Number Sense and Place Value

Lesson Plan: Number Sense and Place Value

Grade Level: Grade 5

Subject: Mathematics

Duration: 2 Weeks (10 class periods, 45 minutes each)

CBSE Alignment:

  • Chapter Reference: NCERT Class 5 Math, Chapter 1: "The Fish Tale" (introduces large numbers and place value) and related concepts from "Building with Bricks" or "Long and Short."
  • Learning Outcomes: Read, write, and compare numbers up to 10,00,000; understand place value up to lakhs; apply number sense in practical situations.

Objectives:

By the end of the two weeks, students will be able to:

  1. Read, write, and count numbers up to 10,00,000 (10 lakhs) in numerals and words.
  2. Identify place value positions (ones, tens, hundreds, thousands, ten thousands, lakhs) in six-digit numbers.
  3. Expand numbers using place value (e.g., 5,67,890 = 5,00,000 + 60,000 + 7,000 + 800 + 90).
  4. Compare and order numbers using symbols (<, >, =) and terms (greatest, smallest).
  5. Skip count by 100s, 1000s, and 10,000s within 10,00,000.
  6. Solve real-life problems involving large numbers (e.g., population, money, distances).

Materials Needed:

  • Number charts (1-10,000, 1-10,00,000)
  • Base-10 blocks (lakhs blocks, ten thousands, thousands, hundreds, tens, ones) or paper cutouts
  • Flashcards with numbers (0-9, 100-1000, 1000-10,000, 10,000-10,00,000)
  • Play money (rupee notes: ₹1, ₹10, ₹100, ₹1000, ₹10,000)
  • Whiteboard/markers or blackboard/chalk
  • Worksheets with place value tasks (e.g., expanded form, comparison)
  • Dice or number spinners for games
  • Ruler, measuring tape, or string for distance activity
  • Colored paper and markers for crafts

Week 1: Numbers up to 10,000 and Introducing Lakhs

Day 1: Review Numbers up to 10,000

Objective: Reinforce place value for four-digit numbers.
Activities:

  1. Warm-Up (5 min): Count aloud by 1000s to 10,000: "1000, 2000…" with finger counting.
  2. Direct Instruction (15 min):
    • Use a 1-10,000 chart. Read numbers (e.g., 4567, 8901).
    • Review: Show 6789 with blocks (6 thousands + 7 hundreds + 8 tens + 9 ones). Ask: "What’s the value of 7?" (700).
  3. Activity (20 min): Place Value Breakdown
    • Students use blocks to show numbers (e.g., 9345 = 9 thousands + 3 hundreds + 4 tens + 5 ones). Write: Th H T O (9 3 4 5).
    • Expand: "9345 = 9000 + 300 + 40 + 5."
  4. Wrap-Up (5 min): Ask: "What is 5 thousands, 2 hundreds, 6 tens, 3 ones?"
    Homework: Write 9900-10,000 and circle the thousands digit.

Day 2: Skip Counting by 100s and 1000s

Objective: Practice skip counting within 10,000.
Activities:

  1. Recap (5 min): Review 9345: "How many thousands? Hundreds?"
  2. Direct Instruction (15 min):
    • Teach: "By 100s: 100, 200, 300… By 1000s: 1000, 2000, 3000…" up to 10,000.
    • Use a chart to highlight patterns (e.g., 1000s change thousands place).
  3. Activity (20 min): Skip Count Challenge
    • In pairs, students roll a die (multiply by 100 or 1000) and count: "1000, 2000…" or "100, 200…"
    • Write the sequence and check with a partner.
  4. Wrap-Up (5 min): Ask: "What’s 3000 more than 4000?"
    Homework: Write 1000s from 1000 to 10,000.

Day 3: Introducing Lakhs (10,000-1,00,000)

Objective: Understand the concept of ten thousands and lakhs.
Activities:

  1. Warm-Up (5 min): Count by 1000s to 10,000, then back.
  2. Direct Instruction (15 min):
    • Show a lakh block (or 10 ten-thousands). Say: "10 thousands = 1 ten thousand = 10,000. 10 ten thousands = 1 lakh = 1,00,000."
    • Count: "10,000, 20,000…1,00,000" with blocks. Write: "1,00,000 = 1 lakh."
  3. Activity (20 min): Lakh Builder
    • Students stack blocks: 1 ten thousand (10,000), 5 ten thousands (50,000), 1 lakh (1,00,000). Write in words and numerals.
    • Add hundreds: "1,23,000 = 1 lakh + 2 ten thousands + 3 thousands."
  4. Wrap-Up (5 min): Ask: "How many ten thousands in 1 lakh?"
    Homework: Write 90,000-1,00,000 and underline the ten thousands digit.

