Rational Numbers Review

Grade Level

6th Grade

Duration

30 minutes

Unit

Mastering Numbers & Ratios (Lesson 27 of 30)

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Common Core State Standards (CCSS)

CCSS.MATH.CONTENT.6.NS.C.7
Understand ordering and absolute value of rational numbers.

• a. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
• b. Understand and apply properties of operations to add, subtract, multiply, and divide rational numbers.
• c. Understand ordering and absolute value of rational numbers.

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Learning Objectives (I Can Statements)

• I can identify and classify rational numbers including positive and negative fractions and decimals.
• I can compare and order rational numbers on a number line.
• I can apply properties of operations (addition, subtraction, multiplication, and division) to rational numbers.
• I can solve real-world problems involving rational numbers.

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Success Criteria

• Students correctly identify rational numbers when presented with a mix of rational and irrational numbers.
• Students demonstrate comparing and ordering rational numbers on a number line with minimal errors.
• Students solve word problems involving operations with rational numbers accurately.
• Students explain their reasoning during peer discussions and problem-solving.

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Materials Needed

• Whiteboard and markers
• Number line strips (individual for each student)
• Set of cards with rational numbers written on them (positive and negative fractions and decimals)
• Worksheets with real-world word problems involving rational numbers
• Dyslexia-friendly fonts and printed materials with ample spacing
• Colored pencils for visual aids

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Lesson Outline

1. Warm-up and Review (5 minutes)

• Begin with a quick oral review: Ask students to recall what rational numbers are and write examples on the board.
• Review the definition: rational numbers are numbers that can be written as a fraction a/b, where b ≠ 0, including integers, fractions, and decimals that terminate or repeat.
• Use “I can” statement on board: I can identify rational numbers.
• Show mix of numbers and ask students to vote thumbs up/down if they think it’s rational.

2. Guided Practice: Ordering Rational Numbers (8 minutes)

• Hand out number line strips and cards containing various rational numbers (mixed positive and negative).
• Students place cards in order on their personal number line strips.
• Teacher models one example on the whiteboard and explains the reasoning aloud.
• Use “I can” statement: I can compare and order rational numbers on a number line.
• Students pair-share their number lines, explaining their placements using comparative language (greater than, less than).
• Highlight absolute values and how they affect ordering of negative numbers.

3. Properties of Operations & Application in Word Problems (10 minutes)

• Quick review of adding, subtracting, multiplying, and dividing rational numbers using properties of operations.
• Provide 2-3 real-world word problems involving rational numbers (e.g., debt/credit scenarios, recipes, temperature changes).
• Model one problem solving step-by-step on the board.
• Students work independently or in pairs to solve the remaining problems on the worksheet.
• Circulate to provide guided support, particularly to students needing differentiation.
• Use “I can” statement: I can solve real-world problems involving operations with rational numbers.

4. Wrap-Up and Formative Assessment (5 minutes)

• Conduct a quick quiz of 3 multiple-choice questions on identifying rational numbers, ordering them, and solving a simple word problem to gauge understanding.
• Allow students to self-check their answers using answer key and discuss any tricky items with the class.
• Encourage students to share how they solved the problems verbally to reinforce math communication.

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Differentiation Strategies

• For students who need extra support:

  • Use color coding on number lines to differentiate positive (blue) and negative (red) numbers.
  • Provide step-by-step scaffolded worksheets with visual cues and extra examples.
  • Pair weaker readers with stronger peers for collaborative tasks.
  • Make numbers and instructions available in dyslexia-friendly fonts with larger spacing.

• For students who need challenge:

  • Introduce problems involving converting repeating decimals to fractions.
  • Provide extension problems solving multistep rational number operations in complex contexts (e.g., budgeting scenarios).
  • Encourage students to create their own rational number word problems for peers to solve.

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Extension Activity (Optional)

• Have advanced learners create a mini-poster illustrating different types of rational numbers and their real-world applications, including an explanation of properties of operations used to manipulate those numbers.

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Dyslexia-Friendly Tips

• Use a sans-serif font like OpenDyslexic or Arial for all printed materials.
• Avoid justified text blocks; use left-aligned text to aid readability.
• Include ample white space and use bullet points rather than long paragraphs.
• Use color contrasts carefully—avoid red/green color combos.
• Provide oral instructions alongside written directions.

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This compact but comprehensive review is designed to build deep conceptual understanding while engaging all learners through a variety of activities and supports. It aligns tightly with Common Core standards to ensure mastery and readiness for the next topics in the unit.