Dividing Mixed Numbers

Lesson Overview

Grade: 6
Class Size: 13 students
Duration: 30 minutes
Unit: Mastering Numbers & Ratios (Lesson 12 of 30)
Lesson Title: Dividing Mixed Numbers: Step-by-Step
Lesson Description:
Students will learn how to divide mixed numbers by converting mixed numbers into improper fractions and then applying division rules for fractions.

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Common Core 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.

CCSS.Math.Content.6.NS.A.1c

• Find the common factors of two whole numbers using prime factorization and use common factors to simplify fractions. (Connected to simplifying fractions after division.)

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Learning Objectives

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

• I can convert mixed numbers to improper fractions accurately.
• I can divide mixed numbers by first converting them to improper fractions.
• I can apply the rule “multiply by the reciprocal” when dividing fractions.
• I can simplify the resulting fraction or mixed number.

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Success Criteria

Students will demonstrate success when they:

• Successfully convert at least 3 mixed numbers into improper fractions.
• Correctly perform division of two fractions using multiplication by the reciprocal.
• Simplify answers to simplest form or mixed number.
• Explain the steps out loud or in writing clearly.

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Materials Needed

• Whiteboard and markers
• Individual whiteboards or paper for each student
• Fraction strips or fraction circles (visual aids)
• Pre-prepared worksheets with mixed number division problems
• Dyslexia-friendly fonts and handouts (e.g., OpenDyslexic font)
• Colored pens to differentiate steps (optional)

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Lesson Breakdown

1. Warm-Up (5 minutes)

• Begin with a quick review: "Who remembers how to convert a mixed number to an improper fraction?"
• Use a visual aid (fraction strips or circles) to demonstrate one example as a class.
• Students convert 1–2 mixed numbers independently on their whiteboards.
• Teacher circulates to offer immediate guidance.

Differentiation: Provide fraction strips/circles to visual learners; verbal explanations for auditory learners.

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2. Direct Instruction & Modeling (10 minutes)

• Introduce the concept: "Dividing mixed numbers means first changing them to improper fractions."
• Write on the board the step-by-step method:
  1. Convert mixed numbers to improper fractions.
  2. Change division to multiplication by the reciprocal of the divisor.
  3. Multiply the numerators and denominators.
  4. Simplify the fraction or convert to a mixed number.
• Work through 2 division problems together, thinking aloud each step.
• Use colored pens: blue for the step of conversion, red for multiplication, green for simplification to help visual tracking.

Dyslexia Reading Tip: Use bullet points, clear spacing, and highlight key words in bold on the board or handout.

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3. Guided Practice (8 minutes)

• Hand out worksheet with 3 division problems involving mixed numbers.
• Students work individually or in pairs to solve.
• Encourage students to verbalize steps to a partner or write “I can…” statements after each problem.
• Teacher supports students needing extra help, especially those struggling to convert or multiply fractions.

Differentiation:

• For students who struggle, provide step-by-step sentence starters (“First, I convert…, then I multiply…”) and fraction strips.
• For advanced learners, add problems where they must simplify complex improper fractions or solve word problems involving mixed number division.

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4. Independent Practice / Assessment (5 minutes)

• Students complete 1 challenge problem on mini-whiteboards and hold up their answers for quick formative assessment.
• Example problem: Divide 3 1/2 by 1 2/3 — show all steps.
• Teacher observes common errors and addresses any misconceptions immediately.

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5. Closure & Reflection (2 minutes)

• Students write an “I can…” statement in their math journals about what they learned today.
• Example: “I can divide mixed numbers by converting them into improper fractions and multiplying by the reciprocal.”
• Quickly review the success criteria: “Did I convert? Did I multiply by the reciprocal? Did I simplify?”
• Preview next lesson: multiplying mixed numbers.

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Extension Activity (For Advanced Learners)

• Challenge students to create their own word problems involving division of mixed numbers and swap with a peer to solve.
• Introduce real-world applications, e.g., recipes or dividing lengths in projects with mixed number measurements.

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Differentiation Strategies for Diverse Learners

• Use visual fraction tools and color-coding to support comprehension.
• Provide stepwise, scaffolded instructions with sentence starters.
• Pair students strategically so stronger students can support peers.
• Minimize reading load by using dyslexia-friendly fonts and clear formatting.
• Allow oral explanations or video tutorials as alternative assessments for students with reading/writing difficulties.

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Assessment Plan

• Ongoing formative assessment via whiteboard checks during guided and independent practice.
• Review of worksheets at end of lesson for accuracy and understanding.
• Exit ticket with one division problem to gauge individual mastery.

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Reflection for Teacher

• Note which students grasped the concept and who requires more intervention.
• Reflect on whether visual aids and “I can…” statements improved engagement and clarity.
• Adjust pacing if students need more time on conversion or multiplication steps.

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This engaging, scaffolded lesson balances conceptual understanding and procedural fluency, ensuring every 6th grader experiences success with dividing mixed numbers according to the Common Core standards.