Day 4: Place Value with Lakhs (1,00,000-5,00,000)

Objective: Represent six-digit numbers up to 5 lakhs.
Activities:

  1. Recap (5 min): Count by 10,000s to 1,00,000, review 1,23,000’s place value.
  2. Direct Instruction (15 min):
    • Show 3,45,678 with blocks: 3 lakhs + 4 ten thousands + 5 thousands + 6 hundreds + 7 tens + 8 ones.
    • Write: L TTh Th H T O (3 4 5 6 7 8). Expand: "3,45,678 = 3,00,000 + 40,000 + 5000 + 600 + 70 + 8."
  3. Activity (20 min): Number Expansion
    • Students use blocks to show numbers (e.g., 2,78,901) and write expanded form (2,00,000 + 70,000 + 8000 + 900 + 1).
  4. Wrap-Up (5 min): Ask: "What’s the value of 4 in 4,56,789?" (4,00,000)
    Homework: Expand 2,34,567 (2,00,000 + 30,000 + 4000 + 500 + 60 + 7).

Day 5: Comparing Numbers (1-5,00,000)

Objective: Compare six-digit numbers using <, >, =.
Activities:

  1. Warm-Up (5 min): Count by 1,00,000s to 5,00,000.
  2. Direct Instruction (15 min):
    • Use blocks: 2,34,567 vs. 2,45,678. Compare place by place (lakhs first). Say: "2,34,567 < 2,45,678."
    • Show: "3,00,000 = 3,00,000." Emphasize starting from the leftmost digit.
  3. Activity (20 min): Comparison Game
    • In pairs, students draw number cards (1,00,000-5,00,000) and write <, >, or = (e.g., 4,56,789 > 4,23,456).
    • Explain: "4,56,789 is greater because 5 ten thousands is more than 2 ten thousands."
  4. Wrap-Up (5 min): Ask: "Which is bigger: 5,00,000 or 4,99,999?"
    Homework: Compare: 3,45,678 __ 3,54,678, 2,00,000 __ 1,99,999 (write <, >, =).

Week 2: Numbers up to 10,00,000 and Applications

Day 6: Counting to 10,00,000

Objective: Count, read, and write numbers up to 10 lakhs.
Activities:

  1. Warm-Up (5 min): Count by 1,00,000s to 5,00,000, then back.
  2. Direct Instruction (15 min):
    • Use a 1-10,00,000 chart (or sections). Count: "1,00,000, 2,00,000…10,00,000."
    • Read and write: "5,67,890 = Five lakh sixty-seven thousand eight hundred ninety."
  3. Activity (20 min): Number Words
    • Students write numbers in words (e.g., 7,89,123 = Seven lakh eighty-nine thousand one hundred twenty-three).
    • Check with a partner using a chart.
  4. Wrap-Up (5 min): Ask: "What comes after 9,99,999?"
    Homework: Write 9,90,000-10,00,000 in numerals and words.

Day 7: Expanded Form and Place Value (5,00,000-10,00,000)

Objective: Expand six-digit numbers up to 10 lakhs.
Activities:

  1. Recap (5 min): Count to 10,00,000 by 1,00,000s, review 5,67,890 in words.
  2. Direct Instruction (15 min):
    • Show 8,76,543: 8 lakhs + 7 ten thousands + 6 thousands + 5 hundreds + 4 tens + 3 ones.
    • Write: L TTh Th H T O (8 7 6 5 4 3). Expand: "8,76,543 = 8,00,000 + 70,000 + 6000 + 500 + 40 + 3."
  3. Activity (20 min): Place Value Craft
    • Students cut paper (lakhs = big square, ten thousands = smaller square, etc.) for a number (e.g., 6,54,321) and write expanded form.
  4. Wrap-Up (5 min): Ask: "What’s the value of 7 in 7,89,123?" (7,00,000)
    Homework: Expand 9,87,654 (9,00,000 + 80,000 + 7000 + 600 + 50 + 4).

Day 8: Skip Counting by 10,000s and Ordering Numbers

Objective: Skip count by 10,000s and order numbers up to 10,00,000.
Activities:

  1. Warm-Up (5 min): Count by 1000s to 10,000, then 10,000s to 1,00,000.
  2. Direct Instruction (15 min):
    • Practice: "10,000, 20,000, 30,000…10,00,000." Highlight pattern (ten thousands place changes).
    • Order: Show 5,67,890, 2,34,567, 8,90,123. Arrange smallest to largest (2,34,567, 5,67,890, 8,90,123).
  3. Activity (20 min): Order Race
    • In groups, students get cards (e.g., 7,89,123, 3,45,678, 9,01,234) and order them. Write: "3,45,678 < 7,89,123 < 9,01,234."
    • Check as a class.
  4. Wrap-Up (5 min): Ask: "What’s between 5,00,000 and 7,00,000?"
    Homework: Order: 6,78,901, 2,34,567, 9,87,654 (smallest to largest).

Day 9: Real-Life Application with Money and Distance

Objective: Apply place value to rupees and measurements.
Activities:

  1. Recap (5 min): Review ordering: "Which is greatest: 6,78,901, 9,87,654?"
  2. Direct Instruction (15 min):
    • Show ₹10,000, ₹1000, ₹100 notes. Make: ₹5,67,890 = 5 lakhs + 6 ten thousands + 7 thousands + 8 hundreds + 9 tens.
    • Measure: "A river is 3,45,678 meters = 3 lakhs + 4 ten thousands + 5 thousands + 6 hundreds + 7 tens + 8 ones."
  3. Activity (20 min): Shop and Travel
    • Students “buy” items (e.g., bike = ₹2,34,567) with play money, breaking into notes.
    • Measure a “distance” (e.g., 1,23,450 cm with string) and write in expanded form.
  4. Wrap-Up (5 min): Ask: "How many ₹10,000 notes in ₹1,00,000?"
    Homework: Draw ₹4,56,789 using notes and write in expanded form.

Day 10: Review and Assessment

Objective: Consolidate number sense and place value skills.
Activities:

  1. Warm-Up (5 min): Count by 10,000s to 10,00,000, then back by 1,00,000s.
  2. Review Game (15 min): Place Value Quiz
    • Use flashcards: Teacher says "8 lakhs, 5 thousands" (8,05,000). Students write. Compare pairs (e.g., 7,89,123 __ 7,98,123).
  3. Assessment (20 min):
    • Worksheet:
      a. Write 9,99,990-10,00,000 in numerals and words.
      b. Expand 6,78,901 (6,00,000 + 70,000 + 8000 + 900 + 1).
      c. Compare: 5,67,890 __ 5,76,890, 8,00,000 __ 7,99,999.
      d. Order: 3,45,678, 9,01,234, 6,78,901.
      e. Problem: "A town has 4,56,789 people. How many lakhs?" (4).
  4. Wrap-Up (5 min): Discuss: "How do big numbers help us?" Celebrate with a cheer.
    Homework: Write a six-digit number (e.g., 7,89,123) and expand it.

Assessment:

  • Formative: Participation in counting, games, and activities; accuracy in worksheets and homework.
  • Summative: Day 10 worksheet (scored out of 10: 2 for numerals/words, 2 for expanded form, 2 for comparison, 2 for ordering, 2 for problem-solving).
  • Observation: Ability to explain place value and solve real-life problems.

Extensions:

  • Field Activity: Estimate and measure school distances (e.g., playground in meters) using place value.
  • Craft: Create a “Number Line” from 1 to 10,00,000 with milestones (e.g., 1 lakh).
  • Problem-Solving: Calculate a family budget (e.g., ₹5,67,890) and break into notes.

Notes for Teachers:

  • Use concrete examples (blocks, money) to reinforce abstract concepts.
  • Relate to CBSE context (e.g., Indian number system with lakhs, rupees) for relevance.
  • Encourage reasoning (e.g., “Why is 5,67,890 less than 5,76,890?”) to deepen understanding.
  • Adjust pace for student readiness; revisit 1-10,000 if needed.