Understanding Decimals

Grade Level: 6th Grade

Duration: 30 minutes

Class Size: 11 Students

Unit: Mastering Numbers & Ratios

Lesson: 7 of 30

Lesson Title: Introduction to Decimals

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Common Core Standards Addressed

• CCSS.MATH.CONTENT.6.NS.B.3
  Fluently divide multi-digit numbers using the standard algorithm.
  (Note: While the full division fluency is not the focus here, understanding decimals relates to division and fractions.)

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

• CCSS.MATH.CONTENT.6.NS.C.6
  Understand a rational number as a point on the number line.

• CCSS.MATH.CONTENT.6.RP.A.3
  Use ratio and rate reasoning to solve real-world problems, including those involving decimals.

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Learning Objectives

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

• I can explain what decimals are and how they relate to whole numbers and fractions.
• I can use visual models to represent decimals and understand their place value.
• I can compare decimals with respect to their position on the number line.

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Success Criteria

• Students accurately identify decimals as numbers between whole numbers.
• Students represent decimals visually (using base-ten blocks or grids).
• Students explain how decimals connect to fractions (e.g., 0.5 = 1/2).
• Students place decimals correctly on a number line.

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Materials Needed

• Whiteboard and markers
• Base-ten block sets or printable decimal grids (10x10 grids highlighting portions)
• Number line printouts (0 to 1, subdivided into tenths and hundredths)
• Dry-erase boards and markers for each student
• Dyslexia-friendly printouts with large, sans-serif font, high contrast colors
• Visual flashcards showing fractions and their decimal equivalents

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Lesson Breakdown

1. Introduction & Hook (5 minutes)

• Engagement: Ask students, “Have you ever split a whole candy bar with friends? How would you show that half or a quarter of it is left?”
• Quickly review fractions (1/2, 1/4) and relate dividing the candy bar to numbers smaller than one.
• Introduce decimals as another way to express parts of a whole. Write 0.5 and 1/2 on the board and ask which represents half.
• Emphasize that decimals and fractions are related and both represent parts of something whole.

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2. Direct Instruction & Modeling (8 minutes)

• Use a 10x10 grid visual (or base-ten blocks) to show 100 parts of a whole. Shade 50 out of 100 squares.
• Relate shading 50/100 to the decimal 0.50 and simplify to 0.5.
• Show how decimals have place values: tenths, hundredths — label the grid rows and columns accordingly.
• Use the number line (from 0 to 1) to place decimals 0.1, 0.5, 0.75, and explain how these are points between whole numbers.
• Reinforce that the digit to the right of the decimal point represents parts less than one.

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3. Guided Practice (10 minutes)

• Provide students with their own base-ten grids or dry-erase boards and markers.
• Call out decimals such as 0.3, 0.7, 0.25, 0.9. Have students shade that portion on their grids.
• After shading, have students write the decimal and its equivalent fraction (e.g., 0.3 = 3/10).
• Project a number line and ask students to place their decimal numbers on it using sticky notes or writing tools on their mini whiteboards.
• Circulate, providing support and correcting misunderstandings.

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4. Independent or Partner Activity (5 minutes)

• In pairs, students receive a set of fraction cards and decimal cards mixed. Their task: match decimals to equivalent fractions using visual models provided (grids or blocks).
• Dyslexia-friendly: Use color-coded cards (e.g., blue cards for decimals, red cards for fractions), large font, and use clear spacing.

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5. Wrap-up & Assessment (2 minutes)

• Recap key points: decimals represent parts of a whole, can be shown on number lines and grids, and connect to fractions.
• Ask students to verbally share one thing they learned — e.g., “I can explain what 0.5 means and show it on a grid.”

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Differentiation Strategies

• For students with learning difficulties or dyslexia:

  • Use dyslexia-friendly fonts on handouts and digital tools.
  • Pair verbal instructions with clear visuals and physical manipulatives.
  • Use color-coding consistently for decimals, fractions, and place values.
  • Offer extra time during activities and one-on-one support where needed.

• For advanced learners:

  • Challenge them to convert decimals to fractions that require simplification (e.g., 0.75 = 75/100 = 3/4).
  • Introduce decimals beyond hundredths (thousandths) with visual models.
  • Provide word problems involving decimals in real-life contexts such as money or measurements.

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Extension Activity (Optional)

• Have students create their own decimal-fraction visual model cards for the next lesson, encouraging creativity (drawing or using digital tools).
• Introduce an online interactive decimal number line game for home practice.

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Reflection for Next Lesson

• Assess areas where students struggled with decimal representation or conversion.
• Plan to deepen understanding with addition and subtraction of decimals using visual models.

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End of Lesson