2/5 cup of sugar, but you only want to make half the recipe. How much sugar do you need?"

Differentiation:

• Provide scaffolded problems with simpler numbers or more visuals for students needing support.
• Challenge advanced learners with multi-step problems or problems involving negative rational numbers.

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5. Formative Assessment and Reflection (10 minutes)

• Exit ticket with 3 problems: one visual model interpretation, one numeric division of fractions, one word problem involving decimals.
• Use student responses to gauge understanding and plan future instruction.
• Brief class discussion on common misconceptions or "aha" moments.

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6. Extension Activity for Advanced Learners

• Introduce dividing rational numbers involving negative values and reflect on how rules still apply.
• Challenge students to create their own division word problem involving fractions or decimals and solve it, sharing with peers.
• Explore real-world applications such as dividing quantities in science experiments or financial computations with rational numbers.

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Differentiation Strategies

• For Struggling Learners:

  • Use visual models extensively.
  • Allow paired work for peer support.
  • Provide step-by-step checklists for solving problems.

• For English Language Learners:

  • Include vocabulary cards and sentence stems (e.g., "When I divide fractions, I...").
  • Use visuals/context to support conceptual understanding.

• For Advanced Learners:

  • Offer extension challenges as described above.
  • Encourage explanation and justification in written or oral form.

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Reflection and Teacher Notes

• Monitor students’ ability to connect visual models with the division algorithm.
• Note which students avoid or struggle with word problems.
• Plan to revisit real-world application if needed, integrating more interactive problems.

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This lesson is designed to build conceptual understanding, fluency, and application of dividing rational numbers, meeting the rigor expected by CCSS for 6th grade while supporting a range of learners with engaging, hands-on methods.