Mathematics - Senior Secondary 1 - Number Bases (I)

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of number bases. Explains that the decimal system (base 10) uses digits 0-9 and is what we commonly use.

Students listen attentively and ask clarifying questions.

Step 2 - Other Bases

Introduces other number bases, focusing on binary (base 2) with digits 0 and 1, and base 7 with digits 0-6 (linking it to the days of the week analogy). Provides examples of where these bases are used (e.g., computers for binary).

Students observe the examples and discuss potential uses of different bases.

Step 3 - Representation

Shows how numbers are represented in different bases using place values (powers of the base). For example, in base 10, 235=2×10²+3×10¹+5×10⁰. Introduces similar representations for binary and base 7.

Students take notes on the representation of numbers in different bases.

Step 4 - Analogy

Uses analogies to help understand different bases, e.g., thinking of counting in groups of 2 (binary) or groups of 7 (base 7).

Students participate in the analogy exercise and share their understanding.

NOTE ON BOARD

Number Bases: - Base 10 (Decimal): Digits 0-9 - Base 2 (Binary): Digits 0-1 - Base 7: Digits 0-6 Place Value in Base b: ... b2, b1, b0

Students copy the notes from the board.

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the method of repeated division by the new base to convert from base 10 to another base. Emphasizes recording the remainders in reverse order.

Students listen carefully and ask questions about the process.

Step 2 - Base 10 to Binary

Demonstrates the conversion of a base 10 number (e.g., 13) to binary by repeatedly dividing by 2 and recording the remainders. Shows how to write the binary equivalent by reading the remainders from bottom to top. Example: 13÷2=6 R 1, 6÷2=3 R 0, 3÷2=1 R 1, 1÷2=0 R 1. Therefore, 13₁₀=1101₂.

Students observe the steps and take detailed notes of the example.

Step 3 - Base 10 to Base 7

Demonstrates the conversion of a base 10 number (e.g., 20) to base 7 by repeatedly dividing by 7 and recording the remainders. Shows the reverse order of remainders. Example: 20÷7=2 R 6, 2÷7=0 R 2. Therefore, 20₁₀=26₇.

Students observe the steps and note the process for converting to a different base.

Step 4 - Guided Practice

Provides several base 10 numbers for students to convert to binary and base 7 under teacher guidance. Encourages working in pairs.

Students practice the conversion process in pairs, seeking help when needed.

NOTE ON BOARD

Conversion from Base 10 to Base b: 1. Repeatedly divide the base 10 number by b. 2. Record the remainders at each step. 3. Read the remainders in reverse order to get the number in base b. Examples shown for binary and base 7 conversion.

Students copy the steps and examples into their notebooks.

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the method of using place values (powers of the base) to convert from another base to base 10.

Students pay attention and ask clarifying questions.

Step 2 - Binary to Base 10

Demonstrates the conversion of a binary number (e.g., 1101₂) to base 10 by multiplying each digit by the corresponding power of 2 and adding the results. Example: 1101₂=(1×2³)+(1×2²)+(0×2¹)+(1×2⁰)=8+4+0+1=13₁₀.

Students observe the steps and take notes on how to use place values for conversion.

Step 3 - Base 7 to Base 10

Demonstrates the conversion of a base 7 number (e.g., 267) to base 10 by multiplying each digit by the corresponding power of 7 and adding the results. Example: 26₇=(2×7¹)+(6×7⁰)=14+6=20₁₀.

Students observe and note the application of place values for a different base.

Step 4 - Guided Practice

Provides several binary and base 7 numbers for students to convert to base 10 under teacher supervision. Encourages individual practice.

Students practice the conversion process individually, seeking assistance when necessary.

NOTE ON BOARD

Conversion from Base b to Base 10: 1. Identify the place value of each digit in the base b number. 2. Multiply each digit by its corresponding power of b. 3. Add the results to get the base 10 equivalent. Examples shown for binary and base 7 conversion.

Students record the steps and examples in their notebooks.