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Subject: Mathematics
Semester: 1
Period: 2
Week: 7
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 7
Lesson Duration: 45 minutes
Week & Period: Week 7, Period 2
Topic: Base Ten Number System
Sub-topic: Place Value and Expanded Form
Learning Objectives
By the end of the lesson, students should be able to:
Define the base ten system
Identify place value of digits in numbers (ones, tens, hundreds, thousands, etc.)
Count, read, and write numbers in base ten
Express numbers in expanded form
Previous Knowledge
Students already know counting numbers, basic addition, and place value up to hundreds.
Instructional Materials
Mathematics textbook for Grade 6, sticks, abacus, chart paper, flashcards.
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks learners to read and write numbers on the board, then identify the value of each digit.
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definition
The Base Ten System, also called the Decimal System, is the number system most commonly used in everyday life. It is a positional number system, which means the value of a digit depends on its position in the number. It uses 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent all numbers.
In this system, each place in a number represents a power of 10:
- The ones place represents 100=110^0 = 1100=1
- The tens place represents 101=1010^1 = 10101=10
- The hundreds place represents 102=10010^2 = 100102=100
- The thousands place represents 103=1,00010^3 = 1,000103=1,000
- The ten-thousands place represents 104=10,00010^4 = 10,000104=10,000, and so on.
This positional value means that a digit’s actual value is the digit multiplied by the place value.
Place Value
The place value of a digit in a number tells you how much that digit is worth. For example, in the number 4,372:
- The digit 4 is in the thousands place, so its value is 4×1,000=4,000
- The digit 3 is in the hundreds place, so its value is 3×100=300
- The digit 7 is in the tens place, so its value is 7×10=70
- The digit 2 is in the ones place, so its value is 2×1=2
Expanded Form
Expanded form is writing a number as the sum of each digit multiplied by its place value. It breaks the number down into parts to show the value of each digit.
For example:
- 4,372=(4×1,000)+(3×100)+(7×10)+(2×1)
1)4,372=(4×1,000)+(3×100)+(7×10)+(2×1)
- 5,604=(5×1,000)+(6×100)+(0×10)+(4×1)
1)5,604=(5×1,000)+(6×100)+(0×10)+(4×1)
- 12,305=(1×10,000)+(2×1,000)+(3×100)+(0×10)+(5×1)
1)12,305=(1×10,000)+(2×1,000)+(3×100)+(0×10)+(5×1)
More Examples
- What is the place value of 8 in 58,297?
- 8 is in the hundreds place, so its value is 8×100=800
- Write 7,019 in expanded form:
- 7,019=(7×1,000)+(0×100)+(1×10)+(9×1) 1)7,019=(7×1,000)+(0×100)+(1×10)+(9×1).
- In the number 203, what is the place value of 2?
- 2 is in the hundreds place, so its value is 2×100=200
- Write the number represented by (3×10,000)+(4×1,000)+(2×10)+(5×1) 1)(3×10,000)+(4×1,000)+(2×10)+(5×1)
- The number is 34,025.
Learners’ Activities (Expanded)
- Activity 1: Represent numbers physically
Provide learners with sticks, bundles of ten sticks, or an abacus. Ask them to represent numbers like 243, 1,305, or 4,672 by grouping ones, tens, hundreds, and thousands. - Activity 2: Reading and writing numbers
Have learners practice reading aloud large numbers you write on the board, such as 12,047; 3,560; 45,620, and 90,007. Then, ask them to write these numbers from words to digits and vice versa. - Activity 3: Writing expanded form
Give learners a list of numbers (e.g., 5,348; 12,705; 8,900) and ask them to write the expanded form for each. - Activity 4: Identifying place values
Call out numbers and ask learners to identify the place value of a specific digit in the number. - Group work:
Learners work in small groups to create flashcards with numbers on one side and their expanded forms on the other. They then quiz each other.
Assessment Checks
- Teacher asks orally:
- “What is the place value of 7 in 4,372?” (Answer: 70 or 7×107 \times 107×10)
- “Write 5,604 in expanded form.” (Answer: 5×1000+6×100+0×10+4×1
- “In the number 28,659, what is the value of 6?” (Answer: 6×10=60)
- “Write the number for (3×1,000)+(5×100)+(0×10)+(7×1).” (Answer: 3,507)
- Quick written quiz with 5 numbers where learners write the expanded form.
Notes (Expanded & Detailed)
Understanding the base ten system is crucial because it is the foundation of all our number systems and arithmetic operations such as addition, subtraction, multiplication, and division. It allows us to read, write, and manipulate numbers efficiently.
The positional nature means that the same digit can represent very different values depending on where it is placed in the number. For example, the digit 4 in 4,372 represents four thousand, but in 24, it represents only twenty.
Learning expanded form helps learners visualize the value of each digit and strengthens the understanding of place value. It also forms a foundation for more advanced math concepts like decimals, algebra, and number operations.
Using manipulatives like sticks and abacuses reinforces learning by making abstract concepts concrete and tangible, which benefits learners with different learning styles.
Additional Assignments
- Write the expanded form for each of the following numbers:
7,219; 15,408; 22,034; 9,001; 3,605 - Identify the place value and the value of the underlined digit:
a) 5,67,432
b) 12,345
c) 83,912
d) 456,789 - Create your own 4-digit number, write it in words, digits, and expanded form.
- Using an abacus or drawing base ten blocks, represent the number 3,746.
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Review definition of base ten, place values, reading/writing numbers, and expanded form.
Evaluation Method (Expanded)
Exit slip/quiz: Write 3 numbers in expanded form and identify place values. Teacher collects slips and provides oral feedback.
Assignment (Expanded):
Write 5 base ten numbers in expanded form and identify each digit’s place value.
Follow-up Activity:
Practice representing numbers using abacus and objects at home.
Differentiation / Inclusive Strategies
Use physical objects for visual learners; peer-assisted reading and writing for slower learners.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☐ Medium ☐ Low