Adding and Subtracting Numbers

Subject: Mathematics

Grade Level: 2nd Grade
Duration: 90 minutes
Class Size: 14 students

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Learning Objective

• Students will add and subtract numbers within 100 using place value strategies and understand the relationship between addition and subtraction.
• Students will interpret diagrams related to addition and subtraction problems.
• Students will solve one-step word problems involving addition and subtraction within 100.

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Learning Standards

• 2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value and the relationship between addition and subtraction.
• 2.OA.A.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
• 2.OA.B.2: Fluently add and subtract within 20 using mental strategies. (Supports extension to 100 fluency.)

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Key Vocabulary

• Addition
• Subtraction
• Altogether
• More than
• Less than
• Diagram
• Sum
• Difference
• Place value
• Equation

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Lesson Timeline

Hook (Launch, Warm-Up) — 10 minutes

Activity:

• Begin with a lively game called "Number Detective." Show 2-3 simple visual diagrams (e.g., 40 dots on one side, 25 dots on the other) with addition or subtraction story prompts.
• Ask students quick oral math questions: “If you have 40 stickers and get 25 more, how many stickers now?”
• Encourage students to explain their thinking in pairs, highlighting words “altogether,” “more than,” and “less than.”
• Purpose: Focus attention on vocabulary and interpreting diagrams, engage collaborative learning early.

Learn (Explore) — 15 minutes

Mini-lesson (I Do):

• Use a whiteboard and place value chart. Model addition and subtraction within 100, e.g., 65 – 23.
• Break down the numbers by tens and ones (60+5 and 20+3). Show how to subtract 20 first, then 3, emphasizing place value understanding.
• Demonstrate interpreting related diagrams (e.g. bar models or part-part-whole diagrams) and translating visual info into equations.
• Discuss the relationship between addition and subtraction (e.g., check answers by addition).

Guided Practice (We Do) — 25 minutes

Activity:

• Divide students into small groups (3-4). Provide manipulatives: base-ten blocks or place value disks.
• Present 3 diagrams representing addition or subtraction problems (e.g., comparing two quantities, total found by combining parts).
• Groups use base-ten blocks to model and solve problems step-by-step, then write the equation for each.
• Teacher circulates, scaffolds thinking, and prompts groups with questions like, “Which numbers are tens? How many left after subtraction?”
• After every problem, groups explain their reasoning aloud to build active learning and discussion skills.

Independent Practice (You Do) — 20 minutes

Activity:

• Provide each student with a worksheet of 8 one-step word problems. Problems require addition or subtraction within 100, without decomposing tens (e.g., 54 + 33, 76 – 25).
• Include simple diagrams alongside word problems for students to interpret.
• Encourage students to underline key words (altogether, more, less) and solve using place value strategies learned.
• Remind students to check their work by reversing the operation.

Closing (Synthesis, Discuss) — 10 minutes

• Bring the class together for a reflective discussion:
  • Invite 3-4 students to share one problem they solved and explain their strategy using place value or diagrams.
  • Highlight how addition and subtraction relate to each other.
  • Review key vocabulary with quick 'pop quiz' style questions (e.g., “What does ‘more than’ usually tell us to do: add or subtract?”)
• Reinforce how diagrams help us understand math problems better.

Fluency Focus — Throughout the lesson

• Incorporate quick oral math fact checks on addition and subtraction within 20 to build mental fluency during transitions.
• Use flashcard warm-ups or “math fact races” for 2 minutes between activities.

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Differentiation

• For students needing extra support:

  • Provide additional guided practice with manipulatives and one-on-one scaffolding.
  • Use simpler numbers first (e.g., adding/subtracting within 50).
  • Provide visual step-by-step flowcharts for problem-solving.

• For advanced learners:

  • Challenge with two-step problems or slightly larger numbers within 100 without regrouping.
  • Encourage creating their own story problems and diagrams to explain.
  • Introduce a simple remainders or estimation activity related to addition/subtraction.

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Assessment

• Formative Assessment:

  • Observation during guided practice and small group discussions.
  • Listening for correct use of vocabulary and strategy explanations.
  • Quick spot-checks of independent practice work.

• Summative Assessment:

  • End with a short quiz covering
    • 3 addition/subtraction problems within 100, no decomposing ten.
    • 2 diagram interpretation questions asking for an equation.
    • 2 one-step story problems to solve and explain.
  • Use rubric focusing on accuracy, proper strategy use, and explanation clarity.

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Materials Needed

• Whiteboard and markers
• Base-ten blocks or place value disks (2 sets for groups)
• Printed diagram cards for group work
• Independent practice worksheets
• Math fact flashcards

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Notes for Teachers

• Emphasize multiple representations (numerical, visual diagrams, manipulatives) to connect abstract and concrete understanding.
• Foster collaborative dialogue—it’s essential for building shared reasoning and confidence.
• Model thinking aloud continuously during the "I Do" and "We Do" phases to demonstrate metacognitive strategies.

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This lesson combines visual, tactile, and verbal learning modalities with collaborative and independent activities, closely aligned to Common Core standards 2.NBT.B.5, 2.OA.A.1, and 2.OA.B.2, designed to build fluency and deep understanding of addition and subtraction within 100.