Subtracting Decimals Intro

Grade Level

5th Grade

Duration

45 minutes

Class Size

21 students

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Unit

Decoding Decimals: A Journey
Lesson 7 of 17

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Common Core Standards

• 5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
• MP.1: Make sense of problems and persevere in solving them.
• MP.4: Model with mathematics.
• MP.7: Look for and make use of structure.

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Learning Objectives

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

1. Use place value understanding and models to subtract decimals to the hundredths place.
2. Apply concrete strategies involving base-ten blocks and place value charts to visualize decimal subtraction.
3. Demonstrate the connection between subtraction of whole numbers and subtraction of decimals.
4. Explain reasoning verbally and in writing when subtracting decimals.

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Materials Needed

• Decimal Place Value Charts (printed handouts and a large classroom version)
• Base-ten blocks or decimal grids (individual sets or classroom manipulatives)
• Dry erase boards and markers for each student
• Whiteboard and markers for teacher demonstrations
• "Subtracting Decimals Task Cards" (prepared in advance)
• Exit Ticket handouts

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Lesson Breakdown

1. Engage & Connect (5 minutes)

• Begin with a quick mental math warm-up: Subtract simple whole numbers, e.g., 24 - 9, 48 - 15, to activate subtraction thinking.
• Ask students how they think subtraction will be different or similar when dealing with decimals, especially when they have decimals up to hundredths.
• Briefly revisit place value with decimals (tenths, hundredths) using the large place value chart. Use student responses to spark curiosity.

2. Direct Instruction: Modeling Subtraction of Decimals (10 minutes)

• Introduce the subtraction problem: 4.25 - 2.13.
• Show the problem on the board using a place value chart.
• Using base-ten blocks/decimal grids:
  • Demonstrate 4 wholes, 2 tenths, and 5 hundredths before subtraction.
  • Physically remove 2 wholes, 1 tenth, and 3 hundredths while explaining place value alignment.
• Emphasize: subtract digits place by place using place value understanding (not just "line up the numbers").
• Highlight any regrouping (borrowing), and why it’s necessary in decimal subtraction.
• Encourage students to ask questions as you model every step explicitly with the visuals.

3. Guided Practice: Hands-On Subtracting Decimals (15 minutes)

• Distribute individual place value charts and decimal grids/base-ten blocks.
• Provide 3 subtraction problems of increasing difficulty, e.g.:
  1. 3.46 - 1.22
  2. 5.70 - 2.58
  3. 7.05 - 3.99 (to introduce regrouping where the digit in the hundredths place requires borrowing)
• Circulate the class, prompting students to:
  • Place decimals on charts
  • Use base-ten blocks/decimal grids to physically subtract
  • Record their calculations on dry erase boards
• Prompt mathematical discussion: "Why did you have to borrow here?" or "How does the place value chart help?"

4. Partner Talk & Reasoning (5 minutes)

• Pair students to explain one of their subtraction problems to each other using the models and place value charts.
• Students should use precise math vocabulary like “tenths,” “hundredths,” “regrouping,” and “subtract.”
• Teacher circulates, listening to explanations and providing scaffolding where necessary.

5. Independent Check: Exit Ticket (7 minutes)

• Give students a subtraction decimal question in their exit ticket, for example: 6.35 - 4.18.
• Students will solve using a place value chart or base-ten blocks illustration and write a short explanation of their strategy.
• Collect exit tickets for assessment.

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Assessment & Evaluation

• Observation of student participation during guided practice and partner talk.
• Review of exit tickets to assess individual understanding of subtracting decimals using place value models and strategies.
• Use exit ticket to adjust next instruction for more complex decimal subtraction or review regrouping if needed.

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Extensions & Differentiation

For Advanced Learners

• Challenge students to create their own subtraction problem involving decimals to hundredths and demonstrate the solution on the place value chart.
• Introduce subtraction with three decimal places for extension.

For Students Needing Support

• Provide additional one-on-one support with base-ten blocks before attempting written subtraction.
• Use simplified subtraction problems (no regrouping) for initial practice until mastery of place value is demonstrated.

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Teacher Reflection Prompts

• Did students independently use models to subtract decimals, or did they rely solely on algorithms?
• Which part of the subtraction process did students find most challenging?
• Were students able to communicate their reasoning effectively during partner talk?
• How might I incorporate technology or digital manipulatives next time for enhanced engagement?

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This lesson balances concrete manipulatives with abstract reasoning, aligns perfectly with Common Core 5.NBT.B.7, and encourages critical thinking through peer discussion and explanations, making decimal subtraction tangible and understandable for all 5th graders